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Is x a multiple of y?

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Source: — Data Sufficiency |
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by Frankenstein » Thu Jun 16, 2011 10:31 pm
hi,
From(1): 3y^2+7y = x
So, x = y(3y+7) = y*(integer)
So, x is multiple of y
Sufficient

From(2): x(x-1) = ky
Not sufficient

Hence, A
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by Anurag@Gurome » Thu Jun 16, 2011 11:35 pm
Ahmed MS wrote:If x and y are integers greater than 1, is x a multiple of y?

a. 3y² + 7y = x
b. x² - x is a multiple of y
Statement 1: x = y(3y + 7) = y*(Some integer)
Therefore, x is a multiple of y

Sufficient

Statement 2: x(x - 1) is a multiple of y.
Therefore, either x or (x - 1) or none of them is multiple of y.

Not sufficient

The correct answer is A.
Last edited by Anurag@Gurome on Fri Jun 17, 2011 1:13 am, edited 2 times in total.
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by kevincanspain » Thu Jun 16, 2011 11:44 pm
It is important to note that x and x-1 share no prime factors. In other words, the only factor they have in common is 1. Thus either x or x-1 is a multiple of y, but it is impossible for both of them to be a multiple of y!
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by Frankenstein » Fri Jun 17, 2011 1:11 am
kevincanspain wrote:It is important to note that x and x-1 share no prime factors. In other words, the only factor they have in common is 1. Thus either x or x-1 is a multiple of y, but it is impossible for both of them to be a multiple of y!
Hi,
Not necessarily.
If x= 10 and y=6
x(x-1) = 90 is multiple of 6 but neither x nor (x-1) is multiple of y.
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by kevincanspain » Fri Jun 17, 2011 2:50 am
Right! Either x or x-1 or neither of these two expressions is a multiple of y
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by amit2k9 » Fri Jun 17, 2011 3:32 am
a y(3y+7) = x 3y+7 = constant meaning y*k = x sufficient.

b x(x-1)/y = integer (as it is multiple)

(x/y)* (x-1) can be analysed as x=y=2 or x=3,y=2. not sufficient.

thus A it clean.
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by [email protected] » Mon Jan 12, 2015 5:31 am
Anurag@Gurome wrote:
Ahmed MS wrote:If x and y are integers greater than 1, is x a multiple of y?

a. 3y² + 7y = x
b. x² - x is a multiple of y
Statement 1: x = y(3y + 7) = y*(Some integer)
Therefore, x is a multiple of y

Sufficient

Statement 2: x(x - 1) is a multiple of y.
Therefore, either x or (x - 1) or none of them is multiple of y.

Not sufficient

The correct answer is A.
What's the logic behind none of them is a multiple of y?
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by GMATGuruNY » Mon Jan 12, 2015 5:42 am
[email protected] wrote:
Anurag@Gurome wrote:
Ahmed MS wrote:If x and y are integers greater than 1, is x a multiple of y?

a. 3y² + 7y = x
b. x² - x is a multiple of y
Statement 1: x = y(3y + 7) = y*(Some integer)
Therefore, x is a multiple of y

Sufficient

Statement 2: x(x - 1) is a multiple of y.
Therefore, either x or (x - 1) or none of them is multiple of y.

Not sufficient

The correct answer is A.
What's the logic behind none of them is a multiple of y?
If y is equal to the product of a factor of x and a factor of x-1, then (x)(x-1) will be a multiple of y, but neither x nor x-1 on its own will be a multiple of y.

To illustrate:
Let x=9, implying that x-1 = 8 and that (x)(x-1) = 9*8 = 72.
If y is equal to the product of 3 (a factor of x) and 2 (a factor of x-1), then y = 3*2 = 6.
In this case:
(x)(x-1) = 72 is a multiple of y=6, but neither x=9 nor x-1=8 on its own is a multiple of y=6.
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by [email protected] » Mon Jan 12, 2015 11:32 am
Hi All,

This DS question can be solved by TESTing VALUES.

We're told that X and Y are INTEGERS that are both > 1. We're asked if X is a multiple of Y. This is a YES/NO question.

Fact 1: 3(Y^2) + 7Y = X

IF....
Y = 2, then X = 26 and the answer to the question is YES.
Y = 3, then X = 48 and the answer to the question is YES.
Y = 4, then X = 76 and the answer to the question is YES.
Y = 5, then X = 110 and the answer to the question is YES.
Etc.
The answer is ALWAYS YES
Fact 1 is SUFFICIENT

Fact 2: X^2 - X is a multiple of Y

IF...
X = 2, then Y would have to be = 2 and the answer to the question is YES
X = 3, then Y could be = 2, 3 OR 6. IF Y = 2, then the answer to the question is NO
Fact 2 is INSUFFICIENT

Final Answer: A

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