GMAT Practice Questions
(3^3+ 3)/3 + (3^2+3^2)/3^2 = 1 5 12 17 30
12
One-fifth of the students at a nursery school are 4 years old or older. If 16 students have not yet reached their third birthday, and a total of 40 students are not between 3 years old and 4 years old, how many children are in the nursery school? 120 96 70 60 24
120
If two positive integers x and y are not both even, then which of the following must be odd? xy x+y x-y x+y+1 2(x+y)+1
2(x+y)+1 (When multiplied by 2, any sum between any two numbers will be a multiple of 2 so it is even. If you add 1 it will be odd)
Thirty percent of the balloons used to decorate a party are red and the rest are yellow. If one-quarter of the yellow balloons have strings and there are a total of 40 balloons, how many of the yellow balloons do not have strings? 6 7 12 18 21
21
A committee consisting of 5 members is to be formed out of 6 men and 4 women. How many committees can be formed so that at least one woman is always in the committee? 252 300 867 123 246
246 (First combination of 10C5 = 252. Then find number when only men are chosen, 6C5 = 6. Then substract 252-6 =246)
A company produces baseball cards in equal numbers of regular packs of 16 and deluxe edition packs of 30. If, on a certain day, a company produces 241 cards, what is the smallest number of additional cards the company needs to produce in order to maintain its regular production practice? 5 11 21 35 46
35
The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 15 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? 41.25 42.5 43.75 45 57.5
43.75
How many integer values of a satisfy the inequality |a-5| <=2.5? 3 4 5 6 7
5 (Factor the inequality to -2.5 <= (a-5) <= 2.5. Then add 5 to isolate a, return 2.5<=a<=7.5. The possible integers would be 3,4,5,6,7)
If m is a positive integer and q+4 = 7^m, which of the following could NOT be a value of q? 3 45 54 339 2397
54 (The question says that q-4 has to be a multiple of 7. So 7-4 = 3, 49-4=45, 56-4=52 but the option says 54 so it is incorrect. Also, 54 is the only even number. Because m is positive, 7^m will always be odd. This means that q+4 must be odd, and in order for q+4 to be odd, q must be odd)
If a represents a single digit and the four-digit integer a12a is divisible by 6, what is a? 2 3 4 6 7
6 (Start taking away options. If a number is divisible by 6, it must be divisible by 2 and 3, and if it is divisible by 2 it means it must be even. So it can be either 2122, or 6126; and 6126 is divisible by 6)
if Square root of a = 3 and square root of b = 4, then square root of a + square root of b/ square root of a+b = a. 1 b. 8/7 c. 7/5 d. 12/5 e. 5
7/5
State | 1980 | 1990 Washington 12% 10% Oregon 17% 17% Iowa 9% 13% Vermont 20% 15% Maine 9% 12% California 33% 33% Total | 1.2 B | 1.6 B The number of matches produced in Oregon in 1980 was approximately the same as the number produced in which state in 1990? Washington Maine California Oregon Iowa
Iowa
If n-rs = n and r<>0, which of the following must be true? r=1 r=s r+s=0 |rs| = 1 s=0
s=0 (Solve for r. The equation equals -rs=0, so rs = 0. If the product is 0, one of them must be 0.)'\
If -3<=X<=1, which if the following inequalities is an algebraic expression for the shaded part of the number line above? |x| <= 1 |x| <= 3 |x-1| <= 2 |x+1| <= 2 |x-2| <=1
|x+1| <= 2 (If x<=1, then |1+1| <= 2, and that is the maximum value of x)
If k = 5p, where p is a prime number greater than 2, how many different positive even divisors does k have, including k? 0 1 2 4 5
0 (Assume p=3, so k=15. Divisors of 15 are 1,3,5, and 15. None are even so it is 0. Also remember 2 is the only even prime number, so if p is greater than 2, it cannot be divisble by an even number)
Two solutions are made by adding Chemical Z to water. Solution A is 40% Chemical Z and Solution B is 80% Chemical Z. A chemist combines Solution A and Solution B to make a mixture. If x percent of the Chemical Z in the combined mixture comes from Solution A, and if y percent of the total volume of the mixture comes from Solution A, which of the following expresses x in terms of y ? 60y/80-y 100y/200-y 120y/200-y 200y/240-y
