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Updated on: 24 Jul 2019, 05:03
Originally posted by Bunuel on 24 Jul 2019, 00:15.
Last edited by Sajjad1994 on 24 Jul 2019, 05:03, edited 1 time in total.
Last edited by Sajjad1994 on 24 Jul 2019, 05:03, edited 1 time in total.
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The arithmetic mean (average) of the numbers a and b is 5, and the geometric mean of the numbers a and b is 8. Then a^2 – 10a =
(Note: the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is,\(\sqrt {2*8}=4\))
(A) –64
(B) 76
(C) 82
(D) 96
(E) 102
Source: Nova GMAT
(Note: the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is,\(\sqrt {2*8}=4\))
(A) –64
(B) 76
(C) 82
(D) 96
(E) 102
Source: Nova GMAT
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24 Jul 2019, 00:22
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\(\frac{a+b}{2}=5\) or \(a+b=10\) which implies \(b=10-a\)
\(\sqrt{ab}=8\) or \(ab=64\)
Since \(b=10-a\)
\(a(10-a)=64\)
\(10a-a^2=64\) or
\(a^2-10a=-64\)
Answer is (A)
\(\sqrt{ab}=8\) or \(ab=64\)
Since \(b=10-a\)
\(a(10-a)=64\)
\(10a-a^2=64\) or
\(a^2-10a=-64\)
Answer is (A)
24 Jul 2019, 00:28
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(a+b)/2 = 5
a + b = 10 ---------(1)
(ab)^1/2 = 8
squaring both sides...
so, ab = 64 -------- (2)
Using (1) and (2)
a*(10-a) = 64
10 a - a^2 = 64
Multiplying both sides by -1,
a^2 - 10a = -64 (A)
a + b = 10 ---------(1)
(ab)^1/2 = 8
squaring both sides...
so, ab = 64 -------- (2)
Using (1) and (2)
a*(10-a) = 64
10 a - a^2 = 64
Multiplying both sides by -1,
a^2 - 10a = -64 (A)
