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Math Expert V
Joined: 02 Sep 2009
Posts: 56257
If a and b are integers such that a + b = 5, which of the following is  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:11) correct 25% (01:22) wrong based on 138 sessions

### HideShow timer Statistics If a and b are integers such that a + b = 5, which of the following is true?

I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.

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

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examPAL Representative P
Joined: 07 Dec 2017
Posts: 1074
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

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Bunuel wrote:
If a and b are integers such that a + b = 5, which of the following is true?

I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.

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

Since our numbers our very small, we'll try picking different numbers instead of solving explicitly.
This is an Alternative approach.

We'll try easy value for a,b: first 0,5 then 1,4 and if we need another than 2,3 or -1, 6.
I. 0*5=0 so this is false.
II. if a = 5 then b = 0, so it is even. if a = 1 then b = 4, so it is even. If a = 3 then b = 2 so it is even.
Even if we're not sure why the statement is true, after 3 examples we should feel OK guessing that it is true.
(Additionally, trying these examples will hopefully have reminded us that odd - odd = even. This is the proof that II is true)
III. a = -1 --> b = 6. a = -2, b = 7.
At this point it should be clear that we've hit on a trend: making a smaller will only make b larger so it is definitely positive.

All in all, I is False, II is true, III is true
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Posts: 411
GMAT 1: 640 Q48 V28 Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

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From a+b=5 we can assume that a and b have opposite even/odd nature

I The product of a and b is odd --> As we know a and b have opposite even/odd nature so their multiple MUST be even --> FALSE
II If a is odd, b is even --> As we know a and b have opposite even/odd nature so if a is odd then b MUST be even --> TRUE
III If a is negative, b is positive -- > if a is negative b Must be positive and moreover |a|=b+5 --> TRUE

So my choice is D
Intern  B
Joined: 07 Jan 2018
Posts: 11
If a and b are integers.....  [#permalink]

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If a and b are integers such that a+b=5, which of the following MUST be true?
I. The product of a and b is odd.
II. If a is odd, b is even
III. If a is negative, b is positive

(A) I only
(B) II only
(C) I and II only
(D) II III only
(E) I,II and III

Please explain with all the possibilities (plugging in numbers?

Posted from my mobile device
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Re: If a and b are integers.....  [#permalink]

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1
mittu wrote:
If a and b are integers such that a+b=5, which of the following MUST be true?
I. The product of a and b is odd.
II. If a is odd, b is even
III. If a is negative, b is positive

(A) I only
(B) II only
(C) I and II only
(D) II III only
(E) I,II and III

Please explain with all the possibilities (plugging in numbers?

Posted from my mobile device

a + b = 5

odd = even + odd...........

thus product can't be odd as even*odd = even.

If a is odd b has to even. fact.

*** 5 is positive value thus if one is negative another has to be positive.

Thus D is the best answer.

Hope it helps.
Math Expert V
Joined: 02 Sep 2009
Posts: 56257
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

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mittu wrote:
If a and b are integers such that a+b=5, which of the following MUST be true?
I. The product of a and b is odd.
II. If a is odd, b is even
III. If a is negative, b is positive

(A) I only
(B) II only
(C) I and II only
(D) II III only
(E) I,II and III

Please explain with all the possibilities (plugging in numbers?

Posted from my mobile device

Merging topics.

Please search before posting and name topics properly. Check rules here: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.
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Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

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Bunuel wrote:
If a and b are integers such that a + b = 5, which of the following is true?

I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.

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

Since a + b = 5, either a is odd and b is even and vice versa, so II is true.

Thus, the product of a and b is even, so I is not true.

Finally if a is negative, then b would have to be positive to get a positive sum, so III is true.

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Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

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Bunuel wrote:
If a and b are integers such that a + b = 5, which of the following is true?

I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.

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

a + b = 5
i.e. (a,b) may be (0,5) (1,4) (2,3) etc.

I. The product of a and b is odd. is NOT true for (2,3)
II. If a is odd, b is even. MUST be true as only sum of even and odd will result in an odd outcome
III. If a is negative, b is positive. MUST be true because if one of the values is negative then for resultant sum to be positive the other value must be positive

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Intern  Joined: 10 Sep 2018
Posts: 2
Re: If a and b are integers such that a + b = 5, which of the following is  [#permalink]

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+1 for D

Product of a and b is not necessarily odd. Consider -1 and 6
Posted from my mobile device Re: If a and b are integers such that a + b = 5, which of the following is   [#permalink] 03 Oct 2018, 01:42
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# If a and b are integers such that a + b = 5, which of the following is  