If a and b are integers such that a + b = 5, which of the following is

Question

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

DavidTutorexamPAL · Answer

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
(D) is our answer.

LevanKhukhunashvili · Answer

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

mittu · Answer

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

KSBGC · Answer

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.

Bunuel · Answer

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ScottTargetTestPrep · Answer

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.

Answer: D

GMATinsight · Answer

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

Answer: Option D

Gaurmitt · Answer

+1 for D

Product of a and b is not necessarily odd. Consider -1 and 6
   Posted from my mobile device

arbazfatmi1994 · Answer

III. If a is negative, b is positive.
 
 Please note - This is  not a necessary condition  for a+b to be equal to 5

It's merely given as  "a condition" /b]

If a and b are integers such that a + b = 5, which of the following is

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If a and b are integers such that a + b = 5, which of the following is

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