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..

_________________

Thanks and Regards

Abhishek....

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