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

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

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New post 12 Apr 2018, 07:25
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A
B
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Difficulty:

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Question Stats:

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

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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

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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


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Re: How many unique values of set (a,b) are possible if a and b are intege  [#permalink]

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New post 12 Apr 2018, 09:57
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.

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Re: How many unique values of set (a,b) are possible if a and b are intege  [#permalink]

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New post 12 Apr 2018, 20:11
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
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Re: How many unique values of set (a,b) are possible if a and b are intege  [#permalink]

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New post 24 Apr 2018, 20:06
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.

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Re: How many unique values of set (a,b) are possible if a and b are intege &nbs [#permalink] 24 Apr 2018, 20:06
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How many unique values of set (a,b) are possible if a and b are intege

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