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chetan2u
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GMAT Focus 1: 735 Q90 V89 DI81
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How many unique values of set (a,b) are possible if a and b are intege 12 Apr 2018, 08:25
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95% (hard)

Question Stats:

25% (01:49) correct 75% (01:54) wrong based on 185 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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D
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How many unique values of set (a,b) are possible if a and b are intege 12 Apr 2018, 10:57
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chetan2u
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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\(a^2-b^2=29\)
\((a-b)*(a+b)=29\)

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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Gladi
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How many unique values of set (a,b) are possible if a and b are intege 12 Apr 2018, 21:11
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chetan2u
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
Show more



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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How many unique values of set (a,b) are possible if a and b are intege 24 Apr 2018, 21:06
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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
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How many unique values of set (a,b) are possible if a and b are intege 02 Mar 2020, 10:22
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Consider following cases
Case 1
a+b = 1
a-b = 29
a = 15 b= -14

Case 2
a+b =29
a-b = 1
a=15 b = 14

Case 3

a-b =-1
a+b = -29
a= -15 ; b = -14

Case 4
a-b =-29
a+b = -1
a= -15 ; b = 14

Hence 4 values . Hence D
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How many unique values of set (a,b) are possible if a and b are intege 01 May 2024, 23:26
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