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What is the least possible product of 5 different integers, each of wh

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What is the least possible product of 5 different integers, each of wh  [#permalink]

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05 Dec 2016, 01:28
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25% (medium)

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79% (01:28) correct 21% (01:41) wrong based on 173 sessions

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What is the least possible product of 5 different integers, each of which is between –5 and 5, inclusive?

A. –1600
B. –1450
C. –1200
D. –840
E. –600

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Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

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05 Dec 2016, 03:33
2
Following 5 distinct values will give the least possible product
(-5)*5*4*(-4)*(-3)
=(-25)*(-16)*(-3)
=-1200
Correct answer is C.
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Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

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27 Oct 2017, 03:11
AR15J wrote:
Following 5 distinct values will give the least possible product
(-5)*5*4*(-4)*(-3)
=(-25)*(-16)*(-3)
=-1200
Correct answer is C.
-------
+1 Kudos if you like the post

Can you help me explain what the rule behind this solution?

Thanks.
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Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

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30 Oct 2017, 13:04
1
Bunuel wrote:
What is the least possible product of 5 different integers, each of which is between –5 and 5, inclusive?

A. –1600
B. –1450
C. –1200
D. –840
E. –600

We want to create the smallest negative number possible. Thus, the smallest product would be:

-5 x 5 x 4 x -4 x -3 = -1200

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Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

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18 Nov 2017, 08:50
Honestly, I don't understand this question...
The Number which we are looking for should be devisible by 5,4,3,2,1 and their negatives.
So, 3*4*5= 60 and 60 is devisible by all of the numbers and their negatives.

Why do we have to calculate this way: (-5)*5*4*(-4)*(-3) ?
And if we do so, why only with (-3) instead of (-5)*5*4*(-4)*(-3)*(3) ?
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What is the least possible product of 5 different integers, each of wh  [#permalink]

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18 Nov 2017, 12:43
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Bunuel wrote:
What is the least possible product of 5 different integers, each of which is between –5 and 5, inclusive?

A. –1600
B. –1450
C. –1200
D. –840
E. –600

Dokami wrote:
Honestly, I don't understand this question...
The Number which we are looking for should be devisible by 5,4,3,2,1 and their negatives.
So, 3*4*5= 60 and 60 is devisible by all of the numbers and their negatives.

Why do we have to calculate this way: (-5)*5*4*(-4)*(-3) ?
And if we do so, why only with (-3) instead of (-5)*5*4*(-4)*(-3)*(3) ?

Dokami , this is really a maximize / minimize and number properties question. Think about multiplying, the product, and the number line -- not divisibility.

You wrote, "Why do we have to calculate this way: (-5)*5*4*(-4)*(-3)?"

Because to maximize the magnitude of a number, you choose the greatest factors. I'll get to your second question.

The "least possible product" means the most negative number, a big number with a negative sign.

So we want the number farthest to the left of 0 on the number line.

To make a number with a large magnitude from of a bunch of factors multiplied, it makes sense to choose the biggest factors. Integer factors from which to choose:

$$-5\leq{x}\leq{5}$$ OR

_-5__-4__-3__-2__-1__0__1__2__3__4__5

I picked +5 and -5 first. They are the greatest factors, so they will maximize the product.

Then I picked the next two factors with greatest magnitude: +4 and -4

Now number properties enter**: do you pick 3, or -3?

With these four numbers, there are two positive numbers, and two negative numbers. Product?
(+)(+)(-)(-) = (+)(+) = (+) Positive.

We need a negative number to make the product negative: an odd number of negative factors makes a product negative.

You don't need to know that number property. These numbers are manageable.
(5 * 4 * -5 * -4) = 20 * 20 = 400, because (-5 * -4) = positive 20.

If you pick 3, you get (20 * 20 * 3) = 1200
Pick -3, and you get (20 * 20 * -3) = -1200

-1200 is the least possible product because it uses the largest factors, and is negative. It's as far from zero to the left as the numbers, multiplied, will get.

**Your second question: "And if we do so, why only with (-3) instead of (-5)*5*4*(-4)*(-3)*(3)[?]"
First, the prompt says only 5 numbers.
Second, the product of your numbers is positive, certainly not the "least possible product"; not the most to the left of 0.

Hope that helps.
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Joined: 22 Oct 2017
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Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

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19 Nov 2017, 05:15
1
Perfect, I got it! Thanks a lot!
Re: What is the least possible product of 5 different integers, each of wh &nbs [#permalink] 19 Nov 2017, 05:15
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