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# Amar has nine friends. He wants to invite them to his birthday party.

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Manager
Joined: 18 Jul 2019
Posts: 54
Amar has nine friends. He wants to invite them to his birthday party.  [#permalink]

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25 Nov 2019, 07:02
3
00:00

Difficulty:

55% (hard)

Question Stats:

54% (02:00) correct 46% (02:19) wrong based on 24 sessions

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Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100
CR Forum Moderator
Joined: 25 Apr 2018
Posts: 674
GMAT 1: 680 Q49 V34
Re: Amar has nine friends. He wants to invite them to his birthday party.  [#permalink]

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25 Nov 2019, 09:18
CaptainLevi wrote:
Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100

Similar question : https://gmatclub.com/forum/a-man-8-frie ... l#p1843646
Manager
Joined: 18 Jul 2019
Posts: 54
Re: Amar has nine friends. He wants to invite them to his birthday party.  [#permalink]

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25 Nov 2019, 09:21
gmat1393 wrote:
CaptainLevi wrote:
Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100

Similar question : https://gmatclub.com/forum/a-man-8-frie ... l#p1843646

Existing question :- 8 friends with at least one friend invitation
New Question :- 9 friends with at least 2 friend invitation
Intern
Joined: 19 Jan 2019
Posts: 11
Re: Amar has nine friends. He wants to invite them to his birthday party.  [#permalink]

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26 Nov 2019, 01:53
can anyone plz explain me this question ?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9871
Location: Pune, India
Re: Amar has nine friends. He wants to invite them to his birthday party.  [#permalink]

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26 Nov 2019, 03:37
1
CaptainLevi wrote:
Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100

Say the 9 friends are A, B, C, D, E, F, G, H, I

There are 2 ways in which he can deal with each one of his friends - he can invite them or not invite them

So there are 2 ways to deal with A - Invite A or not invite A
There are 2 ways to deal with B - Invite B or not invite B
and so on ...

So the total ways in which he can invite/not invite all his friends is 2 * 2 * 2.... (9 times) = 2^9 = 512

This includes 1 way in which he invites no one.
This also includes 9 ways in which he invites only 1 friend (invite only A, invite only B, invite only C ... and so on)

Since he must invite at least 2 friends, the cases in which no friend or only 1 friend is invited should be removed.

Total such cases = 512 - 1 - 9 = 502

_________________
Karishma
Veritas Prep GMAT Instructor

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Joined: 04 Apr 2015
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GMAT 1: 650 Q49 V31
GPA: 3.59
Re: Amar has nine friends. He wants to invite them to his birthday party.  [#permalink]

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26 Nov 2019, 12:04
CaptainLevi wrote:
Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100

i solved with little logic and answer choices : total ways = 512 (1 yes or 1 No ) 2 ways for each 9 friends
so eliminate D and E
now we need to find at least 2 : total - none - 1 friend only ( we can see both none and 1 friend only has to be integer so answer less than 511 )
Eliminate C

left with A and B : mark B confidently as a too small
Re: Amar has nine friends. He wants to invite them to his birthday party.   [#permalink] 26 Nov 2019, 12:04
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