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# If P and Q are positive integers, is the product 3P^Q divisible by 2?

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Math Expert
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If P and Q are positive integers, is the product 3P^Q divisible by 2? [#permalink]

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30 Nov 2015, 04:22
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If P and Q are positive integers, is the product 3P^Q divisible by 2?

(1) 6Q^3 + 2 is an even number
(2) P + 8Q^2 is a prime number
[Reveal] Spoiler: OA

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Re: If P and Q are positive integers, is the product 3P^Q divisible by 2? [#permalink]

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30 Nov 2015, 04:38
3P^Q divisible by 2 if P is even because
3 is odd and does not play a role in making the term even and Q does not effect the even odd nature of the term.
(1) 6Q^3 + 2 is an even number
No information about P is given
Not sufficient.

(2) P + 8Q^2 is a prime number
All prime numbers except 2 are odd .
8Q^2 is even .
Therefore P must be odd .

Sufficient

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Re: If P and Q are positive integers, is the product 3P^Q divisible by 2? [#permalink]

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30 Nov 2015, 08:30
is 3*P^Q even?

St1: 6Q^3 + even = even --> 6Q^3 = even
Q^3 can be even or odd
No information is given about P
Statement 1 alone is not sufficient

St2: P + 8Q^2 = odd
8Q^2 is even
P = odd - even = odd
Since P is odd, 3P^Q is odd
Statement 2 is sufficient

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Re: If P and Q are positive integers, is the product 3P^Q divisible by 2? [#permalink]

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30 Nov 2015, 19:02
1-> We cannot say anything, we don't have the value of P

2-> P + 8Q^2 is a prime number
This means that the number has to be odd
8Qˆ2 is always even.
Therefore P has to be ODD.

Now if we look at the first equation 3P^Q
It doesn't matter how many times we are going to multiple the P, its always going to be Odd:
Odd*Odd=Odd
It means that we cannot divide it by 2

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Re: If P and Q are positive integers, is the product 3P^Q divisible by 2? [#permalink]

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01 Dec 2015, 04:19
Here P and Q are positive integers, and we are asked that whether $$3P^Q$$ is even or not?

Now we are basically concerned with P i.e. is P even or not?
Because 3 multiplied by even is even and any power to even no. gives you even result.

Statement 1 says: $$6Q^3+2$$ is even, but we do not know anything about P.

therefore insufficient.

Statement 2 says : $$P+8Q^2$$ is prime.
Now this Prime must be greater than 2, because both P and Q are Positive Integers.
Now, rest all Primes are odd. Therefore,

Odd-$$8Q^2$$ will give odd result. Therefore P is Odd.

Therefore sufficient.

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Re: If P and Q are positive integers, is the product 3P^Q divisible by 2? [#permalink]

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03 Dec 2015, 08:33
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If P and Q are positive integers, is the product 3P^Q divisible by 2?

(1) 6Q^3 + 2 is an even number
(2) P + 8Q^2 is a prime number

The question is eventually asking whether P is even as 3 cannot be divided by 2.
From condition 2, p+8Q^2 is told to be prime and this means p is odd, so this answers the question 'no' and is therefore sufficient.
From condition 1, the question is asking whether P is even so this is irrelevant to the question, and insufficient.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If P and Q are positive integers, is the product 3P^Q divisible by 2? [#permalink]

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18 Nov 2017, 09:16
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Re: If P and Q are positive integers, is the product 3P^Q divisible by 2?   [#permalink] 18 Nov 2017, 09:16
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# If P and Q are positive integers, is the product 3P^Q divisible by 2?

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