|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
16 May 2018, 06:49
Kudos
Bookmarks
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 94
sessions
History
Date
Time
Result
Not Attempted Yet
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) \(b^{(x+y)} < 1\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
16 May 2018, 11:57
Kudos
Bookmarks
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
Kudos
Bookmarks
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
