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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
Joined: 16 Aug 2015
Posts: 5269
GMAT 1: 800 Q59 V59
GPA: 3.82
How many different sums can be formed by adding 2 different numbers f [#permalink]

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28 Dec 2017, 00:42
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3
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Difficulty:

15% (low)

Question Stats:

79% (01:30) correct 21% (01:05) wrong based on 53 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. $$20$$
[Reveal] Spoiler: OA

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 5776 Re: How many different sums can be formed by adding 2 different numbers f [#permalink] ### Show Tags 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 _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Math Revolution GMAT Instructor 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] ### Show Tags 01 Jan 2018, 02:23 Expert's post 1 This post was BOOKMARKED => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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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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