If x and z are positive integers and xz = 24

[Gmat_mission]

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.

[Jay@ManhattanReview]

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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[Jeff@TargetTestPrep]

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.

We are given that xz = 24 and need to determine the value of x/z. Notice that x and z are factors of 24, that is, each has to be one of the following numbers:

1, 2, 3, 4, 6, 8, 12, and 24

Statement One Alone:

z/2 is not an integer.

We see that z is not even; however, z could still be 1 or 3. When z is 1, x is 24 and when z is 3, x is 8. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x/6 is an integer.

Since x is a multiple of 6, x can be 6, 12, or 24. When x is 6, z is 4; when x is 12, z is 2 and when x is 24, z is 1. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using our two statements, we see that x must be 24 and z must be 1. The ratio of x/z is 24/1.

Answer: C