100y/200-y
If 5a + 2b = 11 and 4a + 3b = 4, then a - b = -7 25/7 48/7 7 15
7
Each day, a vendor rents a booth. She is charged both a flat fee and 5% of her gross sales for booth rental. What is the vendor's gross sales on Tuesday? The vendor's total booth rental expense on Tuesday is $100. On Tuesday, the amount of the flat fee is equal to the amount paid on the percentage of gross sales. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Both statements together are sufficient, but neither statement alone is insufficient
(-4*3)^4/(12*6*2)^2
1
Last month, the price of a gym membership was G dollars. This month, the price of a membership rose 30 percent. To entice purchase of the membership at the new price, a 20 percent discount is offered. If Jim buys his membership this month, how much will he pay as a percent of price G ? 90% 97% 104% 110% 125%
104%
If non-negative integers n and p are not both odd, which of the following must be odd? np np+2 2n+p 2(n+p) 2(n+p)+1
2(n+p)+1 (If they are not both odd, they are both even or one of them is even. Numbers are even if they are a factor of 2. Take option (E), if the sum of ANY two numbers in multiplied by 2. The result will always be even. Then if you add 1, it will always be odd)
A group of friends on a hoke split up into smaller groups. When they formed groups of three, one person was left out. When they formed groups of four, two people were left out. When they formed groups of six, four people were left out. If the group contains at least a dozen people, what is the smallest possible number of people in the group? 10 20 22 26 34
22 (Can't be 10 since it is at least a dozen. If when they split up in groups of 4, there were 2 person left, it means the remainder is 2. So take the middle option and strat working from there. 22 divided by 4, the quotient is 5 and remainder is 2)
Running at the same constant rate, n printing presses can produce a total of 150 newspapers per minute. At this rate, how many newspapers could xsuch machines produce in 90 seconds? 13500/NX 225X/N 150X/N 90X/N 5XN/2
225X/N
In an office there are 4 female staff members and 10 male staff members. In how many ways can a committee of 3 members be formed if it must include at least one female member? 120 244 364 1464 2184
244 (First find the combination of all 14 members, 14C3 = 364. Then find how many committees can be formed only with the men, so 10C3 = 120. Then substract 364-120=244)
If positive integers x and y are not both even, which of the following must be odd? x/y 3xy 2xy-1 x+y x-y
2xy-2 (If they are not both even, it means one of them is odd or both of them are odd. Any two numbers multiplied by 2 will be even, so if you substract 1, it will always be odd)
If a and b are two positive integers whose greatest common divisor is 1, what will be the remainder of a/b, if a/b = 3.75? 1 2 3 4 5
3 (You can rewrite 3.75 as 3/4 + 3, or 3(3/4). The remainder is the numerator in the fraction, so the remainder is 3)
How many even numbers in the range between 10 and 100, inclusive, are not divisible by 3? 15 30 31 33 46
31 (To be divisible by 3, it must be odd or divisible by 6. So the number of even numbers between 11 and 99 is (99-11)/2 = 44+2 (inclusive of 10 and 100) = 46. Then, the first number divisible by 3 is 12, and the last number is 96. So (16-2)+1=15 multiples of 6 between 10 and 100. So total numbers not divisible by 3 are 46+15=31)
In 2015, sales at Company X were 20% less than its sales in 2014. In 2016, sales were 30% greater than sales in 2015. By what percent did company X sales change from 2014 to 2016? 10% decrease 4% increase 5% increase 10% increase 56% increase
4%
