If x and y are integers, and x/y = 1.64, which of the following CANNOT be a value of x?

[BTGModeratorVI]

If x and y are integers, and x/y = 1.64, which of the following CANNOT be a value of x?

A) -656
B) -82
C) 123
D) 205
E) 288

Answer: D
Source: GMAT prep now

[Brent@GMATPrepNow]

If x and y are integers, and x/y = 1.64, which of the following CANNOT be a value of x?

A) -656
B) -82
C) 123
D) 205
E) 288

Answer: D
Source: GMAT prep now

Given: x/y = 1.64
Rewrite as: x/y = 164/100
Simplify: x/y = 41/25
So, it's possible that x = 41 and y = 25

We can also create infinitely many fractions that are EQUIVALENT to 41/25
For example, we can take 41/25 and multiply top and bottom by 2 to get: 82/50
So, it's possible that x = 82 and y = 50

Likewise, we can take 41/25 and multiply top and bottom by 3 to get: 123/75
So, it's possible that x = 123 and y = 75

In general, we can see that x can be ANY multiple of 41

Check the answer choices....
A) -656 IS a multiple of 41. So, x COULD equal -656. ELIMINATE A
B) -82 IS a multiple of 41. So, x COULD equal -82. ELIMINATE B
C) 123 IS a multiple of 41. ELIMINATE C
D) 205 IS a multiple of 41. ELIMINATE D
E) 288 is NOT a multiple of 41.

Answer: E

Cheers,
Brent