Quant

Set X contains 10 consecutive integers. If the sum of the 5 smallest members of Set X is 265, then what is the sum of the 5 largest members of Set X? (A) 290 (B) 285 (C) 280 (D) 275 (E) 270

0, 1, 2, 3, 4 5x+10 = 265 5, 6, 7, 8, 9 5x+35 = 265+25 = 290 A

Is x<y? 1) 1/x < 1/y 2) x/y < 0

1) - x<y if either x or y is a negative number - x>y if both x and y are either positive or negative numbers 2) either x or y is a negative number 1)+2) x<y C

In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. How many boards are in the stack? A. 38 B. 36 C. 35 D. 34 E. 32

19-20-21 16-15-14 20+14 = 34 D

Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. He placed the cards in a box, then drew cards one at a time randomly from the box, without returning the cards he had already drawn to the box. In order to ensure that the sum of all cards he drew was even, how many cards did Jerome have to draw? a. 19 b. 12 c. 11 d. 10 e. 3

20 integers: 10 odds and 10 evens If select 10 cards, there could be no even number picked 11 cards must have at least one even number C

A university awarded grants in the amount of either $7,000 or $10,000 to some incoming freshmen. The total amount of all such awards was $2,300,000. Did the university award more $7,000 grants than $10,000 grants to its incoming freshmen? (1) A total of 275 freshmen received grants in one of the two amounts. (2) The amount of money awarded in $10,000 grants was $200,000 more than the amount of money awarded in $7,000 grants.

7000x+10000y=2300000, x > y ? 1) x+y=275 —> can form equation to solve Sufficient 2) 10000y=200000+7000x Sufficient D

Chauncy, an English bulldog, received 1,618 votes in the Mr. Bulldog USA competition, giving him approximately 20 percent of the vote. Approximately what percent of the remaining votes would he have needed to receive in order to win 30 percent of the total votes? A. 10% B. 12.5% C. 15% D. 17.5% E. 20%

=(0.3v-0.2v)×100/(0.8v) =100/8 =12.5%

A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times? A. 5/8 B. 3/4 C. 7/8 D. 57/64 E. 15/16

=prob(T=2 or T=3 or T=4 or T=5) = 1 - prob(T=0 or T=1 or T=6) T=0: 1 T=1 : 6C1 = 6!/5!1! = 6 T=6: 1 = 1 - 8/64 = 7/8 C

Image (Math Test Bin4: 14) In the multiplication problem below, F, G, and H represent unique odd digits. What is the value of the three-digit number FGF? (A) 151 (B) 161 (C) 171 (D) 313 (E) 353

A

Image (Math Test Bin4: 16) Triangle QSR is inscribed in a circle. Is QSR a right triangle? (1) QR is a diameter of the circle. (2) Length QS equals 3 and length QR equals 5.

A

Is x > y ? (1) x = y+2 (2) x/2 = y-1

A

If k is a positive integer greater than 1, then how many prime factors does 14k have? 1) k^4 is divisible by 100 2) 50k has 2 different prime factors

C

If m and n are both positive, is mn < 10? (1) m < 2 (2) n < 5

C

Image (Math Test Bin4: 20) Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. What is the measure, in centimeters, of the perimeter of ABCD ? (1) x - y = 7 (2) z = 13

C

In the figure shown, what is the value of v+x+y+z+w? Image (3.1 Quantitative Sample Questions: PS10) (A) 45 (B) 90 (C) 180 (D) 270 (E) 360

C

The number of flights leaving a certain airport doubles during every one-hour period between its 9 A.M. opening and noon; after noon, the number of flights leaving from the airport doubles during every two-hour period. If 4 flights left from the airport between 9 and 10 a.m., how many flights left the airport between 2 and 4 P.M.? (A) 32 (B) 48 (C) 64 (D) 128 (E) 256

C

What is the sum of x, y, and z? 1) 2x+y+3z = 45 2) x+2y = 30

C

if S and W are integers, is w/5 an integer? (1) 4s + 2 is divisible by 5 (2) w + 3 = 4s

C

If Amy drove the distance from her home to the beach in less than 2 hours, was her average speed greater than 60 miles per hour? 1) The distance that Amy drove from her home to the beach was less than 125 miles. 2) The distance that Amy drove from her home to the beach was greater than 122 miles

B

If y is a positive integer, is (y^3+5)^2/4 an integer? 1) The square root of y has three prime factors 2) Each prime factor of y^3 is greater than 5

B

During a certain two-week period, 70 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period? A. A/14 B. 5A/7 C. 7A/5 D. 14A E. 35A

C = 70%, D = 5A, C = ?A 6A = 30% —> A = 5% C = 0.7 = ? × 0.05 C = 14A D

A certain stadium is currently full to 13/16 of its maximum seating capacity. What is the maximum seating capacity of the stadium? (1) If 1,250 people were to enter the stadium, the stadium would be full to 15/16 of its maximum seating capacity (2) If 2,500 people were to leave the stadium, the stadium would be full to 9/16 of its maximum seating capacity.

D

Automobile A is traveling at two-thirds the speed that Automobile B is traveling. How fast is Automobile A traveling? (1) If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling. (2) If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling

D

If P is the perimeter of an equilateral triangle, which of the following represents the height of the triangle? (A) P/3 (B) P√3/3 (C) P/4 (D) P√3/6 (E) P/6

D

If a and b are two-digit numbers that share the same digits, except in reverse order, then what is the sum of a and b? (1) a-b=45 (2) The difference between the two digits in each number is 5.

a=10x+y and b=10y+x a+b = 11(x+y) = ? 1) 9(x-y) = 45 —> x-y = 5 Insufficient 2) x-y = 5 Insufficient 1)+2) Insufficient E

If √(3-2x) = √(2x)+1, then 4x² = A) 1 B) 4 C) 2-2x D) 4x-2 E) 6x-1

E

The average (arithmetic mean) of integers r,s,t,u and v is 100. Are exactly two of the integers greater than 100? (1)Three of the integers are less than 50 (2) None of the integers is equal to 100.

