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Is P even?

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Is P even? [#permalink]

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Is P even?

(1) \(P^5\) is even.
(2) 142P – 82 is even.
[Reveal] Spoiler: OA

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Re: Is P even? [#permalink]

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New post 22 Oct 2016, 06:34
St1: P^5 is even --> P can be an even integer or an irrational number. For example P can be 5th root of 2. Insufficient.

St2: 142P – 82 is even --> P can be an even integer, odd integer or a fraction. Insufficient.

Combining St1 and St2: From St1 we know that P is not a fraction and from St2 we know that P cannot be irrational. Hence P has to be an even integer.

Answer: C

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Re: Is P even? [#permalink]

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sandeepnb wrote:
Is P even?

(1) \(P^5\) is even.
(2) 142P – 82 is even.



Statement 1 says \(P^5\) is even . P can be even or irrational number
For example , if \(P^5\) is 2 then P can be 5th root of 2 (that is , 1. something ) or can be even number ( 2, 4 etc )=> Not Sufficient

Statement 2 says 142P – 82 is even . Here P can be even or odd or fraction .
For example, P =1 (odd) then 142 (1) – 82 = 60 (even) ; P= 2 (even) then 142(2) – 82 = 202 (Even) => Not Sufficient

Both Statements combined , then P has to be Even . Hence Sufficient .
Answer is C .

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Re: Is P even? [#permalink]

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New post 29 Dec 2016, 14:39
Vyshak wrote:
St1: P^5 is even --> P can be an even integer or an irrational number. For example P can be 5th root of 2. Insufficient.

St2: 142P – 82 is even --> P can be an even integer, odd integer or a fraction. Insufficient.

Combining St1 and St2: From St1 we know that P is not a fraction and from St2 we know that P cannot be irrational. Hence P has to be an even integer.

Answer: C


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Re: Is P even? [#permalink]

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New post 21 Nov 2017, 14:49
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Hi All,

We're asked if P is EVEN. This is a YES/NO question. We can solve it by TESTing VALUES. To start though, we have not been told ANYTHING about P, so it could be positive, negative, 0, an integer, a fraction, etc.

1) P^5 is EVEN

This tells us that P^5 could be any even number (re: -2, 0, 2, 4, 6, etc.)

IF....
P^5 = 32, then P = 2 and the answer to the question is YES.
P^5 = 2, then P = a non-integer and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) 142P - 82 = Even

With the equation in Fact 2, we're subtracting an even number (82) from 142P and getting an even number, thus 142P is EVEN.

IF....
142P = 142, then P = 1 and the answer to the question is NO.
142P = 284, then P = 2 and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know:
P^5 is even
142P is even

The only values that fit both Facts are even integers, so the answer to the question is ALWAYS YES.

Final Answer:
[Reveal] Spoiler:
C


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Re: Is P even?   [#permalink] 21 Nov 2017, 14:49
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