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25 Apr 2018, 21:48
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
56% (01:54) correct
44%
(01:38)
wrong
based on 195
sessions
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Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are randomly chosen from A, with repetitions allowed, how many different ways, can the least possible value of the product of the 10 integers be obtained?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
25 Apr 2018, 22:49
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Bunuel
So here numbers can be repeated. We can choose all 0's or five 1's and five -4's etc. But the product has to be least. The way to make it least would be to make it negative and as far away from 0 on the number line as possible.
So the product should be a number with highest possible magnitude (absolute value) but with a negative sign before it. Out of given numbers, 5 or -5 have the highest magnitudes. So we need to make the product with all ten 5's, but sign should be negative. So this can be done in following ways:
Nine -5's, One 5
Seven -5's, Three 5's
Five -5's, Five 5's
Three -5's, Seven 5's
One -5, Nine 5's
(We are taking only odd number of negatives here because if we take even number of negative integers, then our product will be positive which we dont want)
So in total, there are five ways as explained.
Hence E answer
ruchirS
Joined: 19 Dec 2017
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GMAT 1: 640 Q48 V31
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25 Apr 2018, 23:01
Kudos
Bookmarks
Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are randomly chosen from A, with repetitions allowed, how many different ways, can the least possible value of the product of the 10 integers be obtained?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Lets consider 10 boxes, we need to fill these boxes with numbers so that the product of all numbers is minimum.
X X X X X X X X X X
We can't have all the 10 numbers as negative (as product of 10 negative numbers will become positive)
As repetitions are allowed, the lowest product will be when all numbers are a combination of 5 and -5
So we need to fill these 10 boxes with 5 and -5 so that product is negative. That is, we need odd number of -5s.
There are 5 ways of doing this :
one (-5), nine (5s)
three (-5s), seven (5s)
five (-5s), five (5s)
seven (-5s), three (5s)
nine (-5s), one (5)
So answer is 5. Option (E)
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Lets consider 10 boxes, we need to fill these boxes with numbers so that the product of all numbers is minimum.
X X X X X X X X X X
We can't have all the 10 numbers as negative (as product of 10 negative numbers will become positive)
As repetitions are allowed, the lowest product will be when all numbers are a combination of 5 and -5
So we need to fill these 10 boxes with 5 and -5 so that product is negative. That is, we need odd number of -5s.
There are 5 ways of doing this :
one (-5), nine (5s)
three (-5s), seven (5s)
five (-5s), five (5s)
seven (-5s), three (5s)
nine (-5s), one (5)
So answer is 5. Option (E)