E

What is x? (1) x = 4y − 4 (2) xy = 8

E (got 2 answers)

Image (GMAT PRACTICE TEST: Q27) The figure above represents a window, with the shaded regions representing openings for glass and the pale regions representing the wood panels between and around the glass. If the window is 4.5 feet high by 2.5 feet wide, and if each of the wooden panels is exactly 4 inches thick, what is the total surface area, in square inches, of glass in the window?(1 foot = 12 inches; figure not drawn to scale) A. 189 B. 378 C. 448 D. 756 E. 1,620

D

Image (Math Test Bin3: 25) Triange ABC is an isosceles right triangle; Triangle DEF is an equilateral triangle with height EG. What is the ratio of the area of ABC to the area of DEF? 1) The ratio of BC to EG is 1:1 2) The ratio of AC to DF is sqrt(3):2

D

Image (Math Test Bin4: 7) The diagram above shows two wheels that drive a conveyor belt. The larger wheel has a diameter of 40 centimeters; the smaller wheel has a diameter of 32 centimeters. In order for the conveyor belt to run smoothly, each wheel must rotate the exact same number of centimeters per minute. If the larger wheel makes r revolutions per minute, how many revolutions does the smaller wheel make per hour, in terms of r? (A) 1280π/3 (B) 75r (C) 48r (D) 24r (E) 64π/3

D=40 and d=32 1 revolution: 40π 1 minute: 40πr 1 hour: 60×40πr = 32πX X = 75r B

If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years? A. 10,000(x^n) B. 10,000(x/100)^n C. 10,000n(x/100) D. 10,000(1+x/100)^n E. 10,000n(1+x/100)

simple interest, not compound (principle)(#year)(interest rate) C

Is x² <= 2x? (1) x > 0 (2) x < 3

x(x-2) <= 0 x ∈ [0,2] 1) x could be 3 2) x could be -1 1)+2) x could be 2.5 E

If IxI-IyI = |x+yI and xy does not equal 0, which of the following must be true? (A) x- y>0 (B) x - Y < 0 (C) x+y>O (D) xy > 0 (E) xy <0

|x|-|y| >= 0 and diff = sum —> diff sign E

If Y and n are positive integers, is yn divisible by 7? (1) n² − 14n + 49 = 0 (2) n + 2 is the first of three consecutive integers whose product is 990.

(1) (n-7)² = 0 Sufficient (2) (n+2)(n+3)(n+4) = 990 = 9×10×11 n=7. Sufficient D

What is x? (1) y = x³ − 1 (2) y = x - 1

(1) + (2) x³−1 = x-1 x(x²−1) = 0 ∴ x = {0, 1, -1} E

Is a > 0? (1) a³-a < 0 (2) 1-a² > 0

(1) a(a-1)(a+1) < 0 If a<0: (a-1)(a+1)>0 —> a<-1 or a>1 —> a<-1 If a>0: (a-1)(a+1)<0 —> -1<a<1 —> 0<a<1 Insufficient (2) (a-1)(a+1) < 0 —> -1 < a < 1 Insufficient (1)+(2) means that case a>0 is true Sufficient C

Is mn < 10? (1) m < 2 (2) n < 5

(1)+(2) m and n could be both negatives E

Is a+2b < c+2d ? (1) a < c (2) d > b

(2) 2b < 2d (1)+(2) a+2b < c+2d C

What is x? (1) 3x/(3y+5z) = 8 (2) 6y+10z = 18

(2) 3y+5z = 9 (1) 3x = 8(3y+5z) (1)+(2) 3x = 8(9) —> x = 24 C

At a college football game, 4/5 of the seats in the lower deck of the stadium were sold. If of all the seating in the stadium is located in the lower deck, and if 2/3 of all the seats in the stadium were sold, what fraction of the unsold seats in the stadium were in the lower deck? (A) 3/20 (B) 1/6 (C) 1/5 (D) 1/3 (E) 7/15

(4/5)L are sold L=(1/4)S 2/3S are sold (1/5)L/(1/3)S = ? = (1/5)(1/4)S/(1/3)S = 3/20 A

f n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ? (1) n is not divisible by 2. (2) n is not divisible by 3.

24 = (8)(3) (1) n-1, n+1 could be 2,4 or 4,6 or 6,8 or ... and (n-1)(n+1) is divisible by 2^n, where n >= 3 Still, not know if it is also divisible by 3 INSUFFICIENT (2) either n-1 or n+1 is divisible by 3 because n-1, n and n+1 are consecutive integers, so one of them must be divisible by 3 Still, not know if it is also divisible by 8 INSUFFICIENT (1) + (2) (n-1)(n+1) is divisible by 8 and 3 r = 0 SUFFICIENT C

The perimeter of a certain isosceles right triangle is 16+16√2. What is the length of the hypotenuse of the triangle? (A) 8 (B) 16 (C) 4√2 (D) 8√2 (E) 16√2

2x + x√2 = 16 + 16√2 x√2(√2 + 1) = 16(1 + √2) x√2 = 16 The length of the hypotenuse of the triangle is 16. B

At Company R, the average (arithmetic mean) age of executive employees is 54 years old and the average age of non-executive employees is 34 years old. What is the average age of all the employees at Company R? (1) There are 10 executive employees at Company R. (2) The number of non-executive employees at Company R is four times the number of executive employees at Company R.

54 = Σe/e and 34 = Σn/n (Σe+Σn)/(e+n) = ? 1) e=10, Σe=540 Insufficient 2) n=4e (Σe+Σn)/(e+n) = (54e+4(34e))/5e Sufficient B

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? A. 10,700 B. 10,800 C. 10,900 D. 11,000 E. 11,100

As "no district is to have a population that is more than 10 percent greater than the population of any other district", then the populations of 11 districts should be in the range: x and 1.1x. So we want to minimize x. To minimize x we should make only one district to have that # of population (minimum possible) and the rest 10 districts to have 1.1x # of population (maximum possible). x + 10(1.1x) = 132000 12x = 132000 x = 11000 Answer: D.

If x is a prime number, what is the value of x? (1) There are a total of 50 prime numbers between 2 and x, inclusive. (2) There is no integer n such that x is divisible by n and 1 < n < x.

For Statement (1), we know that certain numbers are prime and others are not. We also know that x is prime. Therefore, if we were to list all the primes from 2 on up, we eventually would find the 50th-largest prime number. That number must equal x, because x is prime, so it MUST be the 50th item on that list of primes. This information is SUFFICIENT. For Statement (2), we are told that x is not divisible by any integer greater than 1 and less than x. Therefore, x can only have I and x and factors. In other words, x is prime. We already know this result, in fact: it was given to us in the question stem. So Statement (2) does not help us determine what x is. INSUFFICIENT. The correct answer is (A): Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (Incidentally, for those who are curious, the 50th prime number is 229.)

If x is a positive integer, is x³ − 3x² + 2x divisible by 4? (1) x = 4y + 4, where y is an integer (2) x = 2z + 2, where z is an integer

Is x even? OR Is x-I a multiple of 4? D

A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible? A. 70 B. 210 C. 336 D. 840 E. 1680

It's not advisable to tag the questions using its wording. Just because the question uses the word 'arrangement', it doesn't make this an arrangement problem. It is a combination problem and here is why: When you pick the cards, there is only one way in which you can arrange them - the ascending order which will be unique for any 4 cards you pick. Say, I picked up 3, 5, 6, 10. The only way I can arrange them is this: 3, 5, 6, 10. I cannot arrange them as 3, 6, 10, 5 or 6, 5, 3, 10 or any other arrangement that you can have with 4 unique cards. The number of arrangements here is not 4!. Instead it is only 1 since they must be put in ascending order. So all you have to do is find out the number of ways in which you can pick 4 cards out of 8 unique cards. This will be done in 8C4 = 70 ways. The book uses the basic counting principle. Put 4 cards in 4 places in 8*7*6*5 ways and since you can arrange them in only one way, divide by the number of arrangements i.e. 4! When will it be an arrangement problem? "She has students choose 4 cards randomly, then arrange the cards in ANY order." Now each selection will have 4! distinct arrangements. A

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese? (1) 16 students at the school study both French and Japanese. (2) 10 percent of the students at the school who study Japanese also study French.

J >= 100; 0.04F = Both; F > J ? 1) 16 = 0.04F --> F = 400 Insufficient 2) 0.1J = 0.04F --> J:F = 2:5 --> F > J Sufficient B

In a particular state, 70% of the counties received some rain on Monday, and 65% of the counties received some rain on Tuesday. No rain fell either day in 25% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? A) 12.5% B) 40% C) 50% D) 60% E) 67.5%

M=70, T=65, N=25, B=? 70+65+25-B = 100 B = 60 D

If W, X, Y and Z are integers and W + X = Y, is y divisible by Z? (1) W and X each have a remainder of 1 when divided by z (2) z=2

Need to know if z=2 or even and Y is also even (1) z is unknown (2) y is unknown (1)+(2) sufficient C

An automobile dealership sells only sedans and coupes. It sells each in only two colors: red and blue. Last year, the dealership sold 9,000 vehicles, half of which were red. How many coupes did the dealership sell last year? (1) The dealership sold three times as many blue coupes as red sedans last year. (2) The dealership sold half as many blue sedans as blue coupes last year.

RS+RC = BS+BC = 4500 RC+BC=? 1) BC = 3RS Insufficient 2) 2BS = BC got BC, RC is left Insufficient 1)+2) know RC Sufficient C

If a and b are both prime numbers greater than 10, which of the following CANNOT be true? I. ab is an even number. II. The difference between a and b equals 117. III. The sum of a and b is even. (A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II and III

Since a and b are both prime numbers greater than 10, they must both be odd. Therefore ab must be an odd number, so Statement I cannot be true. Similarly, if a and bare both odd, then a - b cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since a and bare both odd, It +bmust be even, so Statement III will always be true. Since Statements I and II CANNOT be true, but Statement III IS true, the correct answer is (B).

Is N divisible by 7? (1) N =x - y, where x and yare integers (2) x is divisible by 7, and y is not divisible by 7.

Statement (1) tells us that N is the difference between two integers (x and y), but it does not tell us anything about whether x or y is divisible by 7. INSUFFICIENT. Statement (2) tells us nothing about N. INSUFFICIENT. Statements (1) and (2) combined tell us that x is a multiple of 7, but y is not a multiple of 7. The difference between x and y can NEVER be divisible by 7 if x is divisible by 7 but y is not. (If you are not convinced, try testing it out by picking numbers.) SUFFICIENT: N cannot be a multiple of7. The correct answer is (C): BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Is k² odd? (1) k - 1 is divisible by 2. (2) The sum of k consecutive integers is divisible by k.

Statement (1) tells us that k - 1 is even. Therefore, k is odd, so k² will be odd. SUFFICIENT. Statement (2) tells us that the sum of k consecutive integers is divisible by k. Therefore, this sum divided by k is an integer. Moreover, the sum of k consecutive integers divided by k is the average (arithmetic mean) of that set of k integers. As a result, Statement (2) is telling us that the average of the k consecutive integers is itself an integer. If the average of this set of consecutive integers is an integer, then k must be odd. SUFFICIENT. The correct answer is (D). EACH statement ALONE is sufficient.

If x > 1, what is the value of integer x? (1) There are x unique factors of x. (2) The sum of x and any prime number larger than x is odd.

Statement (1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1 and x, inclusive, must be a factor of x. Testing numbers, we can see that this property holds for 1 and for 2, but not for 3 or for 4. In fact, this property does not hold for any higher integer, because no integer x above 2 is divisible by x-I. Therefore, x = 1 or 2. However, the original problem stem told us that x > 1, so x must equal 2. SUFFICIENT. Statement (2) tells us that x plus any prime number larger than x is odd. Since x > 1, x must equal at least 2, so this includes only prime numbers larger than 2. Therefore, the prime number is odd, and x is even. However, this does not tell us which even number x could be. INSUFFICIENT. The correct answer is (A): Statement (1) is sufficient to answer the question, but Statement (2) is insufficient.

Image (Math Test Bin4: 25) The figure shown is a regular hexagon with center h. the shaded area is a parallelogram that shares three vertices with the hexagon and its fourth vertex is the center of the hexagon. If the length of one side of the hexagon is 8 centimeters, what is the area of the unshaded region? (A) 16√3 cm² (B) 96 cm² (C) 64√3 cm² (D) 96√3 cm² (E) 256 cm²

The area is equal to 6 equilateral triangle with side 8.. However two of these 6 triangles are shaded.. So area = (√3)/4 × 8² × (6-2) = 64 × √3 cm² C

Jolene began building a picket fence by planting stakes in a row; the stakes were evenly spaced. After planting the first 10 stakes, Jolene measured the length of the row and found that the row was 27 feet long. She continued the row by planting another 10 stakes, then measured the length of the entire row. How many feet long was the row of stakes Jolene had planted? (A) 37 (B) 54 (C) 57 (D) 60 (E) 81

The first 10 stakes: 27 feet long The second 10: 27 feet long Between the first and the second: 27/9 = 3 57 feet C

Is the product of all of the elements in Set S negative? (1) All of the elements in Set S are negative. (2) There are 5 negative numbers in Set S.

