Quant Examples

Chapter 1

In Maria’s Dream, maria and Jamilah are bouncing on a super trampoline. Maria’s feet hit the trampoline once every 12 seconds, and because Jamilah bounces higher, her feet hit the trampoline once every 15 seconds. If both girls begin jumping at the same time, what is the least number of seconds that will pass before their feet hit he trampoline at the same time?

60

is 3660 divisible by 42?

no, because the prime factorization of 42 is not fully encompassed by the prime factorization of 3660

If 100, 18, and 8 are factors of 150k, what is the smallest positive possible value of k?

100= 2×2×5×5 = 2² 5²; 18=23×3=2×3²; 8=2×2×2=2³. the LCM is 1800, so 150k must be divisible by 1800. Since the prime factorization of 1,800=2³ 3² 5² and the prime factorization of 150k= 2×3×5×5*(prime factorization of k), what is left over of the 150k is 2×2×3, so k must =2×2×3, or 12

If positive integer N is divisible by 12 and 20, find all positive integers that must be factors of N

N must also be divisible by 60, given that it must be divisible by the LCM of 12 and 20. It therefore should be divisible by all factors of 60 as well, including, 1,2,3,4,5,6,10,12,15,20,30 and 60.

if N and (25N)/20 are positive integers, what is the greatest integer that must divide evenly into N?

simplify (25/20) to 5/4. we now have (5N)/4, which means that N must be divisible by K, which in this case is 4.

At a certain department store, a rug was originally priced at W dollars, where W is a whole number. During a liquidation sale, the rug was sold for 6 percent of its original price. If the liquidation price is a whole number which of the following could be the liquidation price of the rug?

Anything that is divisible by 3

The product of 29,30,31, and 32 must be divisble by all except which of the following? 4,6,12,18,24?

18

If n is a positive integer, n^4 - 2n³ - n² +2n is divisible by which of the following? 16,20,24,28,32

24

if N is an odd integer, then n²-1 must be divisible by which of the following? 5,6,7,8,9

8

If w is an integer, y=2w and z=y³ +6y² +8y, what is the greatest integer that must be a divisor of z? 6,12,24,48,96?

48

If the remainder of ((28)^(29))/2 is added to the remainder of (15^(401))/3, what is the value of the resulting sum? 0,1,2,3,4

0

When positive integer n is divided by 6, the remainder is 5. What is the remainder when 5n is divided by 30? 5,10,15,20,25

25

When k is a positive integer, what is the difference between the largest possible remainder and the smallest possible remainder when k is divided by 7? 0,1,5,6,7

6

What is the sum of all positive integers less than 100 that leave a remainder of 9 when divided by 23? 165, 174,230,275,307

174

Helen owns between 340 and 360 stamps. If she places 25 stamps on each page of her stamp book, 2 stamps are left over. If she places 15 stamps on each page of her stamp book, 7 stamps are left over. How many stamps does Helen own? 342, 347, 349, 352, 357

352

Positive integer y divides into positive integer w six times with remainder r. If 0<r<32, and w/y = 6.64, what is the value of r? 32,16,8,4,2

16

If X=500×600×700, what is the remainder when X is divided by 8? 0,1,2,3,4

0

How many zeros are to the right of the last non-zero digit in the number 5^18 × 2^ 20

18

What is the largest integer value of k, such that (400!)/5^k is an integer? 100,99,96,85,80

99

if 90!/5^n is an integer, what is the largest possible value of integer n? 18,20,21,22,24

21

What is the largest integer value of n such that (30!)/4^n is an integer?

steps: break 4^(n) into prime factors. 4^n = 2^(2n) . do the division of 30/2, 30/3

answer: 13

When positive integer Q is divided by 11, the remainder is 9 What is the remainder when Q+5 is divided by 11? 1,2,3,4,14

3