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# The difference between the squares of two positive integers is 2011 wh

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Math Expert
Joined: 02 Sep 2009
Posts: 59573
The difference between the squares of two positive integers is 2011 wh  [#permalink]

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12 Nov 2019, 02:33
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45% (medium)

Question Stats:

70% (02:00) correct 30% (02:17) wrong based on 67 sessions

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The difference between the squares of two positive integers is 2011 what is the greatest possible sum of those two integers?

A. 1002
B. 1005
C. 1007
D. 1809
E. None of these

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Math Expert
Joined: 02 Aug 2009
Posts: 8284
The difference between the squares of two positive integers is 2011 wh  [#permalink]

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12 Nov 2019, 05:21
Bunuel wrote:
The difference between the squares of two positive integers is 2011 what is the greatest possible sum of those two integers?

A. 1002
B. 1005
C. 1007
D. 1809
E. None of these

Are You Up For the Challenge: 700 Level Questions

Let the two numbers be a and b, so $$a^2-b^2=2011....(a-b)(a+b)=1*2011$$
$$a-b=1$$ and $$a+b=2011$$...
Straight a+b=2011
OR
Add to get 2a=1+2011...a=1006 and b, therefore,=1005
$$SUM=1005+1006$$

E
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Re: The difference between the squares of two positive integers is 2011 wh  [#permalink]

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20 Nov 2019, 19:14
Bunuel wrote:
The difference between the squares of two positive integers is 2011 what is the greatest possible sum of those two integers?

A. 1002
B. 1005
C. 1007
D. 1809
E. None of these

Are You Up For the Challenge: 700 Level Questions

We can create the equation:

a^2 - b^2 = 2011

(a + b)(a - b) = 2011

Since 2011 is a prime, we see that a + b = 2011 and a - b = 1. We see that the sum of the two integers must be 2011.

Answer: E
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Re: The difference between the squares of two positive integers is 2011 wh  [#permalink]

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24 Nov 2019, 21:05

Solution

Given:
• The difference between the squares of two positive integers = 2011

To find:
• The greatest possible sum of those two integers

Approach and Working Out:
• Given, $$a^2 – b^2 = 2011$$
o Implies, (a + b) * (a – b) = 2011

• We know that 2011 is a prime number, so it can be expressed as product of two positive integers in only one way = 1 * 2011
• Thus, a + b = 2011

Hence, the correct answer is Option E.

Answer: E
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Re: The difference between the squares of two positive integers is 2011 wh   [#permalink] 24 Nov 2019, 21:05
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