GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Apr 2020, 16:36

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62619
The difference between the squares of two positive integers is 2011 wh  [#permalink]

### Show Tags

12 Nov 2019, 01:33
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:03) correct 29% (02:21) wrong based on 115 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8314
The difference between the squares of two positive integers is 2011 wh  [#permalink]

### Show Tags

12 Nov 2019, 04:21
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
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9972
Location: United States (CA)
Re: The difference between the squares of two positive integers is 2011 wh  [#permalink]

### Show Tags

20 Nov 2019, 18:14
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3348
Re: The difference between the squares of two positive integers is 2011 wh  [#permalink]

### Show Tags

24 Nov 2019, 20:05

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.

_________________
Senior Manager
Joined: 13 Feb 2018
Posts: 435
GMAT 1: 640 Q48 V28
The difference between the squares of two positive integers is 2011 wh  [#permalink]

### Show Tags

17 Jan 2020, 03:16
We are given
$$a^2-b^2=2011$$ --> $$(a-b)*(a+b)=2011$$
We want to maximise a+b

I don't know whether 2011 is prime or not
The only thing I know is that it's nor divisible by 2, 3, 5

What to do
Let us glance at the options

1) 1002; we cant multiply 1002 by any integer value to get 2011 (we are looking for integer value because the stem says a and b are integers, so their subtraction would be an integer as well)
B. 1005; nope
C. 1007; no way
D. 1809; definitely no
E. None of these

We are left with E
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4874
Location: India
GPA: 3.5
Re: The difference between the squares of two positive integers is 2011 wh  [#permalink]

### Show Tags

17 Jan 2020, 10:36
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

$$a^2 - b^2 = 2011$$
$$(a + b)(a - b) = 2011$$

Divide 2011/2 = 1005.50

Now, Let a = 1006 & b = 1005

Now, we have -

$$(1006 + 1005)( 1006 - 1005 ) = 2011*1$$

Thus, the greatest possible sum of those two integers must be 2011 , Answer must be (E)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Joined: 29 Nov 2019
Posts: 2
GPA: 3.91
WE: Consulting (Consulting)
Re: The difference between the squares of two positive integers is 2011 wh  [#permalink]

### Show Tags

17 Jan 2020, 10:56
[quote="Bunuel"]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

Can you solve by process of elim here?

(a^2 - b^2 ) = 2011
(a + b ) (a - b) = 2011
therefore:
(a - b) = 2011 / (a + b)
and (a - b) must be a integer.

check divisibility of answer choices. They all fail <-- therefore: none of these (E).

Is this acceptable?
Re: The difference between the squares of two positive integers is 2011 wh   [#permalink] 17 Jan 2020, 10:56
Display posts from previous: Sort by