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

Question

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

ScottTargetTestPrep · Accepted Answer

We can simplify the equation:

x = 1.64y

100x = 164y

100x/164 = y

25x/41 = y

In order for y to be an integer, we see that x must be a multiple of 41, and only 288 is not a multiple of 41.

Answer: E

pushpitkc · Answer

We are given that x and y are integers. Also,  1.64 = \frac{164}{100}

Evaluating answer options

A.  -656 = 164 * -4  ->  \frac{-656}{-400} = 1.64 
B.  -82 = 164 * -\frac{1}{2}  ->  \frac{-82}{-50} = 1.64 
C.  123 = 164 * \frac{3}{4}  ->  \frac{492}{300} = 1.64 
D.  205 = 164 * \frac{5}{4}  ->  \frac{820}{500} = 1.64 
E. The number  288  CANNOT be a value of x.  (Option E)

If we were to prime-factorize 164, we will get  2^2 * 41 . So the number x must be divisible by 41.
Among the answer options, Only Option E( 288 = 2^5 * 3^2 ) does not prime-factorize to yield a 41.

Funsho84 · Answer

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

BrentGMATPrepNow · Answer

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

newdimension · Answer

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.

BrentGMATPrepNow · Answer

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

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