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# If x and z are positive integers and xz = 24 what is the ratio of x to

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
If x and z are positive integers and xz = 24 what is the ratio of x to  [#permalink]

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02 Jan 2018, 23:56
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35% (medium)

Question Stats:

81% (01:32) correct 19% (00:55) wrong based on 40 sessions

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If x and z are positive integers and xz = 24 what is the ratio of x to z?

(1) x/6 is an integer.
(2) z/2 is an integer

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Re: If x and z are positive integers and xz = 24 what is the ratio of x to  [#permalink]

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03 Jan 2018, 00:15
Bunuel wrote:
If x and z are positive integers and xz = 24 what is the ratio of x to z?

(1) x/6 is an integer.
(2) z/2 is an integer

(1) x is a multiple of 6. Eg, x=6, then z=4, ratio is 6:4 or 3:2. But we could also have x=12, z=2, then ratio is 12:2 or 6:1. So Insufficient.

(2) z is even. We could have z=4 and x=6 OR we could have z=2 and x=12. These two cases will give two different ratios. So Insufficient.

Combining the two statements, we could still have two different ratios as explained in above examples. So Insufficient.

Hence E answer
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If x and z are positive integers and xz = 24 what is the ratio of x to  [#permalink]

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03 Jan 2018, 02:34
Bunuel wrote:
If x and z are positive integers and xz = 24 what is the ratio of x to z?

(1) x/6 is an integer.
(2) z/2 is an integer

Given = x*z = 24

Question = x/z

We can do it by factorizing 24,

24 * 1
12 * 2
8 * 3
6 * 4

Statement 1: For x/6 = integer , then x can take three values 24, 12, 6. No info about z = Insufficient

Statement 2: For z/2 = integer, then z can take six values 24, 12, 8, 6, 4, 2. No info about x = Insufficient

Combining 1 & 2 will give us various values of x and z, and different x/z ratios. So combining also Insufficient

(E)
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If x and z are positive integers and xz = 24 what is the ratio of x to   [#permalink] 03 Jan 2018, 02:34
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# If x and z are positive integers and xz = 24 what is the ratio of x to

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