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# If a and b are integers, what is the sum of the reciprocals of a and b

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Math Expert
Joined: 02 Sep 2009
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If a and b are integers, what is the sum of the reciprocals of a and b  [#permalink]

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11 Jan 2018, 21:17
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93% (00:40) correct 7% (01:05) wrong based on 38 sessions

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If a and b are integers, what is the sum of the reciprocals of a and b?

(1) ab = 26
(2) a + b = 15

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Joined: 22 Nov 2017
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Concentration: Technology, Healthcare
Re: If a and b are integers, what is the sum of the reciprocals of a and b  [#permalink]

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11 Jan 2018, 21:22
Sum of reciprocals means 1/a + 1/b = (a+b)/ab.
Statement 1 gives only ab and statement 2 gives only a+b. So answer is C.

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Joined: 14 Mar 2017
Posts: 5
GMAT 1: 650 Q47 V33
Re: If a and b are integers, what is the sum of the reciprocals of a and b  [#permalink]

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12 Jan 2018, 18:32
As, the first option shows that a & b can be either 13 and 2 or 26 and 1. Thus, using only statement 1 will give us two answers for 1/a + 1/b.

If we look at the second option it tells us that a + b = 15 but this alone can be many combinations of a and b.

If we take both the statements together, we see that a and b can only be 13 and 2. So, either a is 13 and b is 2 or a is 2 and b is 13. But, we can easily find out 1/a + 1/b using 1/13 + 1/2.

Hence, answer is C.

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Re: If a and b are integers, what is the sum of the reciprocals of a and b   [#permalink] 12 Jan 2018, 18:32
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# If a and b are integers, what is the sum of the reciprocals of a and b

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