I am completely and utterly confused by this question.
If X and Y are positive integers is Y odd?
1. (Y+2)!/X! is odd integer
2. (Y+2)!/X! is greater than 2
Answer:C
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Data Sufficiency From Adv Quant
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rijul007
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Statement 1avada wrote:I am completely and utterly confused by this question.
If X and Y are positive integers is Y odd?
1. (Y+2)!/X! is odd integer
2. (Y+2)!/X! is greater than 2
Answer:C
1. (Y+2)!/X! is odd integer
Check when this can be possible--
Only when Y+2 = X+1 and Y+2 is odd
If Y+2 is odd, then Y is odd too.
Sufficient
Statement 2
2. (Y+2)!/X! is greater than 2
Case 1:
Y = 3
X = 2
(Y+2)!/X! = 5!/2! (greater than 2)
Y is odd
Case 2:
Y = 4
X = 2
(Y+2)!/X! = 6!/2! (greater than 2)
Y is even
Not sufficient
Option A
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adthedaddy
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Here, Statement 1 can also be proved insufficientIf X and Y are positive integers is Y odd?
1. (Y+2)!/X! is odd integer
If (Y+2)!/X! is Odd then following two possibilities exist -
--> Y=odd, X=Y+1
Then, (Y+2)!/(Y+1) = (Y+2)
As Y is odd, Y+2 is also odd
--> (Y+2)!/X! = 1
(Y+2)! = X!
This can statement can be valid even if Y is even.
e.g. if Y=2, X=4 then (Y+2)!/X! = 1 = odd
Thus, statement 1 is insufficient.
Statement 2 is already proved insufficient by rijul007.
Now, when we combine both the statements,
then (Y+2)!/X! > 2
Thus, the possibility that (Y+2)!/X! = 1 can be ignored.
Only the other possibility assumed above that Y=odd exists.
Thus Y=odd
Ans: Option C
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rijul007
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Thanks for pointing that out!adthedaddy wrote:Here, Statement 1 can also be proved insufficientIf X and Y are positive integers is Y odd?
1. (Y+2)!/X! is odd integer
If (Y+2)!/X! is Odd then following two possibilities exist -
--> Y=odd, X=Y+1
Then, (Y+2)!/(Y+1) = (Y+2)
As Y is odd, Y+2 is also odd
--> (Y+2)!/X! = 1
(Y+2)! = X!
This can statement can be valid even if Y is even.
e.g. if Y=2, X=4 then (Y+2)!/X! = 1 = odd
Thus, statement 1 is insufficient.
Statement 2 is already proved insufficient by rijul007.
Now, when we combine both the statements,
then (Y+2)!/X! > 2
Thus, the possibility that (Y+2)!/X! = 1 can be ignored.
Only the other possibility assumed above that Y=odd exists.
Thus Y=odd
Ans: Option C
