If 2^(x + y) = 4^8, then what is the value of y?
(1) x^2 = 81
(2) x - y = 2
Official Guide question
Answer: B
If 2^(x + y) = 4^8, then
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 83
- Joined: Mon Jul 24, 2017 8:16 am
- Followed by:1 members
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
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: What is the value of y?jjjinapinch wrote:If 2^(x + y) = 4^8, then what is the value of y?
(1) x² = 81
(2) x - y = 2
Official Guide question
Answer: B
Given: 2^(x + y) = 4^8
Rewrite right side with base of 2.
So, first replace 4 with 2² to get: 2^(x + y) = (2²)^8
Simplify right side: 2^(x + y) = 2^16
We can conclude that x + y = 16
Statement 1: x² = 81
This tells us that EITHER x = 9 OR x = -9
Let's test each case.
Case a: If x = 9, then we can take x + y = 16 and replace x with 9 to get: 9 + y = 16. When we solve this equation for y, we get y = 7
Case b: If x = -9, then we can take x + y = 16 and replace x with -9 to get: -9 + y = 16. When we solve this equation for y, we get y = 25
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x - y = 2
Since we also know that x + y = 16 , we now have a system of 2 variables with equations, which we COULD solve for y (but we won't do because we don't want to waste valuable time).
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT
Aside: For "fun" let's solve the following system:
x + y = 16
x - y = 2
If we SUBTRACT the bottom equation from the top equation, we get: 2y = 14, which means y = 7
Voila!
Answer: B
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Hi All,
We're told that 2^(X + Y) = 4^8. We're asked for the value of Y. This question is based heavily on how you recognize patterns and organize your information. To start, we can rewrite the 'right side' of the equation to put it in a 'power of 2.' Since 4 = 2^2, the value 4^8 can be rewritten as (2^2)^8 = 2^16. Thus...
2^(X + Y) = 2^16.... meaning that (X+Y) = 16.
1) X² = 81
With the information in Fact 1, we know that X could be +9 or -9
IF....
X = +9, then Y=7
X = -9, then Y=25
Fact 1 is INSUFFICIENT
2) (X - Y) = 2
Fact 2 gives us a second unique equation using the variables X and Y, so we have a 'system' of equations and we CAN solve for the exact values of X and Y. We don't actually have to do that work, but if we did, we'd find that X=9 and Y=7.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that 2^(X + Y) = 4^8. We're asked for the value of Y. This question is based heavily on how you recognize patterns and organize your information. To start, we can rewrite the 'right side' of the equation to put it in a 'power of 2.' Since 4 = 2^2, the value 4^8 can be rewritten as (2^2)^8 = 2^16. Thus...
2^(X + Y) = 2^16.... meaning that (X+Y) = 16.
1) X² = 81
With the information in Fact 1, we know that X could be +9 or -9
IF....
X = +9, then Y=7
X = -9, then Y=25
Fact 1 is INSUFFICIENT
2) (X - Y) = 2
Fact 2 gives us a second unique equation using the variables X and Y, so we have a 'system' of equations and we CAN solve for the exact values of X and Y. We don't actually have to do that work, but if we did, we'd find that X=9 and Y=7.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
We can simplify the given equation to:jjjinapinch wrote:If 2^(x + y) = 4^8, then what is the value of y?
(1) x^2 = 81
(2) x - y = 2
2^(x + y) = 2^16
x + y = 16
We need to determine the value of y.
Statement One Alone:
x^2 = 81
Since we see that x could be 9 or -9, we cannot determine a unique value for y. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
x - y = 2
We see that x = 2 + y, so, substituting, we have:
2 + y + y = 16
2y = 14
y = 7
Statement two alone is sufficient to answer the question.
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews