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If p is an even integer and q is an odd integer, which of the followin

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If p is an even integer and q is an odd integer, which of the followin  [#permalink]

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New post 05 Nov 2015, 12:36
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A
B
C
D
E

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Question Stats:

96% (00:46) correct 4% (00:43) wrong based on 163 sessions

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Re: If p is an even integer and q is an odd integer, which of the followin  [#permalink]

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New post 05 Nov 2015, 12:52
Bunuel wrote:
If p is an even integer and q is an odd integer, which of the following must be an odd integer?

A. p/q
B. pq
C. 2p+q
D. 2(p+q)
E. 3p/q


A. p/q
p = 6, q = 3 => p/q is odd integer
p = 4, q=3 =>p/q is not integer
B. pq
Must be even
C. 2p+q
2p must be even, q is odd=> 2p+q must be ODD: CORRECT
D. 2(p+q)
must be even
E. 3p/q
Same A

Ans: C
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Re: If p is an even integer and q is an odd integer, which of the followin  [#permalink]

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New post 05 Nov 2015, 13:07
this is a must question:

A. p/q
can be a non-integer

B. pq
always even

C. 2p+q
2p = even -> even+odd = odd

D. 2(p+q)
always even - p+q = odd *2 -> even

E. 3p/q
might be a non integer.

C
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Re: If p is an even integer and q is an odd integer, which of the followin  [#permalink]

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New post 17 Apr 2017, 04:05
Option C

p = Even, q = Odd. Odd: O, Even: E & Fraction: F

A. p/q = E/O = E or F
B. pq = E*O = E
C. 2p+q = 2E + O = O
D. 2(p+q) = 2(E+O) = E
E. 3p/q = 3(E/O) = 3E or 3F
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Re: If p is an even integer and q is an odd integer, which of the followin  [#permalink]

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New post 17 Apr 2017, 22:03
1
Hi All,

If you know the Number Properties involved in this question, then you can get to the correct answer relatively easily. You can also TEST VALUES to get to the answer.

We're told that P is an EVEN integer and Q is an ODD integer. We're asked which of the following must be an ODD integer...

IF....
P = 2 AND Q = 1, then...

Answer A: 2/1 = 2 NOT an odd
Answer B: 2(1) = 2 NOT an odd
Answer C: 2(2) + 1 = 5 This IS an odd
Answer D: 2(2+1) = 6 NOT an odd
Answer E: 3(2)/1 = 6 NOT an odd

Final Answer:

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Re: If p is an even integer and q is an odd integer, which of the followin  [#permalink]

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New post 20 Apr 2017, 16:52
1
Bunuel wrote:
If p is an even integer and q is an odd integer, which of the following must be an odd integer?

A. p/q
B. pq
C. 2p+q
D. 2(p+q)
E. 3p/q


There are three ways to get an odd integer: odd x odd = odd OR odd/odd = odd OR even + odd = odd. Let’s examine our answer choices to determine which must produce an odd integer.

A) p/q

Since p is even and q is odd, p/q will never be an odd integer.

B) pq

Again, since p is even and q is odd, p/q will never be an odd integer.

C) 2p+q

Since 2p is even and q is odd, 2p + q WILL BE an odd integer.

Answer: C
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Re: If p is an even integer and q is an odd integer, which of the followin  [#permalink]

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New post 08 May 2018, 11:04
Top Contributor
Bunuel wrote:
If p is an even integer and q is an odd integer, which of the following must be an odd integer?

A. p/q
B. pq
C. 2p+q
D. 2(p+q)
E. 3p/q


Another approach is to take each answer choice and plug in an even number for p and an odd number for q, and see which answer choices yield an ODD value.
The easiest numbers to test are p = 0 (which is EVEN) and q = 1 (which is ODD)

We get:
A. p/q = 0/1 = 0, which is EVEN. ELIMINATE A
B. pq = (0)(1) = 0, which is EVEN. ELIMINATE B
C. 2p+q = 2(0) + 1 = 1, which is ODD. KEEP C
D. 2(p+q) = 2(0 + 1) = 2, which is EVEN. ELIMINATE D
E. 3p/q = (3)(0)/1 = 0, which is EVEN. ELIMINATE E

Answer: C

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Brent
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Re: If p is an even integer and q is an odd integer, which of the followin   [#permalink] 08 May 2018, 11:04
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