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T1 and T2 are two sets containing integers only. If an integer X is

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T1 and T2 are two sets containing integers only. If an integer X is  [#permalink]

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New post 15 Mar 2018, 23:37
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Question Stats:

51% (01:21) correct 49% (01:17) wrong based on 56 sessions

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T1 and T2 are two sets containing integers only. If an integer X is randomly selected from T1 and another integer Y is randomly selected from T2, what is the probability that Y^X (Y raised to the power X) is even?

(1) T1 = {-16, -4, 0, 6, 12}

(2) T2 = {-17, -15, -11, 19, 25}
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Re: T1 and T2 are two sets containing integers only. If an integer X is  [#permalink]

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New post 17 Mar 2018, 13:59
Odd^Odd is always Odd. and Odd^Even is also always odd. So We just need to know if Y in Y^X is even or ODD. Since all the numbers in Y are odd. The answer will be NO.
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T1 and T2 are two sets containing integers only. If an integer X is  [#permalink]

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New post 21 Mar 2018, 01:04

Solution:



\(X\)-> a number from the set T1.
\(Y\)-> a number from the set T2.

\(Y^X\) is even only when \(Y\) is even and \(X\) is positive.

Thus, we need to find the probability of selecting even values of \(Y\).

Statement-1 is “T1 = {-16, -4, 0, 6, 12}”.

Since only \(X\) is selected from \(T1\), we cannot find the possible values of \(Y\) from this statement.

Thus, Statement 1 alone is not sufficient to answer the question.

Statement-2 is “T2 = {-17, -15, -11, 19, 25}”.

Since \(T2\) does not have any even number. Hence, there are no possible values of \(Y\).

Thus, the probability that \(Y^X\) is even is \(0\).

Statement 2 alone is sufficient to answer the question.

Answer: B
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