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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
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GPA: 3.82
How many different sums can be formed by adding 2 different numbers f [#permalink]

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27 Dec 2017, 23:42
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Question Stats:

87% (01:38) correct 13% (01:31) wrong based on 31 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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Math Expert
Joined: 02 Aug 2009
Posts: 5537
Re: How many different sums can be formed by adding 2 different numbers f [#permalink]

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

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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.

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Re: How many different sums can be formed by adding 2 different numbers f   [#permalink] 01 Jan 2018, 01:23
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