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Wrong answer is given as correct ? Exponentiation DS questio

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Source: — Data Sufficiency |
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by GMATinsight » Tue Jul 22, 2014 9:42 am
sapuna wrote:https://prikachi.com/images.php?images/643/7486643h.jpg

What are your thoughts. I don`t see how I can possibly be wrong here as I tried both 1/2 and 1 for x
Below explanation follows if x and y were NOT given as Positive Integers, which is what the question must have meant

Question : Is (4^x) (1/3^y) < 1?

Question Rephrased : Is (4^x) < (3^y) ?

Statement 1) y=2x

LHS =(4^x) and RHS =3^(2x) = 9^x
For x as positive Integer, @x=1, (4^1)<(9^1)
For x as Negative Integer, @x=-1 4^(-1)>9^(-1)

INSUFFICIENT

Statement 2) y=4
x is unknown therefore comparison can't be established

INSUFFICIENT

Combining the two statements
y = 2x and y = 4
y = 4 and x = 2
therefore,
(4^x) and (3^y) become
(4^2) and (3^4)
therefore, (4^x) < (3^y)

SUFFICIENT

Answer: Option C
Last edited by GMATinsight on Tue Jul 22, 2014 9:49 am, edited 1 time in total.
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by GMATinsight » Tue Jul 22, 2014 9:48 am
sapuna wrote:https://prikachi.com/images.php?images/643/7486643h.jpg

What are your thoughts. I don`t see how I can possibly be wrong here as I tried both 1/2 and 1 for x
Below explanation follows if x and y ARE Positive Integers as mentioned in the question

Question : Is (4^x) (1/3^y) < 1?

Question Rephrased : Is (4^x) < (3^y) ?

Statement 1) y=2x

LHS =(4^x) and RHS = 3^y =3^(2x) = 9^x
For x and Y as positive Integer, @x=1, (4^1)<(9^1)
For x and Y as positive Integer, @x=2, (4^2)<(9^2)

SUFFICIENT

Statement 2) y=4
x is unknown therefore comparison can't be established

INSUFFICIENT

Answer: Option A
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by Brent@GMATPrepNow » Tue Jul 22, 2014 1:06 pm
As it is written in your post, the correct answer is A
If x and y are POSITIVE integers, is (4^x)(1/3)^y < 1?

1) y = 2x
2) y = 4

Target question: Is (4^x)(1/3)^y < 1?

Statement 1: y = 2x
IMPORTANT CONCEPT #1: (1/3)^2x = [(1/3)^2]^x = (1/9)^x
IMPORTANT CONCEPT #2: (a^n)(b^n) = (ab)^n

Take the target question and replace y with 2x to get: Is (4^x)(1/3)^2x < 1?
Apply concept #1 to get: Is (4^x)(1/9)^x < 1?
Apply concept #2 to get: Is (4/9)^x < 1?
If x is a POSITIVE integer, it must be the case that (4/9)^x < 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y = 4
There are several possible conflicting cases. Here are two:
Case a: x = 1 and y = 4, in which case (4^x)(1/3)^y < 1
Case b: x = 10 and y = 4, in which case (4^x)(1/3)^y > 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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