If w, x, y and z are integers such that 1

Question

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

A. 7
B. 11
C. 14
D. 21
E. 42

D3N0 · Answer

Ans: B

wxyz=462 and 1 < w < x < y < z
factors of 462 = 2*3*7*11 so z=11

Ans: B

DavidTutorexamPAL · Answer

If we're not sure where to start, then since the answers are right in front of us we'll just use them.
This is an Alternative approach.

Say (C) were true. Then z = 14 meaning that 14wxy = 462. That is, 462 must be divisible by 14.
Let's factorize 462: 462 = 231 * 2 = 21*11*2 = 7*3*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've seen that the answer has to do with factoring, and we've 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.

(B) is our answer.

nigina93 · Answer

The answer is B. Lets do prime factorization to realize of what factors 462 consists. 462=2*3*7*11, since z is the largest number, 11 or B is the answer. Hope it helps

KSBGC · Answer

we need to find out the value of z. we can do it by prime factorization as follows:

it's given ,

wxyz = 462

462= 2*3*7*11

we also know that 1<w<x<y<z
So, z is biggest among wxyz. Thus , z must be 11.

The best answer is B.

LevanKhukhunashvili · Answer

Factor out 462

462=2*3*7*11 
As z is the biggest integer we can truly assume that z=11

Asn: B

JeffTargetTestPrep · Answer

462 = 2 x 231 = 2 x 11 x 21 = 2 x 3 x 7 x 11; thus, z = 11.

Answer: B

bumpbot · Answer

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If w, x, y and z are integers such that 1 < w < x < y < z and wxyz = 4

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