Question: If w, x, y, and z are integers such that 1 < w < x < y < z and wxyz = 462, then z =?

1. 7
2. 11
3. 14
4. 21
5. 42

Answer:
Solution with Explanation:
Approach Solution (1):

Say (C) is true option, then z = 14 meaning that 14wxyz = 462. That is, 462 must be divisible by 14. Let’s factorize 462: 462 = 231 * 2 = 21 * 11 * 2
So the prime factors of 432 are 2, 3, 7, 11 meaning that it is divisible by 14
But since w, x, y, z must all be factors of 462, z = 14 means that we only have two numbers (3 and 11) to divide amongst three variables (w, x, and y)
So, z = 14 is impossible
Moreover, now that we have seen that the answer has to do with factoring, and we have seen that 462 has exactly 4 prime factors, then we know that w, x, y, z must be these 4 factors, in order
So z is the largest prime factor of 462, that is 11

Correct Option: B

Approach Solution (2):

We need to find out the value of z. we can do it by prime factorization as follows:
It is given:
wxyz = 462
462 = 2 * 3 * 7 * 11
we also know that 1 < w < x < y < z
So z is the biggest among wxyz. Thus, z must be 11

Correct Option: B

Approach Solution (3):

wxyz = 462 and 1 < w < x < y < z
Factors of 462 = 2 * 3 * 7 * 11
So, z = 11

Correct Option: B

“If w, x, y, and z are integers such that 1 < w < x < y < z and wxyz = 462, then z =?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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