This is a tricky problem. Based on what we have learned so far, it would seem that Statement (2) tells us that the product must be negative. (5 is an odd number, and when the GMAT says "there are 5" of something, you CAN conclude there are EXACfLY 5 of that thing.) However, if any of the elements in Set 5 equals zero, then the product of the elements in Set 5 will be zero, which is NOT negative. Therefore Statement (2) is INSUFFICIENT. Statement (1) tells us that all of the numbers in the set are negative. If there are an even num- ber of negatives in Set 5, the product of its elements will be positive; if there are an odd num- ber of negatives, the product will be negative. This also is INSUFFICIENT. Combined, we know that Set 5 contains 5 negative numbers and nothing else. SUFFICIENT. The product of the elements in Set 5 must be negative. The correct answer is (C).

a1 , a2 , a3 , . . . , a15 In the sequence shown, an = an - 1 + k, where 2 ≤ n ≤ 15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10 ? (1) a1 = 24 (2) a8 = 10

We have a sequence of fifteen terms (actually this sequence is an arithmetic progression). As k is nonzero, all elements would be different and the median would be the eighth term, a8. This means that 7 terms will be less than a8 and 7 terms will be more than a8. Note here that it doesn't matter whether k is positive or negative: If k is positive, we'll get an ascending sequence and the terms from from a1 to a7 will be less than a8 and terms from a9 to a15 will be more than a8; If k is negative, we'll get a descending sequence and the terms from from a1 to a7 will be more than a8 and terms from a9 to a15 will be less than a8. Statement (1) is giving the value of a1, but since we don't know the value of k, we can not say how many terms are more than 10: it can vary from 1 (only a1=24>10, if k<=-14) to 15 (if k is positive for instance). Statement (2) is saying that a8=10. As we discussed above, a8 is median value and for any value of k, 7 terms will be more than a8=10 and 7 terms will be less than a8=10. Hence this statement is sufficient. Answer: B.

If 5B>4B+1, is B^2>1?

Yes

A four-character password consists of one letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? (A) 5,040 (B) 18,720 (C) 26,000 (D) 37,440 (E) 52,000

__ __ __ __ 10 26 9 8 × 2 = 37,440 D

What is the remainder when a is divided by 4 ? (1) a is the square of an odd integer. (2) a is a multiple of 3.

a = 4k + r, r=? (1) a = (2n+1)² = 4n² + 4n + 1 —> r = 1 Sufficient (2) a = 3m Insufficient A

If a brokerage firm charged a commission of 2% of the total dollar amount of a certain trade, what was the total dollar amount of that trade? (1) The dollar amount of the trade minus the brokerage firm's commission was $88,000. (2) The brokerage firm's commission decreased the profit earned on the trade by 20%.

c=0.02d, d=? (1) d-c = 88000. Sufficient (2) p-c = 0.08p. Insufficient A

If x > y² > z^4 , which of the following statements could be true? I. x > y > z II. z > y > x III. x > z > y A. I only B. I and II only C. 1 and III only D. II and III only E. I, II and II

if x=1/4, y=1/3, z=1/2 E

x, 3, 1, 12, 8 If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers? (1) x > 6 (2) x is greater than the median of the 5 numbers.

median > mean ? ; mean = (24+x)/5 1, 3, 8, 12 ... x if x <= 3, median = 3 if 3 < x < 8, median = x if x >= 8, median = 8 (1) if x = 7, median = 7, mean = 6.5 if x = 16, median = 8, mean = 8 Insufficient (2) if x = 16, median = 8, mean = 8 Insufficient (1) + (2) Insufficient E

If n is an integer and n³ is between 1 and 100, inclusive, what is the value of n? (1) n =2k + 1, where k is an integer. (2) n is a prime number.

n³∈{1³, 2³, 3³, 4³} 1) n∈odd. Insufficient 2) n could be either 2 or 3. Insufficient 1)+2) n=3. Sufficient

Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address? A) 1/24 B) 1/8 C) 1/4 D) 1/3 E) 3/8

one letter correct: 4!/3! = 4 first correct: 1/4 second wrong: 2/3 third wrong: 1/2 fourth wrong: 1 4 × 1/4 × 2/3 × 1/2 × 1 = 1/3 D

A bookshelf holds both paperback and hardcover books. The ratio of paperback books to hardcover books is 22 to 3. How many paperback books are on the shelf? (1) The number of books on the shelf is between 202 and 247, inclusive. (2) If 18 paperback books were removed from the shelf and replaced with 18 hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be 4 to 1.

p:h = 22:3, p = 22x = ? (1) 202 <= 25x <= 247 8 < x < 10, x= 9 Sufficient (2) 22x - 18 : 3x + 18 = 4 : 1 Sufficient D

Is mn > -12? 1) m > -3 2) n > -4

we wanna know if both m and n are either positive or negative number? 1) m could be either 2) n could be either 1) + 2) still could be either E

If a<>-b, is (a-b)/(b+a) < 1? 1) b^2 > a^2 2) a-b > 1

(a-b)/(a+b) < 1 ? - a = b *True* - |a|>|b|: ++ +- -+ -- *False* - |a|<|b|: (++) (+-) (-+) (--) *True* 1) |a| < |b| *True* 2) a > b ++, +-, -- *True/False* A

If xy=2, xz=8, and yz=5, then the value of xyz is closest to: A) 5 B) 9 C) 15 D) 25 E) 75

(xyz)^2 = 80 --> B

Company X has exactly two product lines and no other sources of revenue. If the consumer products line experiences a k% increase in revenue (where k is a positive integer) in 2015 from 2014 levels and the machine parts line experiences a k% decrease in revenue in 2015 from 2014 levels, did Company X's overall revenue increase or decrease in 2015? (1) In 2014, the consumer products line generated more revenue than the machine parts line. (2) k = 8

-c: k%+ -m: k%- new > old ? (100+k)c + (100-k)m > 100c+100m ? (100+k-100)c > (100-100+k)m ? c > m ? (1) c > m Sufficient (2) Insufficient A

A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $260 before any discount? (A) $130.00 (B) $145.60 (C) $163.80 (D) $182.00 (E) $210.00

0.8(0.7(260)) = 0.56(200+60) = 112+33.6 = 145.6 B

If x is a positive integer, is the greatest common factor of 150 and x a prime number? (1) x is a prime number. (2) x < 4

1) common factor could be 1 in case x=7 2) x ∈ {1,2,3} C

Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average salary of the same 10 employees this year? (1) For 8 of the 10 employees, this year's salary is 15 percent greater than last year's salary. (2) For 2 of the 10 employees, this year's salary is the same as last year's salary.

1) individual is unknown 2) individual is unknown 1)+ 2) individual is unknown E

If p is the perimeter of rectangle Q, what is the value of p? (1) Each diagonal of rectangle Q has length 10. (2) The area of rectangle Q is 48.

p = 2(a+b) = ? 1) d² = a²+b² = 100 —> insufficient 2) ab = 48 —> insufficient 1)+2) p² = 4(a²+2ab+b²) p = √(4(100+2(48))) Sufficient C

If $5,000 invested for one year at p percent simple annual interest yields $500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars? (1) k = 0.8p (2) k = 8

p=10 and 500=principal×k/100 —> need to know k 1) k= 8 —> sufficient 2) k=8 —> sufficient D

The only gift certificates that a certain store sold yesterday were worth either $100 each or $10 each. If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth $10 each did the store sell yesterday? (1) The gift certificates sold by the store yesterday were worth a total of between $1,650 and $1,800. (2) Yesterday the store sold more than 15 gift certificates worth $100 each.

$100 —> x, then $10 —> 20-x Need x to solve this question 1) 1650 < 100x+10(20-x) < 1800 1450 < 90x < 1600 16.1 < x < 17.8 x must be integer which is 17. Sufficient 2) x > 15. Insufficient A

If the length of Wanda's telephone call was rounded up to the nearest whole minute by her telephone company, then Wanda was charged for how many minutes for her telephone call? (1) The total charge for Wanda's telephone call was $6.50. (2) Wanda was charged $0.50 more for the first minute of the telephone call than for each minute after the first.

(1) Clearly insufficient since we don't know the cost per minute of call. (2) So, if the first minute costs $(x+0.5) then each succeeding minute costs $x. Still not sufficient. (1)+(2) We have that (x+0.5)+x(n−1)=6.5, where n is the number of minutes. We have one equation and two unknowns, hence we cannot solve for n. Not sufficient. Answer: E.

What is the perimeter of a isosceles triangle MNP? (1) MN = 16 (2) NP = 20

(1) We only know the length of one side. Not sufficient. (2) We only know the length of one side. Not sufficient. (1)+(2) If MN=MP=16 and NP=20 then the perimeter would be 16+16+20=52 but if MN=16 and NP=MP=20 then the perimeter would be 16+20+20=56. Not sufficient. Answer: E.

Which of the following is equal to (6+√5)/(2-√5) ? A) 17 B) -17 C) 17 + 8√5 D) -17 - 8√5 E) 12 + 12√5

(6+√5)(2+√5) / (4-5) --> D

A grocery store sells two varieties of jelly bean jars, and each type of jellybean jar contains only red and yellow jellybeans. If jar B contains 20% more red jellybeans than jar A , but 10% fewer yellow jellybeans, and jar A contains twice as many red jellybeans as yellow jellybeans, by what percent is the number of jellybeans in jar B larger than the number of jellybeans in jar A?

10%

If the perimeter of a rectangle is less than the perimeter of equilateral triangle then which one of the following is true? I. The larger side of the rectangle must be greater than the side of the triangle. II. The smaller side of the rectangle must be less than the side of the triangle. III. The small side of the rectangle may be equal to the side of the triangle. IV. The triangle and the rectangle can share one side.

2(l+w) < 3s ? I max=square —> l=w even smallest —> 4l < 3s 💡 l ≯ s II min=square —> w=l even biggest —> 4w < 3s💡 w < s III if w=s —> 2l+2w < 3w —> 2l < w💡impossible cause l >= w IV if l=s —> 2l+2w < 3l —> 2w < l💡possible cause it can share l side II, IV are true.

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ? (A) 10^9 (B) 10^8 (C) 10^7 (D) 10^6 (E) 10^5

2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200); 2∗3∗5∗7∗11∗13∗17∗19 ≈10∗20∗200∗200=8∗10⁶ ≈10⁷ Answer: C.

If g(x) = 3x + √x, what is the value of g(d^2 + 6d +9)?

3d^2 + 19d + 30 and 3d^2 + 17d + 24

Is [5^(x+2)] / 25 < 1? (1) 5^x < 1 (2) x < 0

5^x < 1 ? or x < 0 ? 1) directly answers the question 2) directly answers the question D

A department store receives a shipment of 1,000 shirts, for which it pays $9,000. The store sells the shirts at a price 80 percent above cost for one month, after which it reduces the price of the shirts to 20 percent above cost. The store sells 75 percent of the shirts during the first month and 50 percent of the remaining shirts afterward. How much gross income did sales of the shirts generate? (A) $10,000 (B) $10,800 (C) $12,150 (D) $13,500 (E) $16,200

750×9×1.8 + 125×9×1.2 D

During a five day period, monday through friday, the average was 86 degrees. what was the high temperature on Friday? (1) The average high temperature for Monday through Thursday was 87 degrees Fahrenheit. (2) The high temperature on Friday reduced the average high temperature for the week by 1 degree.

86 = (m+tu+w+th+f)/5 m+tu+w+th+f = 86×5 need to know m+tu+w+th 1) 87 = (m+tu+w+th)/4 Sufficient 2) same equation as 1) Sufficient D

The first term in an arithmetic sequence is -5 and the second term is -3. what is the 50th term? (Recall that in an arithmetic sequence, the difference between successive terms is constant.)

93

A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? A) 15 B) 20 C) 30 D) 40 E) 45

A

Eco Wildlife Preserve contains 5x zebras and 2x lions, where x is a positive integer. If the lions succeed in killing z of the zebras, is the new ratio of zebras to lions less than 2 to 1 ? (1 ) z > x (2 ) z = 4

A

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid $3.99 for each additional compact disc purchased. If a preferred customer purchased a total of 6 compact discs and paid $15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following? (A) 5(4.00) + 15.90 (B) 5(4.00) + 15.95 (C) 5(4.00) + 16.00 (D) 5(4.00 - 0.01) + 15.90 (E) 5(4.00 - 0.05) + 15.95

A

The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate. On friday, the ratio of vanilla cones sold to chocolate cones sold was 2 to 3. If the store had sold 4 more vanilla cones, the ratio of vanilla cones sold to chocolate cones sold would have been 3 to 4. How many vanilla cones did the store sell on Friday? a) 32 b) 35 c) 42 d) 48 E) 54

A

Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments, how many of the parents volunteered to bring refreshments? (A) 25 (B) 36 (C) 38 (D) 42 (E) 45

B

A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere? A. √3:1 B. 1:1 C. 1/2:1 D. √2:1 E. 2:1

As mentioned above hemisphere is just a half of a sphere. Now, since the cone is a right circular cone, the vertex of the cone must touch the surface of the hemisphere directly above the center of the base, which makes the height of the cone also the radius of the hemisphere. ...see image (3.1 Quantitative Sample Questions: PS20) Answer: B.

A closed cylindrical tank contains 36π cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground? (A) 2 (B) 3 (C) 4 (D) 6 (E) 9

B

A comedian is playing two shows at a certain comedy club, and twice as many tickets have been issued for the evening show as for the afternoon show. Of the total number of tickets issued for both shows, what percentage has been sold? (1) A total of 450 tickets have been issued for both shows. (2) Exactly 3/5 of the tickets issued for the afternoon show have been sold, and 1/5 exactly of the tickets issued for the evening show have been sold

B

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks? A) 9/50 B) 7/25 C) 7/20 D) 21/50 E) 27/50

B

For which of the following functions does f(x)=f(2-x)? A. f(x)=x+2 B. (fx)=2x-x^2 C. f(x)=2-x D. f(x)=(2-x)^2 E. f(x)=x^2

B

If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? I. 5 II. 13 III. 15 A. I only B. II only C. I and II only D. II and III only E. I, II, and III

B

Suzie's Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $760. How much more do pairs of boots cost than pairs of shoes at Suzie's Discount Footwear? A. $2.50 B. $5.00 C. $5.50 D. $7.50 E. $15.00

B

The number A is a two-digit positive integer; the number B is the two-digit positive integer formed by reversing the digits of A. if Q=10B-A, what is the value of Q? (1) The tens digit of A is 7 (2) The tens digit of B is 6

B

The size of a flat-screen television is given as the length of the screen's diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television? A. 106.75 B. 213.5 C. 427 D. 729 E. 1,156

B

The "competitive edge" of a baseball team is defined by the formula √(W/L) where W represents the number of the team's wins, and L represents the number of the team's losses. This year, the GMAT All-Stars had 3 times as many wins and one-half as many losses as they had last year. By what factor did their "competitive edge" increase? A. √2 B. √6 C. √12 D. 6 E. 12

B (By what factor)

Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January? (1) More of the people in the auditorium have their birthday in February than in March. (2) Five of the people in the auditorium have their birthday in March.

Basically the question is whether we can distribute 66 birthdays between 12 moths so that January to get 0. (1) Let 10 months (except March and January) have 6 birthdays each (maximum possible) --> 6*10=60. As in March there was less birthdays than in February than maximum possible for March is 5 --> total 60+5=65, so even for the worst case scenario (maximum for other months) still 1 birthday (66-65=1) is left for January. Sufficient. (2) Again: let 10 months have 6 birthdays each (maximum possible) --> 6*10=60 + 5 birthdays in March = 65. The same here: even for the worst case scenario (maximum for other months) still 1 birthday (66-65=1) is left for January. Sufficient. Answer: D.

A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios? (1) The retailer has more than 28 radios in inventory (2) The retailer has less than twice as many radios as clocks in inventory.

C

Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? (A) xt/y (B) (x+t)/xy (C) xyt/(x+y) (D) (x+y+t)/xy (E) (y+t)/x - t/y

C

Company Z only sells chairs and tables. what percent of its revenue in 2008 did company derive from its sales of tables? (1) In 2008, the average price of tables sold by company Z was 10% higher than the average price of chairs sold by Company Z? (2) In 2008, Company Z sold 20% fewer tables than chairs.

C

If C + D = 11 and C and D are positive integers, which of the following is a possible value for 5C + 8D? A. 55 B. 61 C. 69 D. 83 E. 88

C+D = 11 --> C = 11-D 5C+8D = 5(11-D) + 8D = 55 + 3D, so the answer must be 55 plus some multiple of 3. Only B and E satisfy this: 61=55+3x2 and 88=55+3x11, but the second case is not possible because in this case D=11 and C=0, and we are told that C is a positive integers. Answer: B.

A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A? A) 40% B) 45% C) 50 % D) 60 % E) 55 %

D

John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John's account 6 months after the account was opened? A) $10,100 B) $10,101 C) $10,200 D) $10,201 E) $10,400

D

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer? (A) 1/720 (B) 1/80 (C) 1/10 (D) 1/9 (E) 1/5

E

A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches? (A) 16/9π (B) 4/√π (C) 12/√π (D) √(2/π) (E) 4√(2/π)

E

If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January? (A) 1/4 (B) 1/2 (C) 2/3 (D) 2 (E) 4

E

The "luminous flux," or perceived brightness, of a light source is measured in lumens and is inversely proportional to the square of the distance from the light. If a light source produces 200 lumens at a distance of 3 meters, at what distance will the light source produce a luminous flux of 25 lumens? A. 6 meters B. √72 meters C. 9 meters D. 24 meters E. 72 meters

Flux is Inversely Proportional to (Distance)^2 F1/F2=(D2/D1)^2 so, 200/25=(D2/3)^2 Answer: Option B

Chris's convertible gets gas mileage that is 40 percent higher than that of Stan's SUV. If Harry's hatchback gets gas mileage that is 15 percent higher than that of Chris's convertible, then Harry's hatchback gets gas mileage that is what percent greater than that of Stan's SUV? (A) 25% (B) 46% (C) 55% (D) 61% (E) 66%

Given x is Stan's SUV Chris's Convertible = 1.4x Harry's Hatchback = 1.15(1.4x) = 1.61x D

A strain of bacteria multiplies such that the ratio of its population in any two consecutive minutes is constant. If the bacteria grows from a a population of 5 million to 40 million over the course on an hour, by what factor does the population increase every 10 minutes?

