If x and y are integers, and x/y = 1.64, which

x/y = 1.64
x/y = 1 + .64
x/y = 1 + 64/100
x/y = 100/100 + 64/100
x/y = 164/100 = 41/25

X has to be a multiple of 41 or 41x.
Scanning the answer choices and realizing that the units digit of 41 is 1, you can quickly tell that multiplying 41*8 will give a value greater than 288. 288 can't be a multiple of 41.

Answer E

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

BrentGMATPrepNow, did you try to divide all the options by 41? Or is there a faster way to do it? We could prime factorize the options, but it wouldn't be necessarily much faster.

Prime factorization or long division works.
That said, since this is one of those questions that require us to check/test each answer choice, I SHOULD HAVE checked the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

Cheers,
Brent

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