GMAT 2020 Quant
https://gmatclub.com/forum/if-the-circle-above-has-center-o-and-circumference-18m-then-the-perim-240741.html If the circle above has center O and circumference 18π, then the perimeter of sector RSTO is? (A) 3π + 9 (B) 3π + 18 (C) 6π + 9 (D) 6π + 18 (E) 6π + 24
Answer = B
How many multiples of 4 are there between 12 and 96, inclusive?(A) 21 (B) 22 (C) 23 (D) 24 (E) 25
Answer = B Last multiple - First multiple all divided by 4 then + 1
How many odd numbers between 10 and 1,000 are the squares of integers? A. 12 B. 13 C. 14 D. 15 E. 16
Answer = C
If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane? (1) The coordinates of C are (a, 1 - b). (2) The coordinates of D are (1 - a, b). 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.
Answer = C
If x11px11p is an odd prime number, where xx is a positive integer and pp is a prime number, what is the least value of xx? A. 22 B. 33 C. 44 D. 66 E. 99
Answer = D
Is ab odd? (1) a is even (2) a is an integer
Answer = E
What is 12323 divided by 11?
Sum of digits on odd places O= 3+3+1=7Sum of digits on even places E= 2+2=4Remainder= E- O = 4-7 = -3Thus remainder is 11-3 =8
For the infinite sequence a1a1, a2a2, a3a3, ... anan, an+1an+1, an=3∗an−1an=3∗an−1 for all n>1. If a5−a2=156a5−a2=156, what is a1a1?A. -1 B. 2 C. 3 D. 4 E. 8
We are given that a(n) = 3 x a(n-1) Thus: a(2) = 3 x a(1) a(3) = 3 x 3 x a(1) = 9a(1) a(4) = 3 x 9 x a(1) = 27a(1) a(5) = 3 x 27 x a(1) = 81a(1)We are given a(5) - a(2) = 156. Thus: 81a(1) - 3a(1) = 156 78a(1) = 156a(1) = 2 Answer: B
What is the sum of all the even integers between 99 and 401? (A) 10,100 (B) 20,200 (C) 37,750 (D) 40,200 (E) 45,150
(C) 37,750 The sum of n terms of the AP is n∗(First term+Last term)2n∗(First term+Last term)2 Which is the same as number of terms∗Average of the first and the last termsnumber of terms∗Average of the first and the last terms. https://gmatclub.com/forum/what-is-the-sum-of-all-the-even-integers-between-99-and-262495.html
All prime numbers except 2 and 5 end in?
1, 3, 7 or 9, since numbers ending in 0, 2, 4, 6 or 8 are multiples of 2 and numbers ending in 0 or 5 are multiples of 5.
What are the 3 Steps to an Effective AWA Essay?
1. Brainstorm. Analyze the argument and note three assumptions an the conclusion . 2. Template. Assign each assumption to a paragraph and be prepared to use your pre-selected transition statements. 3. Write. If you've done steps 1 and 2, the writing should be a formality.
What are the 3 things you should look for to solve exponent problems?
1. Find common bases 2. Factor 3. Find patterns
What is the number of terms in 50......69 inclusive?
20
What is the greatest power that 5 can be raised to so that the resulting number is a factor of 25!? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6
25/5 = 5 25/25 = 1, final answer 5+1 = 6
At a certain high school, the student to teacher ratio is 25:1. If the number of students increases by 50% and 10% of teachers are laid off, what would be the new student to teacher ratio? (Assume that no other changes happen) A. 40:1 B. 125: 3C. 75:2D. 145:9 E. Cannot be determined
2500:100 3750:90 375:9 125:3 B
All prime numbers above 3 are of the form?
6n−1 or 6n+1, because all other numbers are divisible by 2 or 3.
If each term in the sum a1+a2+a3+...+ana1+a2+a3+...+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n? A. 38 B. 39 C. 40 D. 41 E. 42
7x+77y = 350 7x+77y=350, where X is # of 7's and yy is # of 77's, so # of terms nn equals to x+yx+y;7(x+11y)=3507(x+11y)=350 --> x+11y=50x+11y=50 --> now, if x=39x=39 and y=1y=1 then n=x+y=40n=x+y=40 and we have this number in answer choices.Answer: C.
Given that N=a3b4c5N=a3b4c5 where a, b and c are distinct prime numbers, what is the smallest number with which N should be multiplied such that it becomes a perfect square, a perfect cube as well as a perfect fifth power? A. a3b4c5a3b4c5 B. a5b4c3a5b4c3 C. a2b3c5a2b3c5 D. a7b6c5a7b6c5 E. a27b26c25
A perfect square, is an integer that can be written as the square of some integer. For example 16=4^2, is a perfect square. Notice that the powers of the primes of a perfect square are even.A perfect cube, is an integer that can be written as the cube of some integer. For example 27=3^3, is a perfect cube. Notice that the powers of the primes of a perfect cube are multiples of 3.A perfect fifth power, is an integer that can be written as the fifth power of some integer. For example 32=2^5, is a perfect fifth. Notice that the powers of the primes of a perfect fifth power are multiples of 5.According to the above, a number to be a perfect square, a perfect cube as well as a perfect fifth power, must have its primes in power of 30 (the least common multiple of 2, 3, and 5), so it must be a perfect 30th power.The least positive integer a3b4c5a3b4c5 should be multiplied by, in order the powers to be multiples of 30 is a27b26c25a27b26c25: (a3b4c5)(a27b26c25)=a30b30c30=(abc)30(a3b4c5)(a27b26c25)=a30b30c30=(abc)30.
If n = 20! + 17, then n is divisible by which of the following? I. 15 II. 17 III. 19 (A) None (B) I only (C) II only (D) I and II (E) II and II
A) None (B) I only (C) II only (D) I and II(E) II and II
How many of the three-digit numbers are divisible by 7? A. 105 B. 106 C. 127 D. 128 E. 142
Amswer D
During a certain bicycle ride, was Sherry's average speed faster than 24 kilometers per hour? (1 kilometer = 1000 meter) (1) Sherry's average speed during the bicycle ride was faster than 7 meters per second. (2) Sherry's average speed during the bicycle ride was slower than 8 meters per second.
Answer = A
If f(x)=2x−1f(x)=2x−1 and g(x)=x2g(x)=x2, then what is the product of all values of nn for which f(n2)=g(n+12)f(n2)=g(n+12)? A. −145 B. −24 C. 24 D. 145 E. None of the above
Answer = A
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip? (1) 2x + 3y = 280 (2) y = x + 10
Answer = A
What is the decimal equivalent of (15)5(15)5? A) 0.00032 B) 0.0016 C) 0.00625 D) 0.008 E) 0.03125
Answer = A
A food truck sold burritos and tacos in a ratio of 7 tacos for every 3 burritos. If they sold 84 more tacos than burritos, how many total tacos did they sell? A. 126 B. 147 C. 196 D. 210 E. 252
Answer = B
Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD's vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system? A. 1:00 p.m. B. 2:00 p.m. C. 3:00 p.m. D. 5:00 p.m. E. 6:00 p.m.
Answer = B
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301? A. 10,100 B. 20,200 C. 22,650 D. 40,200 E. 45,150
Answer = B
How many integers between 18 and 70, inclusive are divisible by either 7 or 9 but not both? A. 11 B. 12 C. 13 D. 14 E. 15
Answer = B
How many positive three-digit integers are not divisible by 3? A. 599 B. 600 C. 601 D. 602 E. 603
Answer = B
If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^2 have? A. 4 B. 5 C. 6 D. 8 E. 9
Answer = B
Is a an integer? (1) a^3 is an integer. (2) The cube root of a is an integer.
Answer = B
Last year, if Elena spent a total of $720 on newspapers, magazines, and books, what amount did she spend on newspapers? (1) Last year, the amount that Elena spent on magazines was 80 percent of the amount that she spent on books. (2) Last year, the amount that Elena spent on newspapers was 60 percent of the total amount that she spent on magazines and books.
