Test: Factors And Multiples- 3 - GRE MCQ

In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected? 

Does the integer p have an odd number of distinct factors?
1) p = q^2, where q is a nonzero integer
2) p = 2n + 1, where n is a nonzero integer

If n is a non-negative integer such that 12ⁿ is a divisor of 3,176,793, what is the value of n¹² – 12ⁿ ? 

For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?

If P, Q, R, and S are positive integers, and P/Q = R/S, is R divisible by 5?

1) P is divisible by 140
2) Q = 7^x, where x is a positive integer 

What is the positive integer n??

1) The sum of all of the positive factors of n that are less than n is equal to n

2) n < 30 ?

How many numbers that are not divisible by 6 divide evenly into 264,600? 

Does the integer k have a factor p such that 1 < p < k?

1) K > 4!

2) 13! + 2 ≤  k ≤ 13! + 13

If n is a positive integer less than 200 and 14n/60 is an integer, then n has how many different positive prime factors? 

The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?

1) xz is even

2) y is even ?

How many multiples of 4 are there between 12 and 96, inclusive?

10²⁵ – 560 is divisible by all of the following EXCEPT: