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

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If x and y are integers, and x/y = 1.64, which  [#permalink]

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New post 06 Jun 2018, 05:58
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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

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Re: If x and y are integers, and x/y = 1.64, which  [#permalink]

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New post 07 Jun 2018, 16:57
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GMATPrepNow wrote:
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


We can simplify the equation:

x = 1.64y

100x = 164y

100x/164 = y

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
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If x and y are integers, and x/y = 1.64, which  [#permalink]

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New post 06 Jun 2018, 06:49
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GMATPrepNow wrote:
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



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.
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If x and y are integers, and x/y = 1.64, which  [#permalink]

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New post 07 Jun 2018, 17:28
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
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Re: If x and y are integers, and x/y = 1.64, which  [#permalink]

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New post 08 Jun 2018, 07:21
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GMATPrepNow wrote:
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


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
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Re: If x and y are integers, and x/y = 1.64, which  [#permalink]

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Re: If x and y are integers, and x/y = 1.64, which   [#permalink] 12 Jun 2019, 22:49
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