Answer = B
https://gmatclub.com/forum/the-figure-shown-above-represents-a-modern-painting-that-consists-of-f-207313.html The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length ℓ and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles? (A) 15 (B) 20 (C) 25 (D) 30 (E) 40
Answer = B
The sum of first NN consecutive positive odd integers is N2N2 . What is the sum of all odd integers between 13 and 39, inclusive? A. 351 B. 364 C. 410 D. 424 E. 450
Answer = B The sum of all odd integers between 13 and 39, inclusive equals to the sum of all odd integers from 1 to 39, inclusive minus the sum of all odd integers from 1 to 11, inclusive.Since there are 20 odd integers from 1 to 39, inclusive then the sum of all odd integers from 1 to 39, inclusive is 202202;Since there are 6 odd integers from 1 to 11, inclusive then the sum of all odd integers from 1 to 11, inclusive is 6262;So, the required sum is 202−62=364202−62=364.
If n is the least of three different integers greater than 1, what is the value of n ? (1) The product of the three integers is 90. (2) One of the integers is twice one of the other two integers.
Answer = C
If x=232∗254∗276∗298x=232∗254∗276∗298 and is a multiple of 26n26n, where nn is a non-negative integer, then what is the value of n26−26nn26−26n? A. -26 B. -25 C. -1 D. 0 E. 1
Answer = C
Which expression has the greatest value? A. 1 ^ 999 B. 2 ^ 300 C. 3 ^ 200 D. 4 ^ 100 E. 1 ^ 650
Answer = C
David and Stacey are riding bicycles on a flat road at a constant rate. If Stacey is now three miles ahead of David, in how many minutes will Stacey be just two miles ahead of David? (1) Stacey is traveling at rate of 10 mph and David is traveling at a rate of 12 mph. (2) 45 minutes ago Stacey was 4.5 miles ahead of David.
Answer = D
How many miles long is the route from Houghton to Callahan? (1) It will take 1 hour less time to travel the entire route at an average rate of 55 miles per hour than at an average rate of 50 miles per hour. (2) It will take 11 hours to travel the first half of the route at an average rate of 25 miles per hour
Answer = D
If the positive integer n is added to each of the integers 69, 94, and 121, what is the value of n? (1) 69 + n and 94 + n are the squares of two consecutive integers (2) 94 + n and 121 + n are the squares of two consecutive integers
Answer = D
The price per share of Stock X increased by 10 percent over the same time period that the price per share of Stock Y decreased by 10 percent. The reduced price per share of Stock Y was what percent of the original price per share of Stock X ? (1) The increased price per share of Stock X was equal to the original price per share of Stock Y. (2) The increase in the price per share of Stock X was 10/11 the decrease in the price per share of Stock Y.
Answer = D
What is the remainder when 319 is divided by 10 ? a. 1 b. 3 c. 5 d. 7 e. 9
Answer = D
What is the sum of digits in decimal notation of number 1020−161020−16 ? A. 158 B. 162 C. 165 D. 174 E. 183
Answer = D
https://gmatclub.com/forum/m26-184444.html#p2423689
Answer = D
A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs, then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs? A. 5 B. 3 C. 8/3 D. 5/2 E. 7/3
Answer = E
During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During this time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel? A. 36 B. 37.5 C. 40 D. 80 E. 90
Answer = E
Is x an integer? (1) x^2 is an integer. (2) x/2 is not an integer.
Answer = E
In which of the following pairs are the two numbers reciprocals of each other? I. 3 and 1/3 II. 1/17 and -1/17 III. 3√3 and 3√3
Answer = I & III
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p? A. 10 B. 12 C. 14 D. 16 E. 18
Answer = c Given p=30!p=30!.Now, we should check the highest power of 3 in 30!: 303+3032+3033=10+3+1=14303+3032+3033=10+3+1=14. So the highest power of 3 in 30! is 14.
