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GRE Practice - Quantitative Reasoning - Set 12

  1. x, y are integers and x2<36 , 3y2 <17. What is the number of unique values of the product of xy?

Answer: A or C

Solution: This is a tricky one.
x2<36 and 3y2 <17
If you are considering only positive values for x and y you will end up with option A or C as your answer.
But x = -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 (11 values)
And y = -2, -1, 0, 1, 2 (5 values)
If you multiply you will get 11 x 5 = 55 option E but the question says UNIQUE values
Go step by step.
Multiply y = -2 with all 11 values of x and you will get 11 unique products
Multiply y = -1 with all 11 values of x and you will get only 6 additional unique products
For all other values of y you will not get any more unique products
Total: 11+6 = 17

  1. If a is divisible by 12 and b is divisible by 8, then which of the following must be true? Select all that apply
  1. ab is a multiple of 48
  2. 64 is a factor of ab
  3. ab is divisible by 16
  4. 36 is a factor of ab

Answer: A and C

Solution:
a = 12x and b = 8y
ab = 96xy
A: irrespective of the value of xy ab is divisible by 96 and hence 48
B: ab is equal to 96xy which is 32 x 3 times xy so while it is definitely divisible by 32 it’s divisibility by 64 depends on the values of x and y
C: ab is equal to 96xy which is 16 x 6 times xy so it is definitely divisible by 16
D: ab is equal to 96xy which is 8 x 6 x2 times xy so it is divisible by 36 only if xy provides another 3.

  1. When 25! is divided by 5n there is no remainder What is the greatest integer value of n?

Solution: 24! = 1 x 2 x 3 x ….x 23 x 24
The multiples of 5 in the product are 5, 10, 15, 20 and 25
Each of them produce one 5 except 25 which provides 2 5s
So there are 6 5s, n = 6

  1. N is divisible by 18
Quantity A
The number of unique factors of N

Quantity B
5

  1. if Quantity A is greater
  2. if Quantity B is greater
  3. if the two quantities are equal
  4. if the relationship between the two quantities cannot be determined

Solution: Even though we don’t know the number N we know it’s divisible by 18. SO, N = 18k where k = 1,2,3…..
For the least possible value, N = 18
18 has 6 factors {1, 2, 3, 6, 9, 18}
For larger values N will have more factors so in all cases quantity A is greater.

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Q. If the function f(x) is defined as f(x) = 3(x + 1) + 7, then f(a − 2) =

  1. 3a + 5
  2. 3a – 9
  3. 3a + 10
  4. 3a – 4
  5. 3a + 4
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