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# If nCr gives a prime value,is r=n-1?

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Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

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If nCr gives a prime value,is r=n-1? [#permalink]

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14 May 2013, 03:30
00:00

Difficulty:

75% (hard)

Question Stats:

36% (01:10) correct 64% (01:19) wrong based on 27 sessions

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If$$n_{C}_{r}$$ gives a prime value,is $$r=n-1$$?

I. n is prime
II. r is not prime

Question created by me,constructive feedback welcome.Kudos to the first correct answer!
[Reveal] Spoiler: OA

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Kudos [?]: 1355 [0], given: 136

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Re: If nCr gives a prime value,is r=n-1? [#permalink]

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14 May 2013, 03:35
1
KUDOS
If$$n_{C}_{r}$$ gives a prime value,is $$r=n-1$$?

I. n is prime
Case 3C1=3 $$r\neq{}n-1$$
Case 3C2=3 $$r=n-1$$
Not sufficient

II. r is not prime
Case 7C6=7 $$r=n-1$$
Case 7C1=7 $$r\neq{}n-1$$
Not sufficient

I+II) n is prime and r is not prime
Case 3C1=3 $$r\neq{}n-1$$
Case 2C1=2 $$r=n-1$$
Still not sufficient
E
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Kudos [?]: 2327 [1], given: 219

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4426

Kudos [?]: 8452 [0], given: 102

Re: If nCr gives a prime value,is r=n-1? [#permalink]

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14 May 2013, 11:17
vinaymimani wrote:
If$${n}_{C}_{r}$$ gives a prime value,is $$r=n-1$$?

I. n is prime
II. r is not prime

Question created by me,constructive feedback welcome.Kudos to the first correct answer!

Dear vinaymimani
Zarrolou already gave a brilliant solution. I'll just add --- this question doesn't strike me as particularly GMAT-like. Yes, it's a hard question, but I don't know --- it seems very abstractly mathematical and from what I can tell, the most straightforward solutions are simply plug-in of various single digit numbers, as Zarrolou did. On the most challenging math problems, it strikes me that the GMAT creates more elegant problems. It's easier to write a hard problem, but it's more difficult to write an elegant problem. That's just my 2¢
Mike
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Mike McGarry
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Kudos [?]: 8452 [0], given: 102

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Joined: 06 Sep 2013
Posts: 1978

Kudos [?]: 719 [0], given: 355

Concentration: Finance
Re: If nCr gives a prime value,is r=n-1? [#permalink]

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07 Jan 2014, 09:29
mikemcgarry wrote:
vinaymimani wrote:
If$${n}_{C}_{r}$$ gives a prime value,is $$r=n-1$$?

I. n is prime
II. r is not prime

Question created by me,constructive feedback welcome.Kudos to the first correct answer!

Dear vinaymimani
Zarrolou already gave a brilliant solution. I'll just add --- this question doesn't strike me as particularly GMAT-like. Yes, it's a hard question, but I don't know --- it seems very abstractly mathematical and from what I can tell, the most straightforward solutions are simply plug-in of various single digit numbers, as Zarrolou did. On the most challenging math problems, it strikes me that the GMAT creates more elegant problems. It's easier to write a hard problem, but it's more difficult to write an elegant problem. That's just my 2¢
Mike

Agree w/Mr. McGarry here, this doesn't look alike any real GMAT problem i've seen so not likely to come in the test. Still, I congratulate Zarrolou in continuing to provide these hard questions to expand our scope and improve math skills

Cheers!!!
J

Kudos [?]: 719 [0], given: 355

Re: If nCr gives a prime value,is r=n-1?   [#permalink] 07 Jan 2014, 09:29
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