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Is x = y?

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Is x = y?  [#permalink]

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New post 06 Dec 2018, 05:40
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A
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E

Difficulty:

  65% (hard)

Question Stats:

41% (01:10) correct 59% (01:08) wrong based on 76 sessions

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if X and Y are integers, is X = Y?

A. X! = Y!

B. \(X^Y\) = X

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Re: Is x = y?  [#permalink]

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New post 06 Dec 2018, 06:42
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fitzpratik wrote:
if X and Y are integers, is X = Y?

A. X! = Y!

B. \(X^Y\) = X


Target question: Is X = Y?

Given: X and Y are integers

Statement 1: X! = Y!
There are a few possible scenarios that satisfy statement 1. Here are two:
Case a: X = 1 and Y = 1. In this case, the answer to the target question is YES X DOES equal Y
Case b: X = 0 and Y = 1. This works because 0! = 1 = 1!. In this case, the answer to the target question is NO X does NOT equal Y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: X^Y = X
There are several possible scenarios that satisfy statement 2. Here are two:
Case a: X = 1 and Y = 1. 1^1 = 1, perfect. In this case, the answer to the target question is YES X DOES equal Y
Case b: X = 0 and Y = 1. 0^1 = 0, perfect. In this case, the answer to the target question is NO X does NOT equal Y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: X = 1 and Y = 1. 1^1 = 1, perfect. In this case, the answer to the target question is YES X DOES equal Y
Case b: X = 0 and Y = 1. 0^1 = 0, perfect. In this case, the answer to the target question is NO X does NOT equal Y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Re: Is x = y?  [#permalink]

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New post 06 Dec 2018, 06:35
Because 0! is 1 and 1^0=1 ,x and y could be 1 0r 0.So correct answer is E
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Re: Is x = y?  [#permalink]

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New post 06 Dec 2018, 07:20
GMATPrepNow wrote:
fitzpratik wrote:
if X and Y are integers, is X = Y?

A. X! = Y!

B. \(X^Y\) = X


Target question: Is X = Y?

Given: X and Y are integers

Statement 1: X! = Y!
There are a few possible scenarios that satisfy statement 1. Here are two:
Case a: X = 1 and Y = 1. In this case, the answer to the target question is YES X DOES equal Y
Case b: X = 0 and Y = 1. This works because 0! = 1 = 1!. In this case, the answer to the target question is NO X does NOT equal Y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: X^Y = X
There are several possible scenarios that satisfy statement 2. Here are two:
Case a: X = 1 and Y = 1. 1^1 = 1, perfect. In this case, the answer to the target question is YES X DOES equal Y
Case b: X = 0 and Y = 1. 0^1 = 0, perfect. In this case, the answer to the target question is NO X does NOT equal Y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: X = 1 and Y = 1. 1^1 = 1, perfect. In this case, the answer to the target question is YES X DOES equal Y
Case b: X = 0 and Y = 1. 0^1 = 0, perfect. In this case, the answer to the target question is NO X does NOT equal Y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent


Thanks Brent!!!
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Re: Is x = y?  [#permalink]

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New post 06 Dec 2018, 21:06
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Great Qs.

Walked right in to the trap :x
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Re: Is x = y?  [#permalink]

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Re: Is x = y?   [#permalink] 09 Feb 2020, 06:55
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