Gmat_mission wrote:If x and z are positive integers and xz = 24 what is the ratio of x to z?
(1) z/2 is not an integer.
(2) x/6 is an integer.
[spoiler]OA=C[/spoiler].
Experts, can you show me how would you solve this DS question? I don't like the questions with ratios.
We are given that x and z are positive integers and xz = 24.
We have to get the value of x : z.
Let's factorize 24.
xz = 24
>1*24; 24*1
>2*12; 12*2
>3*8; 8*3
>4*6; 6*4
There are many possible values of x : z.
Let's take each statement one by one.
(1) z/2 is not an integer.
=> z is odd.
From the given factors given above, we have z: 1 or 3
If z = 1, x : z = 24/1 = 24
If z = 3, x : z = 8/3
No unique answer. Insufficient.
(2) x/6 is an integer.
=> x is a multiple of 6, thus x is 6, 12 or 24
There are many possible values of x : z. Insufficient.
(1) and (2) together
> x cannot be 6 as 6*4 = 24, but z cannot be an even number (4). x = 6 is ruled out.
> x cannot be 12 as 12*2 = 24, but z cannot be an even number (2). x = 12 is ruled out.
Thus, x = 24 and z = 1 (odd number)
=> x : z = 24 : 1. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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