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Bunuel
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There is a certain number of students in Mr. Stewarts class. Could Mr 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)!

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75% (hard)

Question Stats:

53% (02:13) correct 47% (02:13) wrong based on 137 sessions

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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.
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D
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stne
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There is a certain number of students in Mr. Stewarts class. Could Mr 25 Feb 2023, 09:00
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Bunuel
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.
Show more

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.
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There is a certain number of students in Mr. Stewarts class. Could Mr 13 Mar 2023, 02:03
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Bunuel
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.
Show more
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
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There is a certain number of students in Mr. Stewarts class. Could Mr 21 Aug 2024, 19:39
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Bunuel
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.
Show more
­Hi
This is the logic that I applied:
Let the number of students be 100x. The qs asks me, is 100x divisible by 3. Its a yes/no data sufficiency problem.

St 1- Class size becomes 84x. 84x= 3*7*2*2*x is divisible by 9 (which has two 3s as its factor).
84 has only one 3. Definitely x has to have one 3 as its factor so that 84 x is divisible by 9. Hence sufficient that x is divisible by 3 thus 100x is

St 2- 94x is divisible by 3. 94 doesnt have 3 as its factor. Thus it must be true that x is divisible by 3 so that 94x is. Hence sufficient taht x is divisible by 3 and thus 100x is.

Bunuel chetan2u is this approach correct?
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There is a certain number of students in Mr. Stewarts class. Could Mr 22 Aug 2024, 00:22
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Bunuel
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.
­Hi
This is the logic that I applied:
Let the number of students be 100x. The qs asks me, is 100x divisible by 3. Its a yes/no data sufficiency problem.

St 1- Class size becomes 84x. 84x= 3*7*2*2*x is divisible by 9 (which has two 3s as its factor).
84 has only one 3. Definitely x has to have one 3 as its factor so that 84 x is divisible by 9. Hence sufficient that x is divisible by 3 thus 100x is

St 2- 94x is divisible by 3. 94 doesnt have 3 as its factor. Thus it must be true that x is divisible by 3 so that 94x is. Hence sufficient taht x is divisible by 3 and thus 100x is.

Bunuel chetan2u is this approach correct?
Show more
How could you assume that the number of students in the class is a multiple of 100? However, the overall logic is correct.

There is a certain number of students in Mr. Stewart’s class. Could Mr. Stewart evenly divide the class into 3 study groups?

Let the number of students in the class be \(n\). The question essentially asks whether \(n\) is a multiple 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.

This statement implies that \(\frac{84}{100} * n = \frac{21}{25} * n = 3(\frac{7}{25} * n)\) is a multiple of 9. For \(3(\frac{7}{25} * n)\) to be a multiple of 9, \(n\) must be a multiple of 3. Sufficient.

(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.

This statement implies that \(\frac{94}{100} * n = \frac{47}{50} * n\) is a multiple of 3. For \(\frac{47}{50} * n\) to be a multiple of 3, \(n\) must be a multiple of 3. Sufficient.

Answer: D.­
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