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GRE Math Challenge #41-From the even numbers between 1 and 9

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GRE Math Challenge #41-From the even numbers between 1 and 9 [#permalink] New post 09 Sep 2014, 03:15
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63% (00:56) correct 36% (00:41) wrong based on 30 sessions
From the even numbers between 1 and 9, two different numbers are to be chosen at random. What is the probability that their sum will be 8 ?

A. 1/6
B. 3/16
C. 1/4
D. 1/3
E. 1/2


[Reveal] Spoiler: Explanation
here are four even numbers between 1 and 9 (2, 4, 6,8).

From this set two distinct numbers can be selected in 4C2 ways :


Hence, there are 6 ways to select 2 numbers from the given set.

The number of pairs which sum 8 is 1 ( 2+6 ).
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #41 [#permalink] New post 23 Apr 2015, 15:44
expert advice is needed.I dont agree with the answer.
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Re: GRE Math Challenge #41-From the even numbers between 1 and 9 [#permalink] New post 12 Apr 2018, 22:27
I would say B
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Re: GRE Math Challenge #41 [#permalink] New post 12 Apr 2018, 23:23
sagar wrote:
expert advice is needed.I dont agree with the answer.



The person answering this is expert.

@sandy can you please elaborate how 4C2 is further resolved and in what conditions we use it?
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Re: GRE Math Challenge #41 [#permalink] New post 13 Apr 2018, 01:22
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The way we can select 2 objects from a list of 4 is \(C^{4}_{2}=\frac{4!}{2! \times 2!}=6\). Hence there are 6 ways of choosing a pair of number from 4 numbers.

Now when we eyeball the data we see only one number pair whose sum is 8 (2+4).

Hence the probability is \(\frac{1}{6}\)
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Re: GRE Math Challenge #41-From the even numbers between 1 and 9 [#permalink] New post 22 Apr 2018, 00:43
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Option A :

Different Approach

Sum of two Numbers to be 8 which leaves us with only two possible numbers (2 & 6)

So for the 1st Number we have 2 options either to select 2 or 6 from total of 4 numbers : 2/4

For the 2nd Number since we have already selected 1 out of 2 or 6 , the # of ways to select the other number : 1/3 (Since 1 Number is already selected we only have 3 Numbers Left)

Solutions = 2/4*1/3 = 2/12 = 1/6
Re: GRE Math Challenge #41-From the even numbers between 1 and 9   [#permalink] 22 Apr 2018, 00:43
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GRE Math Challenge #41-From the even numbers between 1 and 9

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