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

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New post 27 Dec 2017, 23:42
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:56) correct 14% (01:21) wrong based on 65 sessions

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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. \(20\)

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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, 04:58
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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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 01 Jan 2018, 01:23
=>
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 &nbs [#permalink] 01 Jan 2018, 01:23
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