In 60 minutes the population increased 8 times. So, if the growth rate per minute is r, then r^60 = 8 = 2^3. The question asks what factor the population will grow by in 10 minutes. The growth rate in 10 minutes is r^10. take 6th root from r^60 = 2^3 r^10 = 2^(1/2) = √2

During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? (A) 80% (B) 100% (C) 116.7% (D) 120% (E) 140%

Kim: 1/20 = K Isabella: 1.5/25 = I I = ?% of K 1.5/25 = x/100 × 1/20 x = 120% D

Lisa spends 3/8th of her salary on rent and 5/12 on food. Her roommate, Carrie earns about twice as much as Lisa, spends 1/4th of her salary on the rent and 1/2 on food. If the two women decide to contribute the rest of their salary to charity every month, what fraction of their combined monthly income will they donate.

L: r=3L/8, f=5L/12 , d=5L/24 C=2L: r=C/4, f=C/2, d=2L/4=L/2 L(5+12)/24 = 3L(17)/72 *So, if they donate 17/24 of x, then they donate 17/72 of 3x.*

If P is a set of integers and 3 is in P, is every positive multiple of 3 in P? (1) For any integer in P, the sum of 3 and that integer is also in P. (2) For any integer in P, that integer minus 3 is also in P.

Positive multiples of 3 are: 3, 6, 9, 12, 15, ... The question asks whether ALL these numbers are in the set P, taking into account that 3 is in this set. 1) we know that 3 is in P and 3+3=6, 6+3=9, ... are also in P. Sufficient. 2) we know that 3 is in P and 3-3=0, 0-3=-3, ... are also in P, but we do not know if 6, 9, ... are in P. Insufficient. A

In a nationwide poll, P people were asked 2 questions. If 2/5 answered "yes" to question 1, and of those 1/3 also answered "yes" to question 2, which of the following represents the number of people polled who did not answer "yes" to both questions? A) 2P/15 B) 3P/5 C) 3P/4 D) 5P/6 E) 13P/15

Q1: yes = 2P/5 Q2: yes = 2P/15 + (no Q1, yes Q2) 1 - yes to both = ? E

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k? (A) one (B) two (C) three (D) four (E) five

Relationship of the Sides of a Triangle: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides. According to the above the following must be true: 7-2 < k < 7+2 5 < k < 9 and 2 < k < 7 k = 6 A

Of the three digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two? A) 90 B) 82 C) 80 D) 45 E) 36

Three digit number can have only following 3 patterns: A. all digits are distinct; B. two are alike and third is different; C. all three digits are alike. We need to calculate B. B=Total - A - C Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700); A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9); C. all three are alike = 3 (777, 888, 999). So, 299-216-3=80. Answer: C.

The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 5 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 12 seconds? A. 18 miles per hour B. 90 miles per hour C. 216 miles per hour D. 1080 miles per hour E. 5400 miles per hour

Velocity =k*Time where k is the constant of proportionality Time = 5 seconds Velocity = 5k = 90 k = 18 Time = 12 seconds Velocity = 18*12 = 216 Answer: Option C

In a survey of retailers, what percent had purchased computers for business purposes? (1) 85 percent of the retailers surveyed who owned their own store had purchased computers for business purposes. (2) 40 percent of the retailers surveyed owned their own store.

We know only retailers who owned their own store, what about who did not? E

a^2b = ? 1) a = -1 2) b is an integer

b could be ³/₂ C

Of the companies surveyed about the skills they required in prospective employees, 20 percent required both computer skills and writing skills. What percent of the companies surveyed required neither computer skills nor writing skills? (1) Of those companies surveyed that required computer skills, half required writing skills. (2) 45 percent of the companies surveyed required writing skills but not computer skills.

b=20; c+20+w+n=100; n=? To know n, need to know both c and w 1) (c+20)/2=b=20 —> c=20 w is still unknown. Insufficient. 2) w=45 c is still unknown. Insufficient. 1)+2) c and w are known, then n can be solved. C

If 0<ab<ac, is a negative? 1) c<0 2) b>c

b~neg OR c~neg 1) c~neg. Sufficient 2) b~neg & c~neg. Sufficient D

On Monday, a certain animal shelter housed 55 cats and dogs. By Friday, 1/5 of the cats and 1/4 of the dogs had been adopted; no new cats or dogs were brought to the shelter during this period. What is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday. A. 11 B. 12 C. 13 D. 14 E. 20

c+d = 55 c/5 and d/4 are adopted c = 5x, d = 4y 5x+4y = 55, max(x+y) = ? - y=5 and x=7, then x+y = 12 - y=10 and x=3, then x+y = 13 C

If 4/x < -1/3, what is the possible range of values for x?

case 1: x<-12 --> x>0. *Impossible* case 2: x>-12 --> x<0. -12 < x < 0

If 4/x < 1/3, what is the possible range of values for x?

case 1: x<12 --> x<0 case 2: x>12 --> x>0 x<0 or x>12

If (x+y)/z > 0, is x < 0 (1) x < y (2) z < 0

case z>0: x+y > 0 case z<0: x+y < 0 1) z is unknown. Insufficient 2) x+y < 0. Insufficient 1)+2) x-y < 0 and x+y < 0 —> 2x < 0 x < 0. Sufficient C

In a relay race, the total distance is covered by multiple athletes through passing of the baton. Initially each player of a team A had to run an equal distance before passing on the baton but due to injury to two team players, each of the remaining players ran some extra distance each during race to compensate for the injured players. What was the original number of players in the team? 1. John, a member of Team A, had to run 400m more than the 600m he was required to run earlier. 2.The total distance to be covered in the race was 3000m.

dist x #ply = t = (dist+e) x (#plyr-2) 1. e=400, dist=600 2. t=3000 A

In a certain classroom, there are 80 books, of which 24 are fiction and 23 are written in Spanish. How many of the fiction books are written in Spanish? (1) Of the fiction books, there are 6 more that are not written in Spanish than are written in Spanish. (2) Of the books written in Spanish, there are 5 more nonfiction books than fiction books.

f+b+s+n = 80 and f+b = 24 and s+b = 23 Need to know either f or s 1) f = b+6 —> can form equation. Sufficient 2) s = b+5 —> can form equation. Sufficient D