The sequence a1a1, a2a2, ... , anan, ... is such that an=2an−1−xan=2an−1−x for all positive integers n ≥ 2 and for certain number x. If a5=99a5=99 and a3=27a3=27, what is the value of x? A. 3 B. 9 C. 18 D. 36 E. 45
Answer A https://gmatclub.com/forum/the-sequence-a1-a2-a-n-is-such-that-an-2an-1-x-46630.html
An "Armstrong number" is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4? A. 2 B. 3 C. 4 D. 5 E. 6
Answer B https://gmatclub.com/forum/an-armstrong-number-is-an-n-digit-number-that-is-equal-to-the-sum-of-305922.html
Which of the following CANNOT be the median of the 3 positive integers x, y, and z? A. x B. z C. x+z D. (x+z)/2 E. (x+z)/3
Answer choice is C https://gmatclub.com/forum/which-of-the-following-cannot-be-the-median-of-the-2436.html
A plane traveled k miles in its first 96 minutes of flight time. If it completed the remaining 300 miles of the trip in t minutes, what was its average speed, in miles per hour, for the entire trip?
Answer is A https://gmatclub.com/forum/a-plane-traveled-k-miles-in-its-first-96-minutes-of-flight-time-232862.html
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be A. 2 B. 5 C. 6 D. 7 E. 14
Answer is E. Break th question down to its prime factors then find the number to multiply by that squares all the prime factors.
What is the greatest integer x for which 64,0002x64,0002x is an integer? A. 6 B. 7 C. 8 D. 9 E. 10
Answer: D
In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females? A. 3/5 B. 2/3 C. 3/4 D. 4/5 E. 5/6
Answer: D.
If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative? (1) rt is negative (2) s is negative
Answer: E
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same route at 40 miles per hour. What is his average rate for the round trip in miles per hour? (A) 50 (B) 48 (C) 47 (D) 46 (E) 45
Average speed = TotalDistance/TotalTime Average speed for the round trip : =20 + 20 / 5/6 =48
Formaul for average speed?
Avg speed = total distance/ total time
A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class? (A) 20 (B) 24 (C) 36 (D) 48 (E) 96
B - https://gmatclub.com/forum/a-gym-class-can-be-divided-into-8-teams-with-an-equal-number-143494.html
If 2x−2x−2= 3∗213 2x−2x−2=3∗213 what is the value of x? A. 9 B. 11 C. 13 D. 15 E. 17
D https://gmatclub.com/forum/if-2-x-2-x-2-3-2-13-what-is-the-value-of-x-130109.html
The positive integer n is divisible by 25. If √n is greater than 25, which of the following could be the value of n/25? (A) 22 (B) 23 (C) 24 (D) 25 (E) 26
E
How many factors does 450 have?
Example: Finding the number of all factors of 450: 450=21∗32∗52450=21∗32∗52 Total number of factors of 450 including 1 and 450 itself is (1+1)∗(2+1)∗(2+1)=2∗3∗3=18(1+1)∗(2+1)∗(2+1)=2∗3∗3= 18 factors.
A farmer constructs a fence along the northern edge of his property, using materials suchthat he places a post every 7 meters. if he uses 100 posts, how many meters will the fence span? a) 686 b) 693 c) 700 d) 707 e) 770
I like the solutions above. I literally drew a picture.For any specific range with "marked off" beginning and end values, there will always be one more tick than interval.Wasn't sure I remembered that rule correctly, so I drew 10 posts, and wrote 7 in between:|7|7|7|7|7|7|7|7|7|Then I counted. 10 fence posts, but only 9 lengths of 7 in between. So 100 fence posts = 99 intervals of 7 meters.99*7 = 693. Answer B
Identical trains A and B are traveling non-stop on parallel tracks from New York to Chicago. Train A leaves New York at 5PM and travels at a constant speed of 55mph (assume constant speed from start of trip). Train B leaves New York at 6:12PM and travels at a constant speed of 66mph (assume constant speed from start of trip). At what time will the two trains be exactly beside each other? (A) 6:00PM (B) 7:12PM (C) 12:00AM (D) 12:12AM (E) 1:12AM
In catching up problems, logic is always easier than algebra. Whenever a train (or car, person, etc). gets a head start and is chased down by something faster, use the following approach: 1. Determine how far behind the faster train is before it starts. In this problem the faster train starts 1 hour and 12 minutes, or 1 and 1/5 hours, after the slower train. In 1 and 1/5 hours the slower train will have traveled 66 miles (1 and 1/5 x 55mph), so the faster train is 66 miles behind when it leaves New York. 2. Take the distance that the faster train is behind and divide it by the differential in rates between the two trains. If the faster train is going 66mph and the slower train is going 55mph, then the faster train catches up 11 miles every hour. Therefore it will take exactly 6 hours (66 miles divided by 11mph) for the faster train to catch up. Thus the correct answer choice is D, because when you add 6 hours to 6:12, you see that they will be exactly beside each other at 12:12AM. NOTE: Do not be intimidated on these problems when there are wrinkles. For instance, what if the question above wanted to know at what time train B would be exactly 22 miles ahead of train A? Do the same calculation above and then realize it will take exactly two hours more for train B to gain 22 miles (2 hours x 11mph).
