If an integer is to be randomly

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NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 amFollowed by: 2 members; Thanked: 3 times

by NandishSS » Sat Jan 14, 2017 6:22 am

Set A = {-5,-4, -1, -3, -2,} Set B = {-2,-1 ,0, 1}

If an integer is to be randomly selected from set A above and an integer is to be randomly selected from set B above, what is the probability that the sum of the two integers selected will be non-positive?
(A) 1 (B) 19/20 (C) 9/10 (D) 17/20 (E) 4/5

OA:A

Source:MATH-REVOLUTION

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Jan 14, 2017 7:33 am

NandishSS wrote:Set A = {-5,-4, -1, -3, -2,} Set B = {-2,-1 ,0, 1}

If an integer is to be randomly selected from set A above and an integer is to be randomly selected from set B above, what is the probability that the sum of the two integers selected will be non-positive?
(A) 1 (B) 19/20 (C) 9/10 (D) 17/20 (E) 4/5

Greatest possible sum = (greatest value in A) + (greatest value in B) = -1 + 1 = 0.
Since the greatest possible sum is non-positive, ALL of the possible sums must be non-positive.
Since any possible sum will be non-positive, P(non-positive sum) = 1.

The correct answer is A.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 14, 2017 9:40 am

NandishSS wrote:Set A = {-5,-4, -1, -3, -2,} Set B = {-2,-1 ,0, 1}

If an integer is to be randomly selected from set A above and an integer is to be randomly selected from set B above, what is the probability that the sum of the two integers selected will be non-positive?
(A) 1 (B) 19/20 (C) 9/10 (D) 17/20 (E) 4/5

OA:A

Source:MATH-REVOLUTION

We can also use the complement
P(Event A happening) = 1 - P(Event A not happening)
So, P(sum is non-positive) = 1 - P(sum is positive)

We can quickly see that it is IMPOSSIBLE to get a positive sum by selecting a number from each set.
In other words, P(sum is positive) = 0

So, P(sum is non-positive) = 1 - P(sum is positive)
= 1 - 0
= 1

Answer: A

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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 » Mon Jan 16, 2017 5:54 am

NandishSS wrote:Set A = {-5,-4, -1, -3, -2,} Set B = {-2,-1 ,0, 1}

If an integer is to be randomly selected from set A above and an integer is to be randomly selected from set B above, what is the probability that the sum of the two integers selected will be non-positive?
(A) 1 (B) 19/20 (C) 9/10 (D) 17/20 (E) 4/5

OA:A

Source:MATH-REVOLUTION

Since there are as many as seven negatives numbers in the sets and only two are non-negative. So, let us figure out what combinations of numbers from set A and from set B make the sum 0 or positive.

Greatest value in set A = -1 and that in set B = 1, thus the sum = -1 + 1 = 0 (non-positive).

Since the greatest possible sum is non-positive, others will also be non-positive. Thus the probability = 1.

Answer: A

Hope this helps!

-Jay
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rsarashi: Master | Next Rank: 500 Posts; Posts: 186; Joined: Sat Dec 24, 2016 12:38 amFollowed by: 3 members; Thanked: 5 times

by rsarashi » Mon Jan 16, 2017 9:38 am

Hi Experts ,

Just a quick question.

Why didn't we take -5 from set A and -2 from set B? If we sum these two, which also gives a non-positive integers.

Same as -4 from A and -2,-1 from B?

Please explain

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jan 16, 2017 9:44 am

rsarashi wrote:Hi Experts ,

Just a quick question.

Why didn't we take -5 from set A and -2 from set B? If we sum these two, which also gives a non-positive integers.

Same as -4 from A and -2,-1 from B?

Please explain

Those two selections definitely produce a non-positive sum.
In fact, EVERY selection will produce a non-positive sum.
That's why the probability = 1

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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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 » Mon Jan 16, 2017 8:12 pm

rsarashi wrote:Hi Experts ,

Just a quick question.

Why didn't we take -5 from set A and -2 from set B? If we sum these two, which also gives a non-positive integers.

Same as -4 from A and -2,-1 from B?

Please explain

As I explained in my post that there are as many as seven negative numbers in the two sets. It's a no-brainer to deduce that the sum of two negatives would be negative (non-positive).

-5 from set A and -2 from set B are minimum and negative numbers; their sum would be negative (-7: non-positive). Why waste our time in analyzing them! By adding the greatest numbers from the two sets, -1 and 1, adding 0 (THE GREATEST POSSIBLE SUM), we can argue that when the greatest sum itself is non-positive, the sums less than that would definitely be non-positive.

Hope this is clear to you.

-Jay

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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 Jan 18, 2017 7:01 pm

rsarashi wrote:Hi Experts ,

Just a quick question.

Why didn't we take -5 from set A and -2 from set B? If we sum these two, which also gives a non-positive integers.

Same as -4 from A and -2,-1 from B?

Please explain

This is a good question, though: as experts I think we sometimes forget to mention that we're using two numbers as one example of a phenomenon, not the SOLE example of that phenomenon.

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