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29 May 2018, 02:19
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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21% (02:29) correct
79%
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wrong
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A function \(F(x, y) =(x^y)^1^/^x\) for positive integers x and y. Is \(F(a, b) > a\), where a and b are positive integers?
(1) \(F(a,ab)≥F(a,a^2)\)
(2) \(F(b^2,b^2)>F(a,a)^2\)
(1) \(F(a,ab)≥F(a,a^2)\)
(2) \(F(b^2,b^2)>F(a,a)^2\)
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29 May 2018, 09:21
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PrayasT
Is \(F(a, b) > a\) \(=>a^\frac{b}{a}>a^1\)
=> Is \(\frac{b}{a}>1=>\) Is \(b>a\) ?
Statement 1: implies \(a^\frac{ab}{a}≥a^\frac{(a^2)}{a}\)
\(=>a^b≥a^a=>b≥a\). Here \(b\) can be equal to \(a\) or greater than \(a\). Hence Insufficient
Statement 2: implies \((b^2)^{\frac{b^2}{b^2}}>(a^{\frac{a}{a}})^2\)
\(=>b^2>a^2=>b>a\), because \(a\) & \(b\) are positive. Sufficient
Option \(B\)
26 Jun 2018, 21:17
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Counterexample: A=1, B=2
This fulfills both conditions 1 and 2:
1. F(1,2) = 1 ≥ F(1,1) = 1
2. F(4,4) = 4 > F(1,1)^2 = 1
Yet does not meet the inequality in the prompt:
F(1,2) = 1 is NOT greater than 1.
Choosing A ≥ 2 would make the answer B, but because we made no such restriction, the answer is E.
This fulfills both conditions 1 and 2:
1. F(1,2) = 1 ≥ F(1,1) = 1
2. F(4,4) = 4 > F(1,1)^2 = 1
Yet does not meet the inequality in the prompt:
F(1,2) = 1 is NOT greater than 1.
Choosing A ≥ 2 would make the answer B, but because we made no such restriction, the answer is E.
