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P is an integer divisible by 4 and Q is an integer divisible by 3. Whi

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Bunuel
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P is an integer divisible by 4 and Q is an integer divisible by 3. Whi [#permalink] New post   01 Jul 2016, 04:06
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P is an integer divisible by 4 and Q is an integer divisible by 3. Which of the following must be odd?

A. Q(P+1)
B. 2P+3Q
C. P*Q^2
D. P^2*Q^3
E. None of the above.
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E
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Re: P is an integer divisible by 4 and Q is an integer divisible by 3. Whi [#permalink] New post   01 Jul 2016, 04:39
Given: P is an integer divisible by 4 and Q is an integer divisible by 3

A. Q(P+1)

Let us take Q=6 (divisible by 3) and P=4 (divisible by 4). Q(P+1) is even.

False.

B. 2P+3Q

Let us again take Q=6 (divisible by 3) and P=4 (divisible by 4). 2P+3Q is even.

False.

C. P*Q^2

Let us again take Q=6 (divisible by 3) and P=4 (divisible by 4). P*Q^2 is even.

False.

D. P^2*Q^3

Let us again take Q=6 (divisible by 3) and P=4 (divisible by 4). P^2*Q^3 is even.

False.

E. None of the above.

E is the answer

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Re: P is an integer divisible by 4 and Q is an integer divisible by 3. Whi [#permalink] New post   28 May 2017, 17:35
P is an integer divisible by 4 and Q is an integer divisible by 3. Which of the following must be odd?

A. Q(P+1)
B. 2P+3Q
C. P*Q^2
D. P^2*Q^3
E. None of the above.

Solution:

Let us take P & Q to be 12 each, since both numbers are divided by 4 & 3 respectively.

A. Q(P+1)
12*13=even

B. 2P+3Q
24*36=even

C. P*Q^2
(12*12)^2= 144^2= even

D. P^2*Q^3
12^2*12^3 = even

Hence, ANSWER E.

Concept used: When multiplied by EVEN numbers, result will ALWAYS be even. Also when an EVEN number is raised to any power, result will ALWAYS be even.
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Re: P is an integer divisible by 4 and Q is an integer divisible by 3. Whi [#permalink] New post   28 May 2017, 21:58
P will Always be even, Q could be either odd or even.

Q(P+1) will be Even if Q is Even.

2P + 3Q will be Even if Q is Even.

P * Q^2 will Always be Even (since P is even)

P^2 * Q^3 will Always be Even (Since P is even)

Hence none of the above, so answer is E
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Re: P is an integer divisible by 4 and Q is an integer divisible by 3. Whi [#permalink] New post   29 May 2017, 01:33
Even * Even = Even
Even * Odd = Even
Odd * Odd = ODD


P = Even (divisible by 4)
Q = Odd / Even (divisible by 3 . Eg 3,6,9,12....)

A. Q(P+1)

Case 1: Odd * Odd = Odd [3(4+1) => 15]
Case 2: Even * Odd = Even [6(4+1) => 20]

Insufficient.

B. 2P+3Q

2P = Always even
3Q = Odd / Even

Case 1: Odd * Odd = Odd
Case 2: Even * Odd = Even

Insufficient

C. \(P*Q^2\)
P = Even
\(Q^2\) = Odd / Even

Insufficient

D.\(P^2*Q^3\)

P = Even
\(Q^2\) = Odd / Even

Insufficient

E. None of the above. Sufficient

Therefor ans : Option E
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Re: P is an integer divisible by 4 and Q is an integer divisible by 3. Whi [#permalink]
29 May 2017, 01:33
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