A post on a website gains a point if a user choose to upvote it and loses a point if a user chooses to downvote it. If a post has a total of 60 points and 40% of the votes were downvotes, how many votes have been cast, in total? A. 100 B. 150 C. 240 D. 300 E. 500
Let X be the total number of votes. Then:0.6X-0.4X=600.2X=60X=300 or You gain a point for an upvote and lose one for a downvote. So 1 downvote cancels out 1 upvote. If 40% of total votes were downvotes, 60% of total were upvotes. The 40% downvotes would cancel 40% upvotes and you will be left with only 20% upvotes to give you points.(20/100)*T = 60T = 300 The answer is D
If 6^y is a factor of (10!)^2, What is the greatest possible value of y ?A. 2 B. 4 C. 6 D. 8 E. 10
Look for the number of sixes in 10! then multiple the number of 6's you find by 2
An assumption
MUST BE TRUE
17. If you roll one fair six-sided die, what is the probability that the number is even or less than 4? (A) 1/6 (B) 1/3 (C) 2/3 (D) 3/4 (E) 5/6
P(A or B) = P(A) + P(B) - P(A and B). Answer is (E)
Probability of atleast 1?
P(atleast 1) = 1 - p( not atleast 1)
What are the 5 paragraphs your essay should have?
Paragraph 1: Introduction Paragraph 2: First Assumption and Explanation Paragraph 3: Second Assumption and Explanation Paragraph 4: Third Assumption and Explanation Paragraph 5: Conclusion
Change in Distance/Change in Rate is used for?
Questions whereby y car has to catch up to another car i.e. https://gmatclub.com/forum/car-a-and-car-b-are-each-traveling-along-the-same-stretch-of-highway-222109.html
Question 1: The nthnth term, tntn, of a certain sequence is defined as tn=tn−1+4tn=tn−1+4. If t1=−11t1=−11, then t82=t82= (A) 313 (B) 317 (C) 320 (D) 321 (E) 340
Solution: The given relation says that every nth term is 4 more than the previous term. So basically, it tells us that the sequence is an AP. a=first term | d= common difference Whew! (An AP is very easy to work with)What is the nth term of an AP? It's a+(n−1)da+(n−1)dWhat is the 82nd term of this AP? It's −11+81∗4=313 https://gmatclub.com/forum/sequences-made-easy-all-in-one-topic-262490.html
Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14
Statement 1: pz^4 < 0i.e. p is Negative because z^4 must be positive for given InequationBut since the sign of z is still unknown hence,NOT SUFFICIENT Statement 2: p + z^4 = 14As per this inequation p and z can have any sign positive or negative hence nothing can be concluded NOT SUFFICIENT Combining the two statementsp is Negative but even after combining the two statement we can't conclude the sign of z. Hence,NOT SUFFICIENT Answer: Option E
Mark bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share? A. $10 B. $11 C. $12 D. $13 E. $14
Suppose that number of shares is n Suppose that price per share is p 1st day: n*p=1000 (1) 2nd day: Price per share is 0.9pNumber of shares is 10+n0.9p * (10+n) =10009p + 0.9n*p = 1000 (2) Replace (1) in (2):9p + 900 = 10009p = 100 p = 11
What is the greatest value y for which 4^y is a factor of 12!? A. 2 B. 3 C. 4 D. 5 E. 6
Take 4 down to its prime factors which is 2 x 2. Then upon doing that cluster them into 4's to see how many 4's you get/come up with.
