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If the sum of two numbers is 19 and their product is 88, wh
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07 Jun 2017, 02:20
07 Jun 2017, 02:20
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Question Stats:
91% (01:09) correct
8% (02:18) wrong based on 109 sessions
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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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If the sum of two numbers is 19 and their product is 88, wh
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03 Aug 2017, 15:27
03 Aug 2017, 15:27
3
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
Answer:
Show: ::
B
Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If the sum of two numbers is 19 and their product is 88, wh
[#permalink]
03 Aug 2017, 15:33
03 Aug 2017, 15:33
2
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
Answer:
Show: ::
B
Cheers,
Brent
