Consecutive integers

[Anitochka]

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

Answer: E

[Brent@GMATPrepNow]

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

Answer: E

Choose nineteen -10's and one 10
So, the product = [(-10)^19][10]
Notice that [(-10)^19] is NEGATIVE, which means [(-10)^19][10] is also NEGATIVE.

So, [(-10)^19][10] = -[(10)^19][10]
= -(10^20)
= E

Cheers,
Brent

[Anitochka]

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

Answer: E

Choose nineteen -10's and one 10
So, the product = [(-10)^19][10]
Notice that [(-10)^19] is NEGATIVE, which means [(-10)^19][10] is also NEGATIVE.

So, [(-10)^19][10] = -[(10)^19][10]
= -(10^20)
= E

Cheers,
Brent

Thank you a lot for your answer! I have one more question. Can I pick 20 identical numbers?

[Brent@GMATPrepNow]

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

Answer: E

Choose nineteen -10's and one 10
So, the product = [(-10)^19][10]
Notice that [(-10)^19] is NEGATIVE, which means [(-10)^19][10] is also NEGATIVE.

So, [(-10)^19][10] = -[(10)^19][10]
= -(10^20)
= E

Cheers,
Brent

Thank you a lot for your answer! I have one more question. Can I pick 20 identical numbers?

Yes, you can choose 20 identical numbers.
HOWEVER, the product of 20 identical numbers will be positive, and our goal is to minimize the product.

Cheers,
Brebt

[[email protected]]

Hi Anitochka,

In certain GMAT questions, the answer choices are designed in such a way as to provide a hint as to what you might focus on to solve it (this is quite common in Verbal SCs). Here, we're clued in that we should think about -10s and +10s and how we might use them to get the LEAST possible product.

With (10)^20 and (-10)^20, we would have the same value - and it would be really big - so that can't be what's needed to get the correct answer here. By 'swapping out' one of those 20 terms for its opposite though, we end up right a negative number that's as far to the left on a Number Line as we can get under these conditions:

(-10)(10)^19 or (10)(-10)^19

Both are the equivalent of -(10)^20.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

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

Answer: E

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 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: E