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

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Math Expert
Joined: 02 Sep 2009
Posts: 51123
If a and b are integers, ab = −5, and a − b > 0, which of the followin  [#permalink]

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12 Jul 2018, 23:57
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:44) correct 47% (01:41) wrong based on 51 sessions

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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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Posts: 665
Location: India
Concentration: Operations, Marketing
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Re: If a and b are integers, ab = −5, and a − b > 0, which of the followin  [#permalink]

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13 Jul 2018, 00:15
Bunuel wrote:
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

Given,
ab = −5

Now, we have 4 cases:
a = 5 b = −1 --> (1)
a = −5 b = 1 --> (2)
a = 1 b = −5 --> (3)
a = −1 b = 5 --> (4)

Also,
a − b > 0
Strike out case (2) and (4), for it does not satisfy above given equation respectively
Valid cases are case (1) and (3)

Hence, C.
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If a and b are integers, ab = −5, and a − b > 0, which of the followin  [#permalink]

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13 Jul 2018, 05:09
Bunuel wrote:
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

Key Fact :

ab = -5.

It means neither a nor b is equal to 0.

-5 = 1 * (-5)

or

-5 = (-1) *5

**** Both a and b are integers.

Given that

a-b>0
a>b

As we already have learnt that a or b is negative , b has to be negative. So a is positive.

I. $$a > -1$$

always true. a is always positive. a can't be 0 also.

II. b is odd

always true.

ab = -5

So, b is either -1 or 5 or vise versa.

III. $$|a|=5$$

Could be true as we can't specify the value of a. a could be 1 or 5. a doesn't have to be 5. a could be 1 also.

Thus the best answer is C.
If a and b are integers, ab = −5, and a − b > 0, which of the followin &nbs [#permalink] 13 Jul 2018, 05:09
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