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Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran

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Bunuel
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Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink] New post   25 Apr 2018, 21:48
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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
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E
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amanvermagmat
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Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink] New post   25 Apr 2018, 22:49
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Bunuel wrote:
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


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
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Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink] New post   25 Apr 2018, 23:01
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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

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)
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Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink] New post   13 May 2018, 09:51
Product will be least when it has negative and highest number

Highest number is 5 so cases

One(-5) nine 5
Three(-5) seven 5
Five(-5) five (5)
Nine(-5) one (5)
Seven (-5) three (5)

So five cases

Give kudos if it helps

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Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink] New post   10 Jul 2020, 18:02
This is a misleading question. Because if we count every possible way, then 5*5*5*5*5*5*5*5*5*(-5) is a different outcome than (-5)*5*5*5*5*5*5*5*5*5. In the former -5 is picked as the last integer and in the latter it is picked first. So if we go by counting all the different ways we can choose -5 and nine 5's that alone is more than 5 ways.
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Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink] New post   10 Jul 2020, 20:32
chacinluis wrote:
This is a misleading question. Because if we count every possible way, then 5*5*5*5*5*5*5*5*5*(-5) is a different outcome than (-5)*5*5*5*5*5*5*5*5*5. In the former -5 is picked as the last integer and in the latter it is picked first. So if we go by counting all the different ways we can choose -5 and nine 5's that alone is more than 5 ways.


The problem didn't ask about the arrangements of the numbers.
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Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink] New post   10 Jul 2020, 21:48
yeah. It asks in how many different ways you can get the lowest value of the product of 10 integers. So different arrangements are different ways. B/c they are different outcomes of the experiment.
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Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink] New post   17 Sep 2022, 11:51
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Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink]
17 Sep 2022, 11:51
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