It would take one copyist 10 minutes to copy a large document and another copyist 12 minutes to copy the same document. How many minutes would it take both copyists, working simultaneously at their respective constant rates, to copy the document? 11/60 5 5 5/11 11 22
5 5/11 (Two ways: I. One copyist rate is 1/10 of a document per minute and the other 1/12 of the document per minute. So together, it would be 1/10 + 1/12 = 6/50+5/60 = 11/60 of the document per minute. So it would take them the reciprocal, 60/11 minutes, to complete the whole document. II. Together, it will take them about half their times to copy the document. So 10/2 = 5 and 12/2 = 6. So it will take both copyists together between 5 and 6 minutes to copy the whole document. Option C is the only one between this range)
Alicia scored an A on 30% of her first g tests during the semester. Deciding to improve her grade, alicia works hard and scores an A on each of her remaining h tests during the same semester. If Alicia scored an A on 50% of her tests over the entire semester, which of the following expresses the ratio of g to h? 1:3 2:5 3:5 5:2
5:2
State | 1980 | 1990 Washington 12% 10% Oregon 17% 17% Iowa 9% 13% Vermont 20% 15% Maine 9% 12% California 33% 33% Total | 1.2 B | 1.6 B The increase in the number of matches produced in California from 1980 to 1990 exceeds by how many million the increase in the number of matches produced in Oregon over the same period? 68 64 16 2.56 1.82
64
If n = 3*4*p, where p is a prime number greater than 3, how many different positive non-prime divisors does n have, excluding 1 and n? 6 7 8 9 10
7 (Assume p =5, so n = 60. Go down the list starting with 1 until you find the number that multiplied by 10 equals n. So 1*60, 2*30, 3*20, 4*15, 5*12, 6*10. Now exclude all primer divisors and 1 and n. So you are left with 4,6,10,12,15,20,30.)
How many integers that have a value less than 4 satisfy the inequality (y+1)(y+2)(y+4)>=0? 4 5 6 7 8
8 (If y < 4, the max value of y is 3. Going down the line you can go until -4 before the result is negative. With -4, (-4+1)(-4+2)(-4+4)=(-3)(-2)(0). 0>=0. The lowest number would be when the biggest product (4) equals 0)
The Amazing soft drink company interviewed c consumers for a market research. The study found that ⅖ of consumers preferred Zing Cola to Diet Zing Cola. Of those who preferred Diet Zing, ⅙ preferred Caffeine Free Diet Zing. How many consumers in terms of c, did not prefer Caffeine Free Diet Zing? c/11 c/10 7c/15 9c/10 10c/11
9c/10
If A=-2.3, B=-0.8, C=0, D=1.3, E=2. Which of the following points has the second least absolute value? A B C D E
B (C is 0 so it is the least absolute value. Determine what is the next value closest to 0. The distance from 0 to B is less than 1 (0.8) so that is the second least absolute value)
A circular patch is placed on a square piece of fabric. What is the perimeter of the square piece of fabric? (1) The radius of the patch is 4 centimeters. (2) Each side of the square piece of fabric is tangent to the patch. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
If County X consists of five towns, A, B, C, D, and E, how many people live in Town A? (1) The total population of the five towns in County X is 21,000. (2) The total population of towns B, C, D, and E is 3,000. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Is X^2 less or equal to 10y^2? (1) 0 <x <2 (2) 1 <y <2 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
If A is a positive integer, is A a multiple of 30? I. A is a multiple of 20 II. Square root of A is a multiple of 24 Statement 1 ALONE is sufficient, but statement 2 is not Statement 2 ALONE is sufficient, but statement 1 is not Both statements TOGETHER are sufficient Each Statement ALONE is sufficient Statements 1 and 2 together are NOT sufficient
Both statements TOGETHER are sufficient (I. There are multiples of 20 that are also multiples of 30 (60, 120, etc) but there are also many that are not multiples of 30 (20,40,80, etc). So it is not sufficient. II. A multiple of 30 must contain all the prime factors of 30: 2,3, and 5. If A is a multiple of 24^2 or (2*2*2*3)^2 but it does not contain 5 so it is not sufficient. But together, it says that if A is a multiple of 20 and is also a factor of 2,3, and 5, it will always be a multiple of 30. So together, they are sufficient)
