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QOTD # 16 If x and y are integers and which of the followin

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QOTD # 16 If x and y are integers and which of the followin [#permalink] New post 12 Sep 2016, 01:10
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Question Stats:

75% (01:23) correct 25% (01:36) wrong based on 16 sessions
If x and y are integers \(x = \frac{(2)(3)(4)(5)(7)(11)(13)}{39y}\) and which of the following could be the value of y ?

    A) 15
    B) 28
    C) 38
    D) 64
    E) 143

Practice Questions
Question: 16
Page: 180
[Reveal] Spoiler: OA

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Re: QOTD # 16 If x and y are integers and which of the followin [#permalink] New post 12 Sep 2016, 01:20
Expert's post
Explanation

The OE is a bit cumbersome and the question might be attacked in a clever way. Boil down the fraction, we ca eliminate 39 at the denominator because 3*13=39 so indeed we will end up with \(\frac{x=2*4*5*7*11}{y}\).

Now. the stem says that X is an integer and to obtain an integer we should find a number for Y that has the same prime factors of the numerator

\(x= \frac{2^3 * 5*7*11}{y}\)

Looking at the answer choice the only number that satisfies our condition is \(28 = 2^2*7\). The other answer choices lack prime numbers that satisfy our condition.

For instance, 15=3*5 but 3 is not in our numerator.

The correct option is B
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Re: QOTD # 16 If x and y are integers and which of the followin [#permalink] New post 12 Jun 2019, 07:44
Expert's post
Carcass wrote:
If x and y are integers \(x = \frac{(2)(3)(4)(5)(7)(11)(13)}{39y}\) and which of the following could be the value of y ?

    A) 15
    B) 28
    C) 38
    D) 64
    E) 143

Practice Questions
Question: 16
Page: 180


GIVEN: \(x = \frac{(2)(3)(4)(5)(7)(11)(13)}{39y}\)

Prime factorize the denominator to get: \(x = \frac{(2)(3)(4)(5)(7)(11)(13)}{(3)(13)y}\)

Simplify: \(x = \frac{(2)(4)(5)(7)(11)}{y}\)

In order for x to be an integer, y must be a divisor of \((2)(4)(5)(7)(11)\)

Scan the answer choices....

28 is a divisor of (2)(4)(5)(7)(11)

Answer: B

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Brent
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Re: QOTD # 16 If x and y are integers and which of the followin   [#permalink] 12 Jun 2019, 07:44
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