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16 May 2018, 06:49
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (02:02) correct
46%
(01:45)
wrong
based on 93
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Given that a > 1 and b > 1. Is \((a^x)(b^y)<1?\)
(1) \(a^{(x+y)} < 1\)
(2) \(b^{(x+y)} < 1\)
(1) \(a^{(x+y)} < 1\)
(2) \(b^{(x+y)} < 1\)
16 May 2018, 11:57
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Bunuel
We need values or relationship between \(a\) & \(b\) and \(x\) & \(y\)
Statement 1: \(a^{(x+y)} < 1=>a^{(x+y)} <a^0\)
Therefore \(x+y<0\). but we cannot get the relationship or values of \(a\) & \(b\) or \(x\) & \(y\). Insufficient
Statement 2: \(b^{(x+y)} < 1=>b^{x+y}<b^0\)
therefore \(x+y<0\). Again same as statement 1: Insufficient
Combining 1 & 2: we cannot get any values, hence Insufficient
Option E
16 May 2018, 18:42
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I approached this problem logically...
Since both a and b are greater than 1, \((a^x)(b^y)\) will be less than 1 if:
-both x and y are negative (and the exact values of a or b dont matter), or
-one of x or y is negative and the other is non negative, but then we need to know how big or small is (a^x) and how big or small is (b^y).... because it's possible that (a^x)(b^y) is something like (1/100)*5 which is less than 1... or (1/2)*4 which is greater than 1
Statement 1
This tells us that x+y is less than 0. We dont know if both x and y are negative. However, we do know that at least one of x and y is negative. We still dont know a and b, thus this statement is insufficient.
Consider a=2, b=10, x=-3, y=2. Then \((a^x)(b^y)=2^{-3}10^2=\frac{1}{8}*100\) .... greater than 1
Consider a=2, b=2, x=-3, y=2. Then \((a^x)(b^y)=2^{-3}2^2=\frac{1}{8}*4\).... less than 1
This example can be used to show that Statement 2 is insufficient and that both statement combined are insufficient.
Answer: E
Since both a and b are greater than 1, \((a^x)(b^y)\) will be less than 1 if:
-both x and y are negative (and the exact values of a or b dont matter), or
-one of x or y is negative and the other is non negative, but then we need to know how big or small is (a^x) and how big or small is (b^y).... because it's possible that (a^x)(b^y) is something like (1/100)*5 which is less than 1... or (1/2)*4 which is greater than 1
Statement 1
This tells us that x+y is less than 0. We dont know if both x and y are negative. However, we do know that at least one of x and y is negative. We still dont know a and b, thus this statement is insufficient.
Consider a=2, b=10, x=-3, y=2. Then \((a^x)(b^y)=2^{-3}10^2=\frac{1}{8}*100\) .... greater than 1
Consider a=2, b=2, x=-3, y=2. Then \((a^x)(b^y)=2^{-3}2^2=\frac{1}{8}*4\).... less than 1
This example can be used to show that Statement 2 is insufficient and that both statement combined are insufficient.
Answer: E
