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26 Jul 2020, 22:51
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Difficulty:
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Question Stats:
79% (01:03) correct
21%
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based on 156
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If ab = 10, what is the value of \(a^{2}\) + \(b^{2}\)?
(1) a + b = 7
(2) 5a = \(\frac{50}{b}\)
(1) a + b = 7
(2) 5a = \(\frac{50}{b}\)
27 Jul 2020, 08:02
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Squaring both sides of Statement 1, we find
a^2 + b^2 + 2ab = 49
and since ab is 10, we can substitute '10' for 'ab' to learn that a^2 + b^2 + 20 = 49, so a^2 + b^2 = 29, and Statement 1 is sufficient.
If we multiply both sides of Statement 2 by b, then divide both sides by 5, we find ab = 10. We knew that already from the question stem, so Statement 2 gives us no new information and is not even remotely useful. The answer is A.
a^2 + b^2 + 2ab = 49
and since ab is 10, we can substitute '10' for 'ab' to learn that a^2 + b^2 + 20 = 49, so a^2 + b^2 = 29, and Statement 1 is sufficient.
If we multiply both sides of Statement 2 by b, then divide both sides by 5, we find ab = 10. We knew that already from the question stem, so Statement 2 gives us no new information and is not even remotely useful. The answer is A.
27 Jul 2020, 08:30
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Statement 1:
a+b = 7
Squaring on both sides,\( (a+b)^2\) =\( 7^2\)
\(a^2\)+2ab+\(b^2\) = 49
\(a^2\)+\(b^2\) = 49-(2*10)
Statement 1 is sufficient.
Statement 2:
5a =\( \frac{50}{b}\)
5ab = 50
ab = 10
From here, we don't know what are the values of a and b
Statement 2 is insufficient
Answer A
a+b = 7
Squaring on both sides,\( (a+b)^2\) =\( 7^2\)
\(a^2\)+2ab+\(b^2\) = 49
\(a^2\)+\(b^2\) = 49-(2*10)
Statement 1 is sufficient.
Statement 2:
5a =\( \frac{50}{b}\)
5ab = 50
ab = 10
From here, we don't know what are the values of a and b
Statement 2 is insufficient
Answer A