A certain restaurant regularly orders tomatoes, pasta, and cheese. The number of pounds of tomatoes ordered, t, is directly proportional to the number of pounds of pasta ordered, p, which in turn is directly proportional to the number of pounds of cheese ordered, c. If t = 150, then what is the value of c ? t = 300 whenever p = 900. p = 300 whenever c = 8 Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Both statements together are sufficient, but neither statement alone is insufficient
Aaron has how many more guitars than Bonnie? The total number of guitars that Aaron and Bonnie have is between 10 and 20. Aaron has 25 percent more guitars than Bonnie. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Both statements together are sufficient, but neither statement alone is insufficient
All of the 121 baseball players participating in a celebrity golf outing were born in either Asia, Australia, North America, or South America. If there are 25 percent fewer players that were born in Australia than were born in Asia, how many of the participating players were born in North America? The number of players who were born in South America is 40 percent greater than the number of players who were born in Asia. The ratio of the number of players who were born in North America to the number of players who were born in South America is 29:14. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Each statement alone is sufficient
In a certain country, m farmers each own n cows, each cow produces p gallons of milk per day. If r percent of the cows suddenly drop production by s percent each, then what is the new daily total production of milk in gallons for all farmers? Mnp - rs Mnp (1 - (rs/10000)) Mnp (1 - (rs/100)) Mnp + mnprs Mnp - mnprs
Mnp (1 - (rs/10000))
A group of 10 roommates share the rent for an apartment equally. If the apartment's monthly rent is r dollars and x of the roommates move out, which of the following is an expression for the additional rent paid by each remaining roommate? RX / 10(10-X) 10R/X R / 10(10-X) R / 10 - X RX / 10 - X
RX / 10(10-X)
Picture: Square embedded in a circle. All points touch the circle. Square: WXZY In a certain playground, a square sand box rests in a circular plot of grass so that the corners of the sandbox just touch the edge of the plot of grass at points W, X, Y and Z, as shown. What is the distance from point W to point Y? (1) The area of the circular plot is 49*pi. (2) The ratio of the area of the sand box to the area of the circular plot is 2/pi Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Is N odd? (1) N is a factor of 100. (2) N is a factor of 135. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Of the 1200 members of a gym, 150 have student memberships and attend fitness classes 2 or more times a week. How many of the 1200 members have students memberships and attend fitness classes fewer than 2 times a week? I. 800 members have non-student memberships II. 650 members attend fitness classes fewer than 2 times a week Statement 1 ALONE is sufficient, but statement 2 is not Statement 2 ALONE is sufficient, but statement 1 is not Both statements TOGETHER are sufficient Each Statement ALONE is sufficient Statements 1 and 2 together are NOT sufficient
Statement 1 ALONE is sufficient, but statement 2 is not (I. If 800 members have non-student memberships, it means that 400 members have student memberships. The questions says that out of those 400, 150 attend classes 2 or more times a week, so 250 attend 2 or less times a week. It is sufficient. II. It states the total number of members who attend classes less than 2 times a week, but does not say how many of those 650 have student membership.)
