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08 Apr 2023, 00:48
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
49% (02:33) correct
51%
(02:24)
wrong
based on 73
sessions
History
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G number of girls and B number of boys are students of a school S. A test is conducted in the school. If all students of school S appeared in the test, is the ratio of students who pass the test to the ratio of students who fail more for girl students than for the entire school S?
(A) The ratio of the number of students who pass to the number of students who fail is more for boy students than for the entire school.
(B) Less than 3/7 of the total students who pass the test are girls and less than 13/25 of the total students who fail the test are boys.
(A) The ratio of the number of students who pass to the number of students who fail is more for boy students than for the entire school.
(B) Less than 3/7 of the total students who pass the test are girls and less than 13/25 of the total students who fail the test are boys.
08 Apr 2023, 01:33
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ChandlerBong
Attachment:
Screenshot 2023-04-08 133241.jpg [ 30.03 KiB | Viewed 1706 times ]
Representations
- Boys Passed = \(B_P\)
- Boys Failed = \(B_F\)
- Girls Passed = \(G_P\)
- Girls Failed = \(G_F\)
Question
\(\frac{G_P}{G_F} > \frac{B_P + G_P}{B_F + G_F}\)
Cross multiplying as the numbers are positive
\((G_PB_F) + (G_PG_F)> (B_PG_F) +(G_FG_P) \)
Substracting \(G_FG_P\) from both sides
\( (G_PB_F)> (B_PG_F)\)
or
\(\frac{B_F}{G_F} > \frac{B_P}{G_P} \)
This is our target question.
Statement 1
(A) The ratio of the number of students who pass to the number of students who fail is more for boy students than for the entire school.
\(\frac {B_P}{B_F} > \frac{B_P+G_P}{B_F+G_F}\)
Cross multiplying as the numbers are positive
\((B_PB_F)+(B_PG_F) > (B_FB_P)+(G_PB_F)\)
Substracting \(B_FB_P\) from both sides
\((B_PG_F) > (B_FG_P)\)
The equation matches the target question, hence this statement is sufficient. We can eliminate B, C, and D.
Statement 2
(B) Less than 3/7 of the total students who pass the test are girls and less than 13/25 of the total students who fail the test are boys.
Less than 3/7 of the total students who pass the test are girls
\(\frac{G_P}{G_P + B_P} < \frac{3}{7}\)
\(7G_P < 3G_P + 3B_P\)
Substracting \(3G_P\) from both sides we get,
\(4G_P < 3B_P\)
\(\frac{G_P}{B_P} < \frac{3}{4} \implies\) \(\frac{B_P}{G_P} > \frac {4}{3} \)
\(\approx \frac{B_P}{G_P} > 1.33 \)
less than 13/25 of the total students who fail the test are boys.
\(\frac{B_F}{G_F + B_F} < \frac{13}{25}\)
\(25 B_F < 13G_F + 13B_F\)
Substracting \(13B_F\) from both sides we get,
\(12 B_F < 13G_F \implies\) \(\frac{B_F}{G_F} < \frac {13}{12} \)
\(\approx \frac{B_F}{G_F} < 1.08\)
Therefore we can conclude that
\(\frac{B_F}{G_F} < \frac{B_P}{G_P} \)
This information is sufficient as well.
Option D
General Discussion
01 Jul 2024, 20:14
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Hello from the GMAT Club BumpBot!
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).
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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.
