Properties of numbers - Explain this problem - The Beat The GMAT Forum

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

Why dont we choose '0' twenty times and get value 0 ? Please explain

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by Anurag@Gurome » Sun Jul 01, 2012 1:44 am

Jeevanantham 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?

We need to select 20 integers such that their product is lowest.
This can be done by selecting 10 once and -10 nineteen times.
Hence, product = 10*[(-10)^19] = -(10)*(10^19) = -(10^20)

The closest answer is E.

Jeevanantham wrote:Why dont we choose '0' twenty times and get value 0?

We can.
But then the product will not be the least possible product.

Last edited by Anurag@Gurome on Sun Jul 01, 2012 1:48 am, edited 1 time in total.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sun Jul 01, 2012 1:47 am

We can solve this problem by checking the options also.

The lowest option is -(10^20)
We can achieve this by selecting 10 once and -10 nineteen times.
Hence, this is a valid product and least of all the options.

The closest answer is E.[/quote]

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