What is the value of (8a+a-b)/a-b? I. 5a+4b/a-b = 2 II. a - b = 9 Statement 1 ALONE is sufficient, but statement 2 is not Statement 2 ALONE is sufficient, but statement 1 is not Both statements TOGETHER are sufficient Each Statement ALONE is sufficient Statements 1 and 2 together are NOT sufficient
Statement 1 ALONE is sufficient, but statement 2 is not (Solve the equation is statement 1 for a = -2b. Then use this to replace in the question formula to solve for b. 9(-2b)-b/-2b-b = 19/3. Then you can replace to find the value of a, but you dont have to and you already know it is sufficient. Statement 2 states that a = b+9. If you also substitute in the equation you get 8b+81/9, so it is not sufficient)
If a and b are positive integers, what is the remainder when 4^(a+1+2b) is divided by 10? I. a is odd II. b = 3 Statement 1 ALONE is sufficient, but statement 2 is not Statement 2 ALONE is sufficient, but statement 1 is not Both statements TOGETHER are sufficient Each Statement ALONE is sufficient Statements 1 and 2 together are NOT sufficient
Statement 1 ALONE is sufficient, but statement 2 is not (when 4^n is divided by 10, a remainder equal to the units digit of the value results. So: 4^1 / 10 = remainder is 4 4^2 /10 = remainder is 6 4^3 / 10 = remainder is 4 4^4 / 10 = remainder is 6 So for all n that is odd, the remainder is 4. And for all n that is even, the remainder is 6. Since 2b will always be even, knowing that a is odd, means that a+1 will always be even and the remainder will always be 4. So statement 1 is sufficient. With statement 2, we still would not know the value of a, and it is needed to determine whether or not the exponent will be even or odd)
A journalist is writing an article on the 100 members of the United States Senate. After researching her article, the journalist classifies the Senators into one of four categories: men who have earned at least one college degree, men who have not earned a college degree, women who have earned at least one college degree, and women who have not earned a college degree. How many Senators are men who have earned at least one college degree? The number of women who have not earned a college degree is 30 percent less than the number of men who have not earned a college degree, and the number of men who have not earned a college degree is 25 percent less than the number of women who have earned a college degree. The number of women who have not earned a college degree is 70 percent of the number of men who have not earned a college degree, and the number of men who have earned at least one college degree is 30 percent of the number of men who have not earned a college degree. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
What is the product of a certain pair of consecutive even integers? At least one of the integers is neither positive nor negative. At least one of the integers is prime. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
What percent of the members of a club attended a certain conference? Twice as many members attended the conference as didn't attend the conference. There are 90 members in the club. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
A rideshare service charges x dollars for the first mile and y dollars for each additional mile. What is the value of y ? A ride of 5 miles costs $5.35. A ride of 7 miles costs $1.30 more than a ride of 5 miles. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Each of the candies in a jar is brown, green, or yellow. If one candy is to be selected at random from the jar, what is the probability that the candy will be brown? There are 25 candies in the jar. The probability that the candy selected will be green or yellow is 2/5. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
What is the remainder when positive integer a is divided by 4 ? When a is divided by 2, the remainder is 1. a is 5 more than a multiple of 8. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
What is the value of x-3y+z/x+z? X + z = 7 3y/x+z = 6 Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
What is the value of y? (1) When y is multiplied by 6, the result is between 40 and 45. (2) When y is multiplied by 3, the result is between 19 and 23. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Statements (1) and (2) TOGETHER are NOT SUFFICIENT
What is the value of x? (1) x2 = 6x - 9 (2) x2 = x + 6 a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. d. EACH statement ALONE is sufficient. e. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
If a/|a| < a and a <>0, then which of the following CANNOT be true? a>1 a<-1 |a|>1 a/|a|=1 a/|a| = -1
a<-1 (If a =2, then a/|a| <a, equals 1<2. So a>1 (A), |a|>1 (C), and a/|a|=1 (D). If a = -1/2, then a/|a|<1 equals -1<-1/2 so option E is also true. Last option is B so it is incorrect)
square root of 99 - square root of 44 + square root of 11 = a. Square root of 11 b. 2 * Square root of 11 c. Square root of 66 d. 12 e. 6 * Square root of 11
b. 2 * Square root of 11
Is the smallest of five consecutive integers even? (1) The product of the five integers is 0. (2) The sum of the five integers is 0. a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. d. EACH statement ALONE is sufficient. e. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
If a,b and c are positive integers such that a is a factor of b, and a is a multiple of c, which of the following is NOT necessarily an integer? bc/a a+b/c c-b/a a+c/c 2bc/a
c-b/a (Assume a=2, b=2, and c=1. Go down the options: (A) 2*1/2 is an integer. (B) 2+2/1 is an integer. (C) 1-2/2 is not an integer)
A circle is inscribed in a square. What is the area of the shaded region? (1) The distance from the center of the circle to a vertex of the square is 2 Square root of 2 (2) The square has a perimeter of 16. a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. d. EACH statement ALONE is sufficient. e. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
d. EACH statement ALONE is sufficient.
