GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2018, 02:11

### 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

# How many unique values of set (a,b) are possible if a and b are intege

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 6965
How many unique values of set (a,b) are possible if a and b are intege  [#permalink]

### Show Tags

12 Apr 2018, 08:25
1
10
00:00

Difficulty:

95% (hard)

Question Stats:

21% (01:49) correct 79% (01:34) wrong based on 93 sessions

### HideShow timer Statistics

How many unique values of set (a,b) are possible if a and b are integers and $$a^2-b^2=29$$?
(A) 1
(B) 2
(C) 3
(D) 4
(E) indefinite

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Senior Manager
Joined: 16 Sep 2016
Posts: 303
GMAT 1: 740 Q50 V40
Re: How many unique values of set (a,b) are possible if a and b are intege  [#permalink]

### Show Tags

12 Apr 2018, 10:57
2
chetan2u wrote:
How many unique values of set (a,b) are possible if a and b are integers and $$a^2-b^2=29$$?
(A) 1
(B) 2
(C) 3
(D) 4
(E) indefinite

$$a^2-b^2=29$$
$$(a-b)*(a+b)=29$$

since 29 is a prime number... so 29 = 1*29 are the only two prime factors.

Only two possibilities:
$$a+b = 29$$
$$a-b = 1$$

&
$$a+b = 1$$
$$a-b = 29$$

for first on solving a = 15 & b = 14
for second on solving a = 15 & b = -14

Hence we have two unique values for the pair (a,b) : (15,14) & (15,-14)

Hence Option (B) is our answer.

Best,
Manager
Joined: 05 Dec 2017
Posts: 52
Location: India
WE: Analyst (Commercial Banking)
Re: How many unique values of set (a,b) are possible if a and b are intege  [#permalink]

### Show Tags

12 Apr 2018, 21:11
chetan2u wrote:
How many unique values of set (a,b) are possible if a and b are integers and $$a^2-b^2=29$$?
(A) 1
(B) 2
(C) 3
(D) 4
(E) indefinite

a^2−b^2=29
(a−b)∗(a+b)=29*1
for a-b = 1 and a+b=29, a=15 and b=14
since we are dealing with even power of a and b, both +ve and -ve values are to be considered

so value of (a,b) = (15,14), (15,-14), (-15,14), (-15,-14)
hence 4 values Option D
Director
Joined: 02 Oct 2017
Posts: 643
Re: How many unique values of set (a,b) are possible if a and b are intege  [#permalink]

### Show Tags

24 Apr 2018, 21:06
One needs to consider possibilities

(a+b)(a-b)=29
a+b=29 a-b=1
Also other cases
a+b=1 a-b=29
a+b=-29 a-b=-1
a+b=-1 a-b=-29

Solve these equation find values.. that's it.

Posted from my mobile device
_________________

Give kudos if you like the post

Re: How many unique values of set (a,b) are possible if a and b are intege &nbs [#permalink] 24 Apr 2018, 21:06
Display posts from previous: Sort by