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x is a factor of y

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Source: — Data Sufficiency |

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by [email protected] » Tue May 19, 2015 9:03 am
Hi j_shreyans,

This question is built on a couple of Number Properties, but can also be solved by TESTing VALUES.

We're told that X and Y are POSITIVE INTEGERS. We're asked if X is a factor of Y. This is a YES/NO question.

Fact 1: X = Y^2

IF....
Y = 1
X = 1
1 is a factor of 1 and the answer to the question is YES

IF....
Y = 2
X = 4
4 is NOT a factor of 2 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: Y > 1

This tells us NOTHING about X, so we cannot answer the question.
Fact 2 is INSUFFICIENT

Combined, we know...
X = Y^2
Y > 1

Given that Y > 1, X MUST be greater than Y (since X = Y^2). With these restrictions, X will NEVER be a factor of Y so the answer to the question is ALWAYS NO.
Combined, SUFFICIENT

Final Answer: C

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Rich
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by prachi18oct » Wed May 20, 2015 10:03 am
From (1)
y^2 = x => y/x = 1/y
Now if x is a factor of y, RHS i.e 1/y has to be an integer.
This can be possible only if y = 1 = > x = 1
For other values, this will not hold true.
INSUFFICIENT

From (2), clearly INSUFFICIENT

Combining, we know that for all y not equal to 1, x is not a factor. Hence definite NO. SUFFICIENT.
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by Brent@GMATPrepNow » Wed May 20, 2015 10:21 am
j_shreyans wrote:If x and y are positive integers, is x a factor of y?

1) x = y²
2) y > 1
Target question: Is x a factor of y?

Given: x and y are POSITIVE INTEGERS

Statement 1: x = y²
This statement seems to SUGGEST that x is greater than 1 (since x and y are POSITIVE INTEGERS).
If x is greater than y, x cannot by a factor of y. So, it would seem, that this statement is sufficient.
HOWEVER, there is one possible value for y that we need to consider and that's y = 1
case a) If y = 1, then x = 1, in which case x IS a factor of y.

However, if y equals any other positive integer other than 1, then we have...
case b) If y = any other positive integer other than 1, then x is GREATER THAN y, which means x is NOT a factor of y.

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y > 1
Since there's no information about x, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 was insufficient, because there are two possible cases that reveal DIFFERENT answers to the target question:
case a) If y = 1, then x = 1, in which case x IS a factor of y.
case b) If y = any other positive integer other than 1, then x is GREATER THAN y, which means x is NOT a factor of y.

Statement 2 RULES OUT case a, which means case b is the ONLY POSSIBLE case.
This means that we can conclude that x is NOT a factor of y

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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