GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Sep 2018, 13:45

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49251
What is the least possible product of 5 different integers, each of wh  [#permalink]

### Show Tags

05 Dec 2016, 02:28
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:02) correct 22% (01:18) wrong based on 169 sessions

### HideShow timer Statistics

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

_________________
Senior Manager
Joined: 21 Aug 2016
Posts: 277
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

### Show Tags

05 Dec 2016, 04:33
2
Following 5 distinct values will give the least possible product
(-5)*5*4*(-4)*(-3)
=(-25)*(-16)*(-3)
=-1200
-------
+1 Kudos if you like the post
Intern
Joined: 21 Apr 2015
Posts: 5
Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

### Show Tags

27 Oct 2017, 04:11
AR15J wrote:
Following 5 distinct values will give the least possible product
(-5)*5*4*(-4)*(-3)
=(-25)*(-16)*(-3)
=-1200
-------
+1 Kudos if you like the post

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

Thanks.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

### Show Tags

30 Oct 2017, 14:04
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

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 22 Oct 2017
Posts: 31
Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

### Show Tags

18 Nov 2017, 09:50
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) ?
Senior SC Moderator
Joined: 22 May 2016
Posts: 1977
What is the least possible product of 5 different integers, each of wh  [#permalink]

### Show Tags

18 Nov 2017, 13:43
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

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.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Intern
Joined: 22 Oct 2017
Posts: 31
Re: What is the least possible product of 5 different integers, each of wh  [#permalink]

### Show Tags

19 Nov 2017, 06:15
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, 06:15
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.