When posting questions, please use brackets and spaces to avoid ambiguity.gdshamain wrote:41. Is 4^x+y = 8^10?
(1) x-y = 9
(2) y/x = 1/4
Based on your solution, the question SHOULD read:
Does 4^(x+y) = 8^10?
1) x - y =9
2) y/x = 1/4
Cheers,
Brent
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OG 13 - problem 41
Source: Beat The GMAT — Data Sufficiency |
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Brent@GMATPrepNow
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Based on your solution, the question SHOULD read:
Does 4^(x+y) = 8^10?
1) x - y =9
2) y/x = 1/4
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
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Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
- GMAT Score:770
This is a great candidate for rephrasing the target question.Does 4^(x+y) = 8^10?
1) x - y = 9
2) y/x = 1/4
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Target question: Does 4^(x+y) = 8^10?
Take 4^(x+y) = 8^10 and rewrite each side with the same base of 2 to get:
(2^2)^(x+y) = (2^3)^10
Simplify to get: 2^(2x + 2y) = 2^30 [power of a power rule]
For this equation to hold true, it must be the case that 2x + 2y = 30
Divide both sides by 2 to get x + y = 15
We can now REPHRASE our target question...
REPHRASED target question: Does x + y = 15?
Statement 1: x - y = 9
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 12 and y = 3, in which case x + y = 15
Case b: x = 10 and y = 1, in which case x + y ≠15
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y/x = 1/4
Cross multiply to get: x = 4y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 12 and y = 3, in which case x + y = 15
Case b: x = 8 and y = 2, in which case x + y ≠15
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x - y = 9
Statement 2 tells us that x = 4y
We now have a system of TWO linear equations with TWO variables, so we COULD easily solve this system for x and y, which means we COULD determine whether x + y = 15.
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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GMATGuruNY
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To answer the question stem, we need to know the value of x+y.gdshamain wrote:41. Is 4^(x+y) = 8^10?
(1) x-y = 9
(2) y/x = 1/4
Question stem, rephrased: What is the value of x+y?
Statement 1: x-y=9
If x=9 and y=0, then x+y = 9+0 = 9.
If x=10 and y=1, then x+y = 10+1 = 11.
Since x+y can be different values, INSUFFICIENT.
Statement 2: y/x = 1/4
Cross-mulitplying, we get:
4y = x.
If y=1 and x=4, then x+y = 4+1 = 5.
If y=2 and x=8, then x+y = 8+2 = 10.
Since x+y can be different values, INSUFFICIENT.
Statements combined:
Since we have 2 variables and 2 distinct linear equations, we can solve for each variable.
Thus, the value of x+y can be determined.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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