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C
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Difficulty:
15%
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Question Stats:
83% (01:09) correct
17%
(01:35)
wrong
based on 291
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History
Date
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If \(x = \sqrt[3]{a^6}\), \(y = \sqrt[3]{b^6}\), \(b ≠ 0\), and \(a = 4b\), then \(\frac{x}{y}=\)
A. 4
B. 8
C. 16
D. 32
E. 64
A. 4
B. 8
C. 16
D. 32
E. 64
The correct answer is 16.
24 Mar 2024, 01:53
Kudos
Bookmarks
machag
If \(x = \sqrt[3]{a^6}\), \(y = \sqrt[3]{b^6}\), \(b ≠ 0\), and \(a = 4b\), then \(\frac{x}{y}=\)
A. 4
B. 8
C. 16
D. 32
E. 64
A. 4
B. 8
C. 16
D. 32
E. 64
The correct answer is 16.
However, I obtained an incorrect answer of 4 by using the following method, please describe why this method is incorrect and how to obtain the correct answer:
\(\sqrt[3]{a^6}\) = a^(6/3) = a^2
\(\sqrt[3]{b^6}\) = b^(6/3) = b^2
Since a = 4b, a^2 = (4b)^2.
Therefore, \(\frac{x}{y}\) = \(\frac{4b^2}{b^2}\) = 4.
Thank you for your time and consideration.
EDIT: I just realized my mistake a minute after posting this. Since a = 4b, a^2 would equal 16b^2, not (4b)^2. Therefore, \(\frac{x}{y}\) = \(\frac{16b^2}{b^2}\) = 16.This is so embarrassing lol.
How did I make such a stupid mistake? I have a new question: how does one go about deleting a thread on this forum? I can't find a "delete" button anywhere.
However, I obtained an incorrect answer of 4 by using the following method, please describe why this method is incorrect and how to obtain the correct answer:
\(\sqrt[3]{a^6}\) = a^(6/3) = a^2
\(\sqrt[3]{b^6}\) = b^(6/3) = b^2
Since a = 4b, a^2 = (4b)^2.
Therefore, \(\frac{x}{y}\) = \(\frac{4b^2}{b^2}\) = 4.
Thank you for your time and consideration.
EDIT: I just realized my mistake a minute after posting this. Since a = 4b, a^2 would equal 16b^2, not (4b)^2. Therefore, \(\frac{x}{y}\) = \(\frac{16b^2}{b^2}\) = 16.This is so embarrassing lol.
How did I make such a stupid mistake? I have a new question: how does one go about deleting a thread on this forum? I can't find a "delete" button anywhere.
\(x = \sqrt[3]{a^6}=a^2\)
\(y = \sqrt[3]{b^6}=b^2\)
\(y = \sqrt[3]{b^6}=b^2\)
Thus, \(\frac{x}{y}=\frac{a^2}{b^2}\). Since \(a = 4b\), then \(\frac{a^2}{b^2}=\frac{(4b)^2}{b^2}=\frac{16b^2}{b^2}=16\).
Answer: C.
P.S. You can only delete your post if it's the last one in the thread. Once it receives replies, you are no longer allowed to delete it.
18 Apr 2025, 14:36
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Bookmarks
Hello from the GMAT Club BumpBot!
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
