If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer.
(2) 28x is an integer.

Target question: Is it possible to write x as a terminating decimal?

This is a great candidate for rephrasing the target question. Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Given: 0 < x < 1
Let's say that x = a/b where the fraction a/b is written in simplest terms.
There's a nice rule that says something like,
If a/b results in a terminating decimal, then the denominator, b, MUST be the product of 2's and 5's only!
So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.

REPHRASED target question: Is b the product of 2's and 5's only?

Statement 1: 24x is an integer.
x = a/b. So, if 24x is an integer, b must be a divisor of 24.
So, b could equal 2, 3, 4, 6, 8, 12, or 24 [aside: I omitted 1 as a possibility, since we're told that 0 < x < 1]
So, for example, b could equal 8, in which case b IS the product of 2's and 5's only
Or b could equal 3, in which case b is NOT the product of 2's and 5's only
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: 28x is an integer.
x = a/b. So, if 28x is an integer, b must be a divisor of 28.
So, b could equal 2, 4, 7, 14, or 28
So, for example, b could equal 4, in which case b IS the product of 2's and 5's only
Or b could equal 7, in which case b is NOT the product of 2's and 5's only
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 says that b could equal 2, 3, 4, 6, 8, 12, or 24
Statement 2 says that b could equal 2, 4, 7, 14, or 28
So, we can conclude that b = 2 or 4
Both of these possible b values ARE the product of 2's and 5's only.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent