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How many different sums can be formed by adding 2 different numbers f

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GMAT 1: 800 Q59 V59
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How many different sums can be formed by adding 2 different numbers f [#permalink]

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New post 28 Dec 2017, 00:42
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[GMAT math practice question]

How many different sums can be formed by adding \(2\) different numbers from the set {\(1, 2, 4, 8, 16, 32, 33\)}?

A. \(16\)
B. \(17\)
C. \(18\)
D. \(19\)
E. \(20\)
[Reveal] Spoiler: OA

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Math Expert
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Re: How many different sums can be formed by adding 2 different numbers f [#permalink]

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New post 28 Dec 2017, 05:58
MathRevolution wrote:
[GMAT math practice question]

How many different sums can be formed by adding \(2\) different numbers from the set {\(1, 2, 4, 8, 16, 32, 33\)}?

A. \(16\)
B. \(17\)
C. \(18\)
D. \(19\)
E. \(20\)



choose 2 out of 7 \(= 7C2=\frac{7!}{5!2!}=21\)
however 1+33 is SAME as 2+32, so subtract 1 to get different SUM = 21-1=20
E

NOTE :- one of the choices should have been 21 to make it more challenging
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Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 5269
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: How many different sums can be formed by adding 2 different numbers f [#permalink]

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New post 01 Jan 2018, 02:23
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All choices of two different numbers from this set give rise to different sums apart from \(1 + 33\) and \(2 + 32\).
The number of ways to choose \(2\) numbers from the set {\(1, 2, 4, 8, 16, 32, 33\)} of \(7\) numbers is 7C2 = \(\frac{(7*6)}{(1*2)}\) = \(21\).
Since two of these choices, \(1, 33\) and \(2, 32\), have the same sum, we need to subtract \(1\) from \(21\).
Then we have \(21 – 1 = 20\) possible choices.

Therefore, the answer is E.
Answer: E
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Re: How many different sums can be formed by adding 2 different numbers f   [#permalink] 01 Jan 2018, 02:23
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