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

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Joined: 12 Sep 2015
Posts: 4076
If x and y are integers, and x/y = 1.64, which  [#permalink]

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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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07 Jun 2018, 16:57
6
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.

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

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06 Jun 2018, 06:49
1
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, $$1.64 = \frac{164}{100}$$

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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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.

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Joined: 12 Sep 2015
Posts: 4076
Re: If x and y are integers, and x/y = 1.64, which  [#permalink]

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08 Jun 2018, 07:21
Top Contributor
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

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.

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

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12 Jun 2019, 22:49
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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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