Is 8^x>4^y?
1) x>y
2) 3x>2y
* A solution will be posted in two days.
Is 8^x>4^y? 1) x>y 2) 3x>2y
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- John fran kennedi
- Junior | Next Rank: 30 Posts
- Posts: 26
- Joined: Tue Feb 02, 2016 10:25 am
- Thanked: 1 times
Let me try to solve this
Statement 1:
I first plug 2 for x and 1 for Y
8^2 > 4^1. YES
I plug -2 for x and -3 for y
1/8^-2 > 1/4^-3. NO.
Hence, statement 1 is insufficient
Statement 2
I plug 1 for both x and y
8 > 4. Yes
I plug -1 for x and -2 for y
1/8 > 1/4^2, yes
Statement 2 is sufficient.
CMIW.
Statement 1:
I first plug 2 for x and 1 for Y
8^2 > 4^1. YES
I plug -2 for x and -3 for y
1/8^-2 > 1/4^-3. NO.
Hence, statement 1 is insufficient
Statement 2
I plug 1 for both x and y
8 > 4. Yes
I plug -1 for x and -2 for y
1/8 > 1/4^2, yes
Statement 2 is sufficient.
CMIW.
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Is 8^x > 4^y?Max@Math Revolution wrote:Is 8^x > 4^y?
1) x > y
2) 3x > 2y
This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Notice that we can rewrite 8 and 4 with the same BASE to get: Is (2³)^x > (2²)^y?
Now apply the power of a power law to get: Is 2^3x > 2^2y?
Since 2^2y is always positive, we can safely divide both sides by 2^2y to get: Is (2^3x)/(2^2y) > 1?
Simplify to get: Is 2^(3x -2y) > 1?
For 2^(3x -2y) to be greater than 1, the exponent, 3x - 2y, must be greater than 0.
So, we get:
REPHRASED target question: Is 3x - 2y > 0?
At this point, the question can be handled quickly
Statement 1: x > y
Can we use this information to answer the REPHRASED target question?
No.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 1. In this case 3x - 2y = 3(2) - 2(1) = 4. In other words, 3x - 2y > 0
Case b: x = -3 and y = -4. In this case 3x - 2y = 3(-3) - 2(-4) = -1. In other words, 3x - 2y < 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3x > 2y
Subtract 2y from both sides to get 3x - 2y > 0
PERFECT!!
This means we can answer the REPHRASED target question with certainty. So, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
Is 8^x>4^y?
1) x>y
2) 3x>2y
When you modify the original condition and the question, 3x>2y? is derived from 2^3x>4^2y?, which makes B the answer.
Is 8^x>4^y?
1) x>y
2) 3x>2y
When you modify the original condition and the question, 3x>2y? is derived from 2^3x>4^2y?, which makes B the answer.
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]