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13 Mar 2018, 01:12
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:16) correct
27%
(01:16)
wrong
based on 286
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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
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
13 Mar 2018, 01:24
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Bunuel
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.
13 Mar 2018, 01:28
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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
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
