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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]  12 Sep 2016, 01:10
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Question Stats:

77% (01:20) correct 22% (02:26) wrong based on 62 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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Founder
Joined: 18 Apr 2015
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Kudos [?]: 2810 [1] , given: 10653

Re: QOTD # 16 If x and y are integers and which of the followin [#permalink]  12 Sep 2016, 01:20
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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]  12 Jun 2019, 07:44
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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 $$(2)(4)(5)(7)(11)$$

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

Cheers,
Brent
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Re: QOTD # 16 If x and y are integers and which of the followin [#permalink]  13 Sep 2019, 04:11
Factor out the 3 and 13 and you're left with 2 4 5 7 11. Write that as a row. Then write the row of answer choices below it. Look what answers can be formed by multiplying any of the factors from the top row. The only possibility is 28.

2 4 5 7 11
15 28 38 69 143

Ex. any of the factors multiply to get 15? No.
4*27 = 28, so yes for 28
the rest are no.
Re: QOTD # 16 If x and y are integers and which of the followin   [#permalink] 13 Sep 2019, 04:11
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