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76% (02:48) correct
24%
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There are two positive integers \(𝑎\) and \(𝑏\), where \(𝑎 > 𝑏\). The sum of the squares of these integers is equal to 5 times their sum. The difference of the squares of these integers is equal to 9 times their difference. What is the value of \(𝑎 − 𝑏\)?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
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18 Apr 2022, 05:48
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18 Apr 2022, 02:15
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GMATNinja
There are two positive integers \(𝑎\) and \(𝑏\), where \(𝑎 > 𝑏\). The sum of the squares of these integers is equal to 5 times their sum. The difference of the squares of these integers is equal to 9 times their difference. What is the value of \(𝑎 − 𝑏\)?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
given
a>b
a^2+b^2 = 5*( a+b)
a^2-b^2= 9* (a-b)
add both
2*a^2 = 14a-4b
a^2 = 7a-2b
plugin values we see at a = 6 and b = 3 expression is valid
a-b= 3 correct option a
