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# If positive integers a and b are both odd, which of the following must

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Math Expert
Joined: 02 Sep 2009
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If positive integers a and b are both odd, which of the following must [#permalink]

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10 Dec 2016, 05:25
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69% (00:45) correct 31% (00:42) wrong based on 200 sessions

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If positive integers a and b are both odd, which of the following must not be odd?

A. ab
B. a(ab)
C. b – a – 1
D. (a + b)/2
E. a – b
[Reveal] Spoiler: OA

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Re: If positive integers a and b are both odd, which of the following must [#permalink]

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10 Dec 2016, 05:29
Odd -Odd => Even
Hence E can never be even.

Hence E

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Kudos [?]: 998 [0], given: 682

Manager
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Location: India
Re: If positive integers a and b are both odd, which of the following must [#permalink]

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10 Dec 2016, 08:10
If positive integers a and b are both odd.
A. ab ----- Odd * Odd = Odd
B. a(ab)-- Odd * Odd * Odd = Odd
C. b – a – 1 -- Odd - Odd - 1 = Odd
D. (a + b)/2 -- Odd + Odd / 2 = Odd
E. a – b ---- Odd - Odd = Even in all the cases. Hence answer is E.

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Re: If positive integers a and b are both odd, which of the following must [#permalink]

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10 Dec 2016, 08:41
1
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Bunuel wrote:
If positive integers a and b are both odd, which of the following must not be odd?

A. ab
B. a(ab)
C. b – a – 1
D. (a + b)/2
E. a – b

A. ODD * ODD = ODD

B. ODD(ODD*ODD) = ODD

C. ODD - ODD = EVEN - 1 = ODD

D. ODD + ODD = EVEN/2 = EVEN/ODD

E. ODD - ODD = EVEN

So, Correct answer will be (E)
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Re: If positive integers a and b are both odd, which of the following must [#permalink]

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17 Apr 2017, 01:40
Option E

a & b are Odd integers. Odd: O, Even: E & Fraction: F.

A. ab = O*O = O
B. a(ab) = O(O*O) = O
C. b – a – 1 = O - O - 1 = E - 1 = O
D. (a + b)/2 = (O + O)/2 = E/2 = O
E. a – b = O - O = E
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Re: If positive integers a and b are both odd, which of the following must [#permalink]

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22 Apr 2017, 23:18
A. o1*o2=o
B. o1(o1*o2)=o
C. o2-o1-1=o
D. (o1+o2)/2=o
E. o1-o2=e

Hence E

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Intern
Joined: 30 Jul 2016
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Re: If positive integers a and b are both odd, which of the following must [#permalink]

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20 Jun 2017, 06:51
How come D is not the answer if we apply 3+5/2=4 , therefore even?

Bunuel wrote:
If positive integers a and b are both odd, which of the following must not be odd?

A. ab
B. a(ab)
C. b – a – 1
D. (a + b)/2
E. a – b

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Re: If positive integers a and b are both odd, which of the following must [#permalink]

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20 Jun 2017, 07:02
Yoohanna wrote:
How come D is not the answer if we apply 3+5/2=4 , therefore even?

Bunuel wrote:
If positive integers a and b are both odd, which of the following must not be odd?

A. ab
B. a(ab)
C. b – a – 1
D. (a + b)/2
E. a – b

Good observation, thats why I mentioned the result of (D) may/may not be EVEN
Abhishek009 wrote:
D. ODD + ODD = EVEN/2 = EVEN/ODD

You have considered the numbers as 3 and 5 , see if I take the numbers as 1 and 5

$$\frac{(a + b)}{2} = \frac{6}{2} = 3 (ODD)$$

Thus, (D) may/may not be even...

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Abhishek....

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Re: If positive integers a and b are both odd, which of the following must [#permalink]

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04 Dec 2017, 13:24
Hi All,

This question can be approached with Number Property rules. We're told that A and B are both ODD, POSITIVE INTEGERS. We're asked which of the following MUST NOT be odd.

Answer A: (A)(B) = (odd)(odd) = odd
Answer B: (A)(A)(B) = (odd)(odd)(odd) = odd
Answer C: B - A - 1 = (odd) - (odd) - (odd) = odd
Answer D: (A+ B)/2 = (odd + odd)/2 = (even)/2 = COULD be even (re: 4/2 = 2) OR odd (re: 6/2 = 3)
Answer E: A - B = (odd) - (odd) = EVEN

There's only one answer that can NEVER be odd.

[Reveal] Spoiler:
E

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Re: If positive integers a and b are both odd, which of the following must [#permalink]

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11 Jan 2018, 13:45
Bunuel wrote:
If positive integers a and b are both odd, which of the following must not be odd?

A. ab
B. a(ab)
C. b – a – 1
D. (a + b)/2
E. a – b

Since odd - odd = even, answer choice E, a - b is not odd.

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Re: If positive integers a and b are both odd, which of the following must   [#permalink] 11 Jan 2018, 13:45
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