If a and b are integers, ab = 5, and a b 0, which of the followin

Question

If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?

I.  a > -1 
II. b is odd
III.  |a|=5

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

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mpobisetty · Answer

Two combinations possible for a and b: (5,-1) or (1,-5).

Hence, option C.

nasgmatbag · Answer

If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?

We can make 2 cases to satisfy the prompt
1) a = 1 and b = -5
2) a = 5 and b = -1

Now onto the questions
I. a > -1
as we can see from our breakdown a can be 1 or 5, therefore a > -1 (keep)

II. b = odd
as we can see from our breakdown b can be -5 or -1, which are both odd (keep)

III. |a| = 5
from our breakdown a can be 5, which makes this statement true, but a can also be 1, therefore this one must not be true

Answer C

RC_xx · Answer

I'm in trubble with this kind of question, I totally agree with your approach, I followed it as well, however I tought if a > -1 a could be 0 then a*b is not -5.

Bunuel

Bunuel · Answer

a  cannot be 0 precisely because we are told that ab = -5. We are given some conditions, and then are asked which of the following MUST be true. ab = -5, and a - b > 0 implies that  a  must be a positive number. For ANY positive number, it will be true to say that it is more than -1; however, it does not mean that  a  can be any number greater than -1.

shreysigulati10 · Answer

I understand the explanation but since the Q claims that a-b> 0, does it not imply that a is larger than b and hence must be 5 and not 1

Bunuel · Answer

a and b are integers, ab = −5, and a − b > 0 implies that we can have the following two cases:

a = 5 and b = -1
a = 1 and b = -5

As you can see, in both cases a > b.

bumpbot · Answer

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If a and b are integers, ab = 5, and a b > 0, which of the followin

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