If x(p+q) = x and x<>0, which of the following must be true? p=q p>q p+q=0 q=1-p q=p-1
q=1-p (Since x cant be 0, divide both sides of the equation by x to leave p+q=1. This can also be written as p = 1 -q or as in option D q=1-p)
The ratio of flour to sugar to baking soda in a recipe is x:y:z. A cook accidentally triples the ratio of baking soda to sugar and halves the ratio of flour to sugar. If the altered recipe will have x total grams of sugar, which of the following expresses the grams of flour it will contain? x^2/2y 2y/x^2 xz/y yz/3x
x^2/2y
Representation in a local community board is based on the community's population, with 25 board members representing the first 500,000 people, and each additional board member representing an additional 30,000 people. Is the population of the town less than 500,000? (1) There were 23 members on the community board. (2) If the population were three times as large, the community board would have had 51 members. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
EACH statement ALONE is sufficient.
Bill went shopping for fruits and vegetables. He purchased a number of potatoes, onions and lemons in the ratio of 1:3:5, respectively. How many potatoes did Bill buy? I. Bill bought a total of 27 potatoes, onions and lemons II. Bill bought 9 onions Statement 1 ALONE is sufficient, but statement 2 is not Statement 2 ALONE is sufficient, but statement 1 is not Both statements TOGETHER are sufficient Each Statement ALONE is sufficient Statements 1 and 2 together are NOT sufficient
Each Statement ALONE is sufficient (Statement 1 says p+o+l= 27. The question says the ratio is 1+3+5=9. Divide 27 by the number of parts of the ratio and it is sufficient. Also can solve with the equation x+3x+5x=27. It is sufficient. Then statement 2, if we know the quantity of one item purchased we can find the other values with the ratio. Also if Bill bought 9 onions and x is the number of potatoes, solve for 9=3x, x =3. Both statements are sufficient)
Jack is standing in line. If there are 8 more people in front of Jack than behind him, how many people are in line? There are 4 people behind Jack. There are three times as many people in front of Jack as behind him. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Each statement alone is sufficient
Last year, Jill spent $2000 on clothes. She spent half as much on shoes as she spent on clothes. What percent of her income did Jill spend on clothes last year? Jill's income last year was $40000 Jill's income last year was 40 times as much as she spent on shoes Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Each statement alone is sufficient
If X<0, which of the following statements must decrease as x decreases? I. 10x-100 II. (x-1)/x III. x^2 - x I only III only I and II I and III II and III
I and II (Consider each step separately. Statement I, with every unit decrease in x, 10x decreases by 10 units. This statement must decrease as x decreases. Statement II, as x decreases, the numerator is always 1 more than the denominator so the expression gets closer to 1. The closer that X is to 0 (the higher x), the greater the result. So as x decreases so does the equation. No need to evaluate Statement III)
Which of the following is an integer? I. 14!/8! II. 14!/10! III. 14!/9!6! I only II only I and II only II and III only I, II and III
I and II only (Evaluate each statement. (I) would be 14*13*12*11*10*9 is an integer. (II) would be 14*13*12*11 is an integer (III) would be 14*13*12*11*10/6*5*4*3*2 migh not be an integer)
Which of the following is an integer? I. 10!/6! II. 10!/5! III. 10!/5!3! I only II only I and II only II and III only I, II and III
I, II and III (Simplify each fraction to find if they are integers. (A) 10*9*8*7 is an integer. (B) 10*9*8*7*6 is an integer. (C) 10*9*8*7*6/6 is an integer.)
