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Senior Manager  P
Joined: 16 Oct 2016
Posts: 258
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38 GMAT 2: 680 Q48 V35 GRE 1: Q160 V163
GPA: 3.05
WE: Pharmaceuticals (Health Care)

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7 00:00

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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Chasing the dragon
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4329
Re: Is x = y?  [#permalink]

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5
Top Contributor
1
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

Cheers,
Brent
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##### General Discussion
Manager  G
Joined: 02 Sep 2018
Posts: 117
Re: Is x = y?  [#permalink]

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Because 0! is 1 and 1^0=1 ,x and y could be 1 0r 0.So correct answer is E
Senior Manager  P
Joined: 16 Oct 2016
Posts: 258
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38 GMAT 2: 680 Q48 V35 GRE 1: Q160 V163
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Re: Is x = y?  [#permalink]

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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

Cheers,
Brent

Thanks Brent!!!
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Chasing the dragon
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Joined: 27 Jul 2018
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WE: Engineering (Manufacturing)
Re: Is x = y?  [#permalink]

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1
Great Qs.

Walked right in to the trap Non-Human User Joined: 09 Sep 2013
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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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