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20 Feb 2023, 07:37
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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:
75%
(hard)
Question Stats:
53% (02:13) correct
47%
(02:15)
wrong
based on 135
sessions
History
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Not Attempted Yet
There is a certain number of students in Mr. Stewart’s class. Could Mr. Stewart evenly divide the class into 3 study groups?
(1) If Mr. Stewart reduced the number of students in his class by 16 percent he could evenly divide the class into groups of 9.
(2) If Mr. Stewart reduced the number of students in his class by 6 percent he could evenly divide the class into groups of 3.
(1) If Mr. Stewart reduced the number of students in his class by 16 percent he could evenly divide the class into groups of 9.
(2) If Mr. Stewart reduced the number of students in his class by 6 percent he could evenly divide the class into groups of 3.
25 Feb 2023, 09:00
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Bunuel
We need to know whether \(s\) is a multiple of \(3 \)
\(s =\) # of students hence \(s\) needs to be an integer.
(1) If Mr. Stewart reduced the number of students in his class by 16 percent he could evenly divide the class into groups of 9.
\(\frac{84}{100}*s = 9*y \)
\(s= \frac{9*y}{84}*100\)
\(s= \frac{ 3 * y}{7}*25\)
Since \(s\) is an integer \(y\) has to be a multiple of \(7\) , so we can remove the \(7\) from the denominator
\(s=3*25 \)
We can ans YES to the stem as \(s\) is a multiple of \(3 \)
SUFF.
(2) If Mr. Stewart reduced the number of students in his class by 6 percent he could evenly divide the class into groups of 3
\(\frac{94}{100}*s = 3*y \)
\(s= \frac{3*y}{94}*100\)
\(s= \frac{3*y}{47}*50\)
Since \(s\) needs to be an integer \(y\) is a multiple of \(47 \), hence the \(47\) in the denominator gets cancelled out.
\(s=3*50 \)
We can ans YES to the stem as \(s\) is a multiple of \(3 \)
SUFF.
Ans D
Hope it helps.
13 Mar 2023, 02:03
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Bunuel
Solution:
Pre Analysis:
- Let the number of students in the class be \(n\)
- We are asked if n is divisible by 3 or not
Statement 1: If Mr. Stewart reduced the number of students in his class by 16 percent he could evenly divide the class into groups of 9
- According to this statement, \(n(1-\frac{16}{100})=9k\) where k is a positive integer
\(⇒n\times \frac{84}{100}=9k\)
\(⇒n=\frac{9k\times 100}{84}\)
\(⇒n=3\frac{k\times 100}{28}\)
\(⇒n=3Q\) where \(Q=\frac{k\times 100}{28}\) is a positive integer - Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: If Mr. Stewart reduced the number of students in his class by 6 percent he could evenly divide the class into groups of 3
- According to this statement, \(n(1-\frac{6}{100})=3k\) where k is a positive integer
\(⇒n\times \frac{94}{100}=3k\)
\(⇒n=\frac{3k\times 100}{94}\)
\(⇒n=3\frac{k\times 100}{94}\)
\(⇒n=3Q\) where \(Q=\frac{k\times 100}{94}\) is a positive integer - Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