What is the remainder when 1049+21049+2 is divided by 11? A. 1 B. 2 C. 3 D. 5 E. 7
The answer is = A
What is the largest prime factor of 27^3−9^3−3^6? A. 2 B. 3 C. 5 D. 7 E. 11
The equation tells us that all are with base 3..We should simplify equation. 273−93−36=(33)3−(32)3−36...=39−2∗36=36(33−2)=36∗25..273−93−36=(33)3−(32)3−36...=39−2∗36=36(33−2)=36∗25..so 5 is the Greatest prime factor C
Train A is traveling at 40 miles per hour and Train B is traveling on a parallel track in the same direction at 60 miles per hour. Currently, Train A is 15 miles ahead of Train B. How many minutes will it take Train B to catch up with Train A? A. 45 B. 60 C. 75 D. 80 E. 90
Thus, Train A's distance is 40t and Train B's distance is 60t.Since Train B travels 15 more miles than Train A: 40t + 15 = 60t 15 = 20t 15/20 = 3/4 t3/4 (60) = 45 minutes Answer: A
In a certain medical survey, 45 percent of the people surveyed had the type A antigen in their blood and 3 percent had both the type A antigen and the type B antigen. Which of the following is closest to the percent of those with the type A antigen who also had the type B antigen? A. 1.35% B. 6.67% C. 13.50% D. 15.00% E. 42.00%
Type A = 45 Type A and B = 3. The percent of those with the type A antigen who also had the type B antigen =(Type A and B)(Type A)∗100=345∗100=203≈6.67 Answer: B.
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment? a) $100 b) $115 c) $125 d) $130 e) $135
We are given that a shipment of 1500 heads of cabbage costs 600 dollars, or 600/1500 = $0.40 per cabbage. We are given that 2/3 x 1500 = 1,000 heads of cabbage sold for 1.25 x $0.40 = $0.50. So, a total of 1,000 x $0.50 = $500 was made on the sale of those heads of cabbage. The next day, 500 heads of cabbage were sold at a price of 0.9 x $0.50 = $0.45, so a total of 500 x $0.45 = $225 dollars was made on the sale of those heads. Thus, a total of 500 + 225 = $725 was made.Thus, profit = 725 - 600 = $125. Answer: C
If x = 7!, which of the following is a factor of the integer (x + 1)? A. 7 B. 8 C. 70 D. 71 E. 80
We know, 2! onwards every factorial value is an even numberHence, x = 7! is also evenTherefore, x + 1 = 7! + 1 is an odd numberSo, 8, 70, and 80 cannot be a factor of x + 1Also, 7 is a factor of x, hence it cannot be a factor of x + 1So, automatically the answer becomes 71Hence, the correct answer is option D.Answer: D
A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9. If n is a positive integer, for which of the following values of k is 25∗10n+k∗102n25∗10n+k∗102n divisible by 9? A. 9 B. 16 C. 23 D. 35 E. 47
We need to determine for which value of k 25*10^n + k*10^2n is divisible by 9.We see that 10^n and 10^2n will always have a digit of 1 and then zeros. So, excluding k, the sum of the digits in our expression is 2 + 5 = 7 (since (25)(10^n) has a 2, 5, and zeros).We need to determine, of our answer choices, which when added to 7 will produce a sum that is divisible by 9. Scanning our answer choices, we see that 47 is the correct answer.2 + 5 + 4 + 7 = 18, which is divisible by 9. Answer: E
is 0 an integer(yes or no)?
Yes
Or means?
add
And means?
multiply
What is the lowest common multiple?
the lowest quantity that is a multiple of two or more given quantities (e.g. 12 is the lowest common multiple of 2, 3, and 4
If x represents the product of the first 100 positive odd integers and y represents the sum of the first 100 positive odd integers, then the value of x−y is A. Even B. Odd C. Negative D. Divisible by 3 E. Divisible by 6
x=1∗3∗5.......∗199x=1∗3∗5.......∗199... Product of odd integers will be ODDy=1+3+5.......+199y=1+3+5.......+199, there are 100 numbers of ONE type, so irrespective of all being ODD or all being even, the SUM will be EVENso x-y = Odd-Even = Odd..
