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If an integer is to be randomly

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

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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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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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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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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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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,
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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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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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