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# If Jay has 99 problems, in how many ways can he select k of them to ra

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Math Expert
Joined: 02 Sep 2009
Posts: 43894
If Jay has 99 problems, in how many ways can he select k of them to ra [#permalink]

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18 Apr 2017, 03:54
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Difficulty:

85% (hard)

Question Stats:

40% (01:07) correct 60% (01:00) wrong based on 114 sessions

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If Jay has 99 problems, in how many ways can he select k of them to rap about?

(1) Jay can select k+1 of his problems in 3764376 different ways.
(2) Jay can select k–1 of his problems in 4851 different ways.
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5660
If Jay has 99 problems, in how many ways can he select k of them to ra [#permalink]

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18 Apr 2017, 17:37
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Bunuel wrote:
If Jay has 99 problems, in how many ways can he select k of them to rap about?

(1) Jay can select k+1 of his problems in 3764376 different ways.
(2) Jay can select k–1 of his problems in 4851 different ways.

Hi,

We do not and we should not get overwhelmed by the huge numbers here..
the main point is that we require two figures here to get on to value of k, and thus C should be the answer

Why?
Let's try with a smaller number.. 5
Choosing one out of 5 or 4 out of 5 is SAME.
$$5C1=\frac{5!}{1!(5-1)!}=\frac{5!}{1!/4!}=5C4$$....
So it can be 1 or 4, and therefore we require TWO relations of k to get to the value of k...

Let's see the statements..
First let's check the smaller number
II. Choosing k-1 gives 4851 ways..
$$99C(k-1)=4851=99*49=\frac{99*98}{2}=\frac{99*98*97*96*.....*2*1}{2*97*96*..*2*1}=\frac{99!}{2!97!}$$
So k-1 can be 2 or 97, thus k can be 2+1=3 OR 97+1=98..
Insuff alone

I. Choosing k+1is 3764376...
Insufficient

Combined..
If k is 98, k+1 is 99... BUT choosing 99 out of 99 is 1 so eliminate
Therefore k+1 must be 3+1=4 and k MUST be 3
Sufficient

C
_________________

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

BANGALORE/-

If Jay has 99 problems, in how many ways can he select k of them to ra   [#permalink] 18 Apr 2017, 17:37
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