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From the consecutive integers -10 to 10 inclusive, 20

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Re: From the consecutive integers -10 to 10 inclusive, 20 [#permalink]

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New post 28 Mar 2016, 01:42
Bunuel wrote:
mbaspire wrote:
From the consecutive integers -10 to 10, inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers?

A \((-10)^{20}\)
B \((-10)^{10}\)
C 0
D \(-(10)^{19}\)
E \(-(10)^{20}\)


Hi Bunuel,

I'm confused. I have referred to gmat club math book about multiply 2 number with exponents. the base should be the same to allow sum of the exponent while in this question the base is 10 & -10. So we can't sum 10^10 * (-10)^19. Do I miss something?

Thanks

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Re: From the consecutive integers -10 to 10 inclusive, 20 [#permalink]

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New post 28 Mar 2016, 02:01
Mo2men wrote:
Bunuel wrote:
mbaspire wrote:
From the consecutive integers -10 to 10, inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers?

A \((-10)^{20}\)
B \((-10)^{10}\)
C 0
D \(-(10)^{19}\)
E \(-(10)^{20}\)


Hi Bunuel,

I'm confused. I have referred to gmat club math book about multiply 2 number with exponents. the base should be the same to allow sum of the exponent while in this question the base is 10 & -10. So we can't sum 10^10 * (-10)^19. Do I miss something?

Thanks


Notice that (-10)^19 = (-1)*(10)^19. This way you'll get the same base.

Hope it's clear.
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Re: From the consecutive integers -10 to 10 inclusive, 20 [#permalink]

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New post 04 May 2016, 09:48
catty2004 wrote:
From the consecutive integers -10 to 10 inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers?

A. (-10)^20
B. (-10)^10
C. 0
D. –(10)^19
E. –(10)^20


This problem is testing our knowledge of the multiplication rules for positive and negative numbers. Remember that when we multiply an even number of negative numbers together the result is positive and when we multiply an odd number of negative numbers together the result is negative.

Because we are selecting 20 numbers from the list, we want to start by selecting the smallest 19 numbers we can and multiplying those together. In our list the smallest number we can select is -10. So we have:

(-10)^19 (Note that this product will be negative.)

Since we need to select a total of 20 numbers we must select one additional number from the list. However, since the final product must be as small as possible, we want the final number we select to be the largest positive value in our list. The largest positive value in our list is 10. So the product of our 20 integers is:

(-10)^19 x 10 (Note that this product will still be negative.)

This does not look identical to any of our answer choices. However, notice that
(-10)^19 can be rewritten as -(10)^19, so

(-10)^19 x 10 = -(10)^19 x (10)^1 = -(10)^20.

Answer is E.
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Re: From the consecutive integers -10 to 10 inclusive, 20 [#permalink]

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New post 04 May 2016, 10:49
catty2004 wrote:
From the consecutive integers -10 to 10 inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers?

A. (-10)^20
B. (-10)^10
C. 0
D. –(10)^19
E. –(10)^20


Just adding a bit of more information ( I am with the OA as E )

Here is something interesting for those who might have hard time with this question..


Think of the question in smaller terms

Quote:
From -10 to 10 ; select 4 numbers (repetition allowed) having the least possible product


Possible numbers are

{ -10 , -9, -8, -7, -6, -5, -4, -3, -2, -1 , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Now you can select any number right ? But what is the best way to select least possible number ?

Take 3 negative numbers (repetition allowed)

\({-10}^3\) = -1000

Can you make any smaller number than this ? Don't stress, you can't ...

Now you have product of 3 negative numbers , multiplying with another negative number will result in a positive number, so that is not our objective...

So select a positive number . But which number to choose 1 or 10, lets see..

\({-10}^3\) x 1 => \(-1000\)

\({-10}^3\) x 10 => \(-10000\)

Which is smaller -1000 or -10000 ?

It's definitely -10000....


The similar logic applies to this problem..

Hope it helps someone, having difficulty understanding this problem..

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Re: From the consecutive integers -10 and 10, inclusive, 20 integers are r [#permalink]

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New post 08 Dec 2016, 10:33
In order to minimize the product we can choose 19 biggest positive integers and then multiply their product by the smallest integer. That is |X| should be max if repetition is allowed.

We have: \(10^{19}*(-10) = (-1)*10^{20} = -(10)^{20}\)

Answer E.

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Re: From the consecutive integers -10 and 10, inclusive, 20 integers are r [#permalink]

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New post 08 Dec 2016, 10:44
(-10)^20 is a positive number. So let's limit to (-10)^19.

now the last number should still keep this negative and minimize it further. for example, 1x (-10)^19>2x(-10)^19.....so on..

Therefore the minimum this can be is 10x(-10)^19 = -1x(10^20)
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Re: From the consecutive integers -10 to 10 inclusive, 20 [#permalink]

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New post 18 Dec 2016, 07:00
i cannot even approach this kind of exercises, can someone elaborate? i would be grateful

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Re: From the consecutive integers -10 to 10 inclusive, 20 [#permalink]

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New post 18 Dec 2016, 23:03
stampap wrote:
i cannot even approach this kind of exercises, can someone elaborate? i would be grateful


Here are several solutions from previous two pages of discussion:
from-the-consecutive-integers-10-to-10-inclusive-135518.html#p1102718
from-the-consecutive-integers-10-to-10-inclusive-135518.html#p1102722
from-the-consecutive-integers-10-to-10-inclusive-135518.html#p1142435
from-the-consecutive-integers-10-to-10-inclusive-135518.html#p1665047
from-the-consecutive-integers-10-to-10-inclusive-135518.html#p1665048
from-the-consecutive-integers-10-to-10-inclusive-135518-20.html#p1680537

Hope it helps.
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Re: From the consecutive integers -10 to 10 inclusive, 20 [#permalink]

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New post 19 Dec 2016, 04:18
thank you a lot bunuel

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Re: From the consecutive integers -10 to 10 inclusive, 20 [#permalink]

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New post 25 Aug 2017, 10:46
Clearly answer is E
See attached pic
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Re: From the consecutive integers -10 to 10 inclusive, 20   [#permalink] 25 Aug 2017, 10:46

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