From July 1 to July 31 in the same year, the water remaining in a reservoir decreased. What was the volume of water in the reservoir on July 1 ? During this period, the decrease in the volume of the reservoir was 26 percent. If, during the first ten days of July in this period, the decrease in the volume of the reservoir had been 18 percent, the reservoir would have had 32.8 km3 of water on July 10. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
In a class of 25 students, 15 students had an average score of a and the other 10 students had an average score of b. What is the average score of the entire class? (a+b)/2 = 80 3a + 2b = 395 Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
Jane and Chris work at a factory producing widgets. If Jane produces 4 more widgets per hour than does Chris, what is their combined rate? Last week, Chris and Jane together produced a total of 96 widgets. Last week, Chris worked twice as long as Jane and produced the same number of widgets as she did. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
In a certain club, how many people serve on both the Recruitment and Marketing committees? The recruitment committee has 3 more members than the marketing committee. At a joint meeting of both the recruitment and the marketing committee, there were 8 people present, and no member of either committee was absent. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statements 1 and 2 together are not sufficient
What is the value of x ? x2 - y2 = 27 x = 2y Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient Statements 1 and 2 together are not sufficient
Statements 1 and 2 together are not sufficient
If a is an integer greater than 0, then a(a+1)(a+3) is: even only when a is even even only when a is odd odd whenever a is odd divisible by 3 only when a is odd divisible by 4 whenever a is odd
divisible by 4 whenever a is odd (If a is odd, we know a= 2n+1. So replace that in the equation: (2n+1)(2n+1+1)(2n+1+3) = (2n+1)(2n+2)(2n+4). Factor out a 2 from each the second and third factors, to get 4(2n+1)(n+1)(n+2) so it is divisible by 4. Also can try to plug in values of a as an even or odd number. Look for difference between whenever and "only". Because a is also divisible by 3 but not only when it is odd)
For the convenience of walkers and runners, a linear exercise track m meters in length has a distance marker placed at the beginning and end of the track, as well as every fourth of its length and at every fifth of its length. If a runner were to travel the total length of a section of the track between consecutive markers, which of the following expresses the distance the runner could travel, in meters? m/10 and m/5 only m/5 and m/4 only m/20, m/10, m/5, and m/4 m/20, m/10, 3m/20, and m/5 m/20, m/10, 3m/20, m/5, and m/4
m/20, m/10, 3m/20, and m/5
During the first hour of a day, a stationary store sells only $1.50 worth of envelopes, $2.25 worth of pens, and a three-ring binder for $5.25. If the store had $20 in the cash register at the beginning of the day, and the store charges 8 percent sales tax on all purchases, how much money is in the register at the end of the first hour? $29.72 $27.92 $20.72 $9.72 $7.92
$29.72
Expression: (a^2 + b)/(b-a) In the expression above, if a <> b, and a is replaced with -b, the reciprocal of the resulting expression is equal to: (1+b/2) (2/1+b) (1-b/2) (2/1-b)
(2/1+b)
When x = 0.2, what is the value of 3x^2-1.3x-0.9? -3.38 -2.30 -1.04 -0.76 -0.04
-1/04
1 - q-1/q = 1/q 1+q/q 1-q/1+q 1 - q q
1/q
Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcels are the same size, what is the number of acres in one of the smaller parcels? (1) The combined size of the larger parcel and one of the smaller parcels is 416 acres. (2) The size of the larger parcel is 312 acres. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
EACH statement ALONE is sufficient.
(S - T/S+T). If s <> 0 and t<> 0, and if t is replaced by 1/t everywhere in the expression above, then the resulting expression is equal to: S-T/S+T S+T/S-T ST-1/ST+1 ST+1/ST-1 1-ST/1+ST
ST-1/ST+1
Does a^2 = ab? (1) Cubic root of b^3 = a (2) b = absolute value of a Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
If x<> 0, is x greater than y? (1) x > y + 2 (2) 2 + x > y Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Is x an integer? (1) x + 5 is an integer. (2) x / (1/4) is an integer. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Triangle: a=6 b = ? c = ? Angle ab = 90 In the right triangle above, is c less than 10? (1) b < 8 (2) c > 9 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
If n=p^2m where p is a prime number greater than 2, how many different positive odd divisors does n have, including n? 0 1 2 3 4
Three (Assume p =3, so n=9. Divisors are 1,3,9. It has three positive odd divisors. Also works with any prime number greater than 2)
If m,n and p are constants, m<n<p, and y^3- y = (y+m)(y+n)(y+p) for all numbers y, what is the value of n? -3 -1 0 1 3
0 (Factor the left side of the equation to put it into a form equivalent to (y+m)(y+n)(y+p): y^3-y = y(y^2-1) = y(y-1)(y+1) = (y+0)(y-1)(y+1) So the values are -1,0 and 1. The question states that m<n<p, so the values are m=-1, n=0, and p = 1.
If x is an integer, then what is the least possible value of |99-7x|? 0 1 5 98 107
1 (We are looking to how close to 0 we can get. What number multiplied by 7 gets the closest to 99 but is still less than 99. The number is 14, |99-7(14)|= |99-98|= 1)
If h < -1 < j < 0, which of the following is true for the reciprocate of h and j? -1 < 1/h < 1/j 1/h < 1/j < -1 1/j < 1/h < -1 1/h < -1 < 1/j 1/j < -1 < 1/h
1/j < -1 < 1/h
Bracelets cost p dollars each at a discount store. At a neighboring retail chain store, the same bracelets cost $1 more each, which means that x dollars will buy 10 more bracelets at the discount store than at the retail chain store. What is the value of x in terms of p? 10 (p+1) 10 (p-1) 10 (p^2 + p) 10 (p^2 - p) 10 (p^2 + p + 1)
10 (p^2 + p)
If the cost per unit of item A increases by r percent and the profit per unit of item A decreases by s percent, where s > r, then in terms of r and s, by what percent is the ratio of profit per unit to cost per unit decreased? r/s 100 (r-s) / 100 + r 100 (s+r) / 100 + r 100 (r+s) / 100 + s 100 (s-r)/ 100 + s
100 (s+r) / 100 + r
If k is a positive integer and the ratio of s to r is equivalent to k/1000, then r is what percent of s, in terms of k? 1000k 1/1000k 1/10k k/100 100000/k
100000/k
In 1990, those who invested money in fund Z for the entire year received a return of 9 percent on their investment. Roberta invested a certain amount in fund Z on January 1, 1990, and neither added to nor subtracted from her investment during the year; her investment and return for the entire year equaled $15,260. How much money did Roberta invest in fund Z on January 1, 1990? 13000 13260 14000 14360 14750
14000
y | (0,8) B | (0,3) A | | _ _ _ _ 7 _ _ _ _ _ _ _ _ _ _ _ x In the coordinate plane above, if line 1 || line 2 || x-axis and point a on line 2 is exactly 13 units away from point b on line 1, what is the x-coordinate of point b ? 19 17 15 12 8
19
If the ratio of the number of men to the number of women is the same in Department A and Department B, what is the ratio of the number of women in Department A to the number of women in Department B ? The ratio of the number of men in Department A to the number of men in Department B is 2 to 3. There are 300 more women in Department A than in Department B. Statement 1 alone is sufficient, but statement 2 alone is not sufficient Statement 2 alone is sufficient, but statement 1 alone is not sufficient Both statements together are sufficient, but neither statement alone is insufficient Each statement alone is sufficient
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
If the product of integer m and integer n is odd, then which must be even? n/m m-n m+2n m/n - 1 2 *(m/n)
m-2 (If the product of m and n is odd, it means both m and n are odd. An odd number minus an odd number must be even. Remember decimals can not be either even or odd, so answer must be an integer)