Which of the following equations has no solution for a? A) a^2 - 6a + 7 = 0 B) a^2 + 6a - 7 = 0 C) a^2 + 4a + 3 = 0 D) a^2 - 4a + 3 = 0 E) a^2 - 4a + 5 = 0

find b^2 - 4ac < 0 ---> E [-b+-√(b^2 - 4ac)] / 2a

If k is a positive integer, is k the square of an integer? 1) k+1 is divisible by only two different numbers 2) k is divisible by only nine different numbers

k = i^2 -> prime factors have *EVEN POWER* # factors of k = (power1 + 1)(power2 + 1)... ∈ even + 1 ∈ odd -> odd×odd ∈ odd 1) k+1 ∈ prime number -> k+1 = 5 —> k=4 ✔️ -> k+1 = 7 —> k=6 ❌ 2) 9 ∈ odd ✔️ B

In the xy-plane, if line k has negative slope and passes through the point (-5,r) , is the x-intercept of line k positive? (1) The slope of line k is -5. (2) r > 0

m<0 and passes (-5,r) and x-intercept (x,0) x>0 ? m = (r-0)/(-5-x) -5m-mx = r —> need to know r and m 1) m=-5 —> r is still unknown. Insufficient 2) r>0 and m<0 x = (-r/m) - 5 -r/m is some positive value but we still don't know whether it more than 5 or not. Insufficient 1)+2) 25+5x=r > 0 —> x > -5 x could be either positive or negative Insufficient E

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9? (1) y > 3x (2) y > x > 3

max-min > 9 ? 1) if x=1 —> y>=4 —> range=6-1 < 9 if x=10 —> y>=31 —> range=31-3 > 9 Insufficient. 2) if x=4 —> y>=5 —> range=6-3 < 9 if x=20 —> y>=21 —> range=21-3 > 9 Insufficient. 1)+2) x>=4 and y>=13 —> range 13-3 > 9 Sufficient. C

If mn = 3(m + 1) + n and m and n are integers, m could be any of the following values EXCEPT: (A) 2 (B) 3 (C) 4 (D) 5 (E) 7

mn = 3(m + 1) + n mn - n = 3(m + 1) n(m-1) = 3(m+1) n = 3(m + 1)/(m-1) n won't be an integer only if m = 5 (from the options). Answer: D.

Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

new: 1.1R, 1.05S, 1.08(R+S) 2R = 3S —> R:S=3:2 1.1R/1.08(R+S) = 1.1(3)/1.08(5) = 22/36 = 11/18

Every attendee at a monster truck rally paid the same admission fee. How many people attended the rally? (1) If the admission fee had been raised to $20 and twice as many people had attended, the total admission fees collected would have been three times greater. (2) If the admission fee had been raised to $30 and two-thirds as many people had attended, the total admission fees collected would have been 150% of the actual admission fees collected.

p=?, p*fee=total 1) 20*2p = 3fp 40=3f. Insufficient. 2) 30*2p/3 = 1.5fp 10=1.5f. Insufficient. 1)+2) Insufficient. E

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ? (A) 2 (B) 4 (C) 8 (D) 20 (E) 45

r = 12t/100 = 3t/25, which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3 Answer. E.

An employee at a company was given the task of making a large number of copies. He spent the first 45 minutes making copies at a constant rate on copier A, but copier A broke down before the task was completed. He then spent the next 30 minutes finishing the task on copier B, which also produced copies at a constant rate. How many total minutes would the task have taken had copier A not broken down? (1) Copier A produced twice as many copies in its first 5 minutes of operation as copier B produced in its first 15 minutes. (2) Copier B produces 10 copies per minute.

rate = work/time —> work = rate×time wA = rA×45 and wB = rB×30 Wanna know time for A in wB Need to know rB in term of rA 1) rA×5 = 2rB×15 —> rA = 6rB Now we got what we want to know Sufficient 2) rB = 10 then wB = 300 No link to A at all. Insufficient A

If Paula drove the distance from her home to her college at an average speed that was greater than 70 kilometers per hour, did it take her less than 3 hours to drive this distance? 1) The distance that Paula drove from her home to her college was greater than 200 kilometers. 2) The distance that Paula drove from her home to her college was less than 205 kilometers.

speed = distance/time time = distance/speed speed>70 and time<3 ? Need to find distance that is limited 1) ∞/∞ = ∞ Insufficient. 2) 205/∞ ≈ 0 Sufficient. B

Image (Math Test Bin3: 3) What is the area of the shaded region in the figure shown? (1) The area of the rectangle ABCD is 54. (2) AE = 2ED

split the rectangle ABCD into two rectangles by drawing the height of triangle ABE, then the shaded region will be seen as half of each rectangle which means the area of shaded region ABCD is also the half of ABCD A

A steamer that travels at a constant speed of 10 miles per hour in still water starts from one end of the 50 miles of English Channel. How long will the steamer take to cross a distance of 50 miles, if water currents are favorable for the first half and unfavorable for the second half of the length of the channel? Consider the speed of water current to be same both upstream and downstream. 1) The water flows at a constant speed of ¹⁰/₃ mph 2) The steamer's average speed during the second half of its trip is reduced to half of its average speed during the first half of its trip

still water 10mph, 50m, t=? 1st: 10+c * t1 = 25 2nd: 10-c * t2 = 25 1) c = 10/3. Sufficient. 2) 10+c = 20-2c. Sufficient. D

A foot race will be held on Saturday. How many different arrangements of medal winners are possible? (1) Medals will be given for 1st, 2nd, and 3rd place. (2) There are 10 runners in the race.

we need to know the number of participants and the number of winners 1)+2) C

Sarah's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her d dollars per delivery plus c cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ? A. 7cdx/100 B. d + 7cx/100 C. 7d + xc/100 D. 7d + 7xc/100 E. 7cdx

x = sum/7 sum = 7x cost = 7d + 7xc/100 D

If x+y≠0, |x+y| = ? 1) |x| = 1 2) |y| = 1

x and y need to have same sign C

In isosceles triangle ABC, what is the value of <C? 1) The measure of <B is 42. 2) The measure of <A is 96.

|A-B| < C < A+B and A+B+C = 180 1) if B=A then C=96 or if B=C=42 then A=96 2) 2A > 180 then C must be 42 B