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

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
If the sum of two numbers is 19 and their product is 88, what is the  [#permalink]

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17 May 2018, 04:58
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85% (00:58) correct 15% (01:00) wrong based on 64 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

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Re: If the sum of two numbers is 19 and their product is 88, what is the  [#permalink]

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17 May 2018, 11:00
Bunuel 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

$$a + b = 19$$
$$ab = 88$$

Or, $$a = 19 - b$$

So, We have : $$(19 - b)b = 88$$

Or, $$b^2 - 19b + 88 = 0$$

Or, $$b^2 -11b - 8b + 88 = 0$$

Or, $$b(b - 11) -8(b - 11) = 0$$

So, $$b = 11$$ and $$8$$

Thus, difference of the numbers is 3, answer must be (B)
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Re: If the sum of two numbers is 19 and their product is 88, what is the  [#permalink]

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17 May 2018, 15:41
Abhishek009 wrote:
So, We have : $$(19 - b)b = 88$$

Or, $$b^2 - 19b + 88 = 0$$
Or, $$b^2 -11b - 8b + 88 = 0$$
Or, $$b(b - 11) -8(b - 11) = 0$$
So, $$b = 11$$ and $$8$$

Thus, difference of the numbers is 3, answer must be (B)

I think that this is enough to stop here (19−b)b=88 and pick a number, rather than to solve quadratic equation. One of the aim of this forum is to teach people to use their time effectively.
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Re: If the sum of two numbers is 19 and their product is 88, what is the  [#permalink]

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19 May 2018, 09:39
we know a+b = 19
and ab=88

there aren't many numbers that can add to 19

so if we start from 10 and 9
10*9=190
11* 8 = 88 ( satisfies ab=88)
so 11-8 = 3
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Re: If the sum of two numbers is 19 and their product is 88, what is the  [#permalink]

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28 Feb 2019, 00:07
(x+y)^2-(x-y)^2=4xy
x+y=19
xy=88
substituting values
(x-y)^2=9
x-y=3

Posted from my mobile device
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Re: If the sum of two numbers is 19 and their product is 88, what is the  [#permalink]

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28 Feb 2019, 06:02
Bunuel 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

a+b=19
ab=88
so
a=88b
solve
we get a=11,b=8
difference = 3
IMO B
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Posts: 905
Re: If the sum of two numbers is 19 and their product is 88, what is the  [#permalink]

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07 Mar 2019, 10:04
Archit3110 wrote:
Bunuel 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

a+b=19
ab=88
so
a=88b
solve
we get a=11,b=8
difference = 3
IMO B

sorry, did you mean a=$$\frac{88}{b}$$ or a=88b? Please can you check.
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Re: If the sum of two numbers is 19 and their product is 88, what is the   [#permalink] 07 Mar 2019, 10:04
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