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# Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is

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Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is  [#permalink]

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30 Jun 2017, 06:57
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Difficulty:

5% (low)

Question Stats:

92% (01:12) correct 8% (01:07) wrong based on 52 sessions

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Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is an odd integer, then which of the following must be true?

i. Q is odd
ii. R is odd
iii. S is odd

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III only

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Joined: 02 Sep 2009
Posts: 54376
Re: Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is  [#permalink]

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30 Jun 2017, 07:16
mkrishnabdrr wrote:
Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is an odd integer, then which of the following must be true?

i. Q is odd
ii. R is odd
iii. S is odd

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III only

PQ + RS = odd

even*Q + RS = odd

even + RS = odd (PQ will be even regardless of Q)

RS = odd - even = odd

The product of two integers to be odd both must be odd.

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Re: Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is  [#permalink]

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30 Jun 2017, 07:18
mkrishnabdrr wrote:
Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is an odd integer, then which of the following must be true?

i. Q is odd
ii. R is odd
iii. S is odd

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III only

(P*Q + R*S) = Odd integer,
P = Even Integer
So,
Even Integer + Odd Integer = Odd Integer
On LHS, for 2nd item (RS) to be ODD, both R & S has to be odd

Even if Q is EVEN, result wouln't change

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Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is  [#permalink]

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30 Jun 2017, 22:43
mkrishnabdrr wrote:
Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is an odd integer, then which of the following must be true?

i. Q is odd
ii. R is odd
iii. S is odd

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III only

This question takes less than 30 seconds because of the answer choices.

1. The sum of two numbers (PQ) and (RS) will be odd when one number is odd and the other is even.
O + E = O, or E + O = O

2. P is even. Only odd times odd = odd. P times odd or even will be even.

(That means (RS) is odd, which turns out not to matter because of answer choices.)

3. Assessing I, must Q be odd? From #2: No. P (even) times even or odd will be even.

Answers A, B, C, and E all include I as a "must." It isn't.

4. Only answer D does not include that incorrect answer. Reject the other four.

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Suppose P, Q, R, and S are integers. If P is even and (P*Q + R*S) is   [#permalink] 30 Jun 2017, 22:43
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