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At least 15 percent of the students registered for Professor Tyler’s

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At least 15 percent of the students registered for Professor Tyler’s  [#permalink]

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New post 28 Feb 2019, 00:20
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At least 15 percent of the students registered for Professor Tyler’s course dropped out before the end of the course. The drop-out rate for Professor Quin’s course was 20 percent greater than that for Professor Tyler’s course. If 120 students remained on the last day of Professor Quin’s class, which of the following could be the number of students who signed up for Professor Quin’s class?

I. 147
II. 162
III. 185

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III

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Re: At least 15 percent of the students registered for Professor Tyler’s  [#permalink]

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New post 28 Feb 2019, 07:11
Bunuel wrote:
At least 15 percent of the students registered for Professor Tyler’s course dropped out before the end of the course. The drop-out rate for Professor Quin’s course was 20 percent greater than that for Professor Tyler’s course. If 120 students remained on the last day of Professor Quin’s class, which of the following could be the number of students who signed up for Professor Quin’s class?

I. 147
II. 162
III. 185

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


If the drop out rate of prof. Tayler class is at least 15% and drop out rate of prof. Quin class is 20% greater, it means that the drop out rate of Prof. Quin class ;
(1+0.2)*0.15 = 0.18.

There are 120 student at the end of the course, this means that 120 = X - 0.18X, where X is the total number of students at the beginning.
It is easy to find that the minimal starting number of students is ~146 .
Thus all the choice reporting a number greater than 146 are correct
IMO E
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Re: At least 15 percent of the students registered for Professor Tyler’s  [#permalink]

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New post 07 Mar 2019, 14:30
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Bunuel wrote:
At least 15 percent of the students registered for Professor Tyler’s course dropped out before the end of the course. The drop-out rate for Professor Quin’s course was 20 percent greater than that for Professor Tyler’s course. If 120 students remained on the last day of Professor Quin’s class, which of the following could be the number of students who signed up for Professor Quin’s class?

I. 147
II. 162
III. 185

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


20% greater than 15% = 15% + 2(1.5) = 18% = \(\frac{18}{100}\) = \(\frac{9}{50}\)
Since the dropout rate for Tyler's course is at least 15%, the dropout rate for Quin's course must be greater than or equal to \(\frac{9}{50}\).

I: 147
Since 120 students remain in the course, 27 students drop out, implying the following dropout rate:
\(\frac{27}{147} = \frac{9}{49}\)
Since \(\frac{9}{49} > \frac{9}{50}\), option I is possible.
Eliminate C.

II: 162
Since 120 students remain in the course, 42 students drop out, implying the following dropout rate:
\(\frac{42}{162} ≈ \frac{40}{160} = \frac{1}{4}\)
Since \(\frac{1}{4} > \frac{9}{50}\), option II is possible.
Eliminate A and D.

III: 185
Since 120 students remain in the course, 65 students drop out, implying the following dropout rate:
\(\frac{65}{185} ≈ \frac{60}{180} = \frac{1}{3}\)
Since \(\frac{1}{3} > \frac{9}{50}\), option III is possible.
Eliminate B.


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Re: At least 15 percent of the students registered for Professor Tyler’s  [#permalink]

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New post 07 Mar 2019, 23:15
Archit3110 wrote:
Bunuel wrote:
At least 15 percent of the students registered for Professor Tyler’s course dropped out before the end of the course. The drop-out rate for Professor Quin’s course was 20 percent greater than that for Professor Tyler’s course. If 120 students remained on the last day of Professor Quin’s class, which of the following could be the number of students who signed up for Professor Quin’s class?

I. 147
II. 162
III. 185

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


If the drop out rate of prof. Tayler class is at least 15% and drop out rate of prof. Quin class is 20% greater, it means that the drop out