Probability

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pmFollowed by: 6 members

by BTGmoderatorRO » Sun Oct 08, 2017 11:57 am

If two different numbers are to be selected from set {1, 2, 3, 4, 5, 6}, what is the probability that the sum of two numbers is a square of an integer?

A. 1/2
B. 1/3
C. 1/5
D. 1/9
E. 1/30
can anyone assist me with this question? Thanks

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Source: Beat The GMAT — Problem Solving | Sun Oct 08, 2017 11:57 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun Oct 08, 2017 8:33 pm

Roland2rule wrote:If two different numbers are to be selected from set {1, 2, 3, 4, 5, 6}, what is the probability that the sum of two numbers is a square of an integer?

A. 1/2
B. 1/3
C. 1/5
D. 1/9
E. 1/30
can anyone assist me with this question? Thanks

Probability that the sum of two numbers is a square of an integer is given by "(Number of pairs that make the sum a perfect square) / (Total number of selections of two numbers out of the given six numbers)"

Total number of selections of two numbers out of given six numbers = 6C2 = (6.5) / (1.2) = 15;

To get the value of 'Number of pairs that make the sum a perfect square,' you should use the brute force. Add all the possible pairs of two numbers from the set and see which of the pairs render 4 (min. possible value) or 9 (max. possible value).

We see that only three pairs qualify: {1, 3); {3, 6}; and {4, 5}

Thus, the probability that the sum of two numbers is a square of an integer = [spoiler]3/15 = 1/5[/spoiler].

The correct answer: C

Hope this helps!

-Jay

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Tue Oct 10, 2017 6:41 am

Hello Roland.

In this question you should first calculate the total of different ways to choose 2 numbers from 6. This number is given by 6C2=6!/(4!)(2!)=6*5/2*1=15.

Now, you have to select the posible 2 numbers which their sum is a perfect square. This 2 numbers can be:

- 1 and 3: their sum is 4=2^2.
- 3 and 6: their sum is 9=3^2.
- 4 and 5: their sum is 9=3^2.

As you can see, there are only 3 posible cases. So, the probability to select 2 numbers from the given set, that their sum is a perfect square is 3/15=1/5.

So, the correct answer is C.

I hope this approach can help you.

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Oct 11, 2017 5:35 pm

Minimum sum = 3
Maximum sum = 11

Only squares in there: 4, 9

Possible sums: 1 + 3, 3 + 6, 4 + 5

So three possible pairs out of (6 choose 2) distinct pairs, or 3/(6!/4!2!), or 1/5

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Probability

by Scott@TargetTestPrep » Thu Jan 23, 2020 9:22 am

BTGmoderatorRO wrote: ↑
Sun Oct 08, 2017 11:57 am
If two different numbers are to be selected from set {1, 2, 3, 4, 5, 6}, what is the probability that the sum of two numbers is a square of an integer?

A. 1/2
B. 1/3
C. 1/5
D. 1/9
E. 1/30
can anyone assist me with this question? Thanks

The total number of ways of choosing 2 numbers from 6 is 6C2 = (6 x 5)/2 = 15.

The following pairs of two numbers sum to be a square:

1 + 3 = 4

3 + 6 = 9

4 + 5 = 9

So, the overall probability is:

3/15 = 1/5

Answer: C

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