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# If the sum of two numbers is 19 and their product is 88, wh

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If the sum of two numbers is 19 and their product is 88, wh [#permalink]  07 Jun 2017, 02:20
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If the sum of two numbers is 19 and their product is 88, what is the difference between the numbers?

A) 2

B) 3

C) 4

D) 5

E) 6
[Reveal] Spoiler: OA

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GRE Instructor
Joined: 10 Apr 2015
Posts: 637
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Kudos [?]: 449 [1] , given: 3

Re: If the sum of two numbers is 19 and their product is 88, wh [#permalink]  03 Aug 2017, 15:27
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Expert's post
Carcass wrote:

If the sum of two numbers is 19 and their product is 88, what is the difference between the numbers?

A) 2

B) 3

C) 4

D) 5

E) 6

If the sum of two numbers is 19 and their product is 88
A quick solution is to examine all pairs of INTEGERS that have a product of 88
They are:
1 and 88
2 and 44
4 and 22
8 and 11

Notice that one pair (8 and 11) meets the second condition that the sum of the two numbers is 19
So, the two numbers must be 8 and 11

What is the difference between the numbers?
11 - 8 = 3

[Reveal] Spoiler:
B

Cheers,
Brent
_________________

Brent Hanneson – Founder of greenlighttestprep.com

Check out the online reviews of our course

GRE Instructor
Joined: 10 Apr 2015
Posts: 637
Followers: 29

Kudos [?]: 449 [1] , given: 3

Re: If the sum of two numbers is 19 and their product is 88, wh [#permalink]  03 Aug 2017, 15:33
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Expert's post
Carcass wrote:

If the sum of two numbers is 19 and their product is 88, what is the difference between the numbers?

A) 2

B) 3

C) 4

D) 5

E) 6

Another approach:

Let x = one of the numbers
Let y = the other number

The sum of two numbers is 19....
We can write: x + y = 19

... and their product is 88
xy = 88

We have two equations:
x + y = 19
xy = 88

Rewrite x + y = 19 as y = 19 - x
Now take xy = 88 and replace y with 19 - x to get: (x)(19 - x) = 88
Expand to get: 19x - x² = 88
Rearrange to get: x² - 19x + 88 = 0
Factor to get: (x - 11)(x - 8) = 0
So, EITHER x = 11 OR x = 8
If x = 11, then y = 8
If x = 8, then y = 11

What is the difference between the numbers?
In either case, the difference = 11 - 8 = 3

Cheers,
Brent

[Reveal] Spoiler:
B

Cheers,
Brent
_________________

Brent Hanneson – Founder of greenlighttestprep.com

Check out the online reviews of our course

Re: If the sum of two numbers is 19 and their product is 88, wh   [#permalink] 03 Aug 2017, 15:33
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