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655-705 (Hard)|   Exponents|      
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fitzpratik
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If x and y are integers, is x = y ? (1) x! = y! (2) x^y = x 06 Dec 2018, 06:40
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

44% (01:20) correct 56% (01:08) wrong based on 170 sessions

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If x and y are integers, is x = y ?

(1) x! = y!
(2) x^y = x
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E
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BrentGMATPrepNow
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If x and y are integers, is x = y ? (1) x! = y! (2) x^y = x 06 Dec 2018, 07:42
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fitzpratik
if X and Y are integers, is X = Y?

A. X! = Y!

B. \(X^Y\) = X
Show more

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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If x and y are integers, is x = y ? (1) x! = y! (2) x^y = x 06 Dec 2018, 07:35
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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
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If x and y are integers, is x = y ? (1) x! = y! (2) x^y = x 06 Dec 2018, 08:20
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fitzpratik
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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Thanks Brent!!!
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If x and y are integers, is x = y ? (1) x! = y! (2) x^y = x 06 Dec 2018, 22:06
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Great Qs.

Walked right in to the trap :x
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If x and y are integers, is x = y ? (1) x! = y! (2) x^y = x 22 Dec 2021, 11:23
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fitzpratik
if X and Y are integers, is X = Y?

A. X! = Y!

B. \(X^Y\) = X
Show more


1) x can be 0 or 1 similarly y
0!=1! You get a NO
1!=1! You get a Yes
Clearly insufficient

2) possible only when Y=1 how? Log x base x is 1
Y =1 and X can be any integer
Hence insufficient

Combining both
Y =1 substituting in first statement

X! =1 so x can be 0 or 1

Hence not sufficient

Option E

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If x and y are integers, is x = y ? (1) x! = y! (2) x^y = x 03 Apr 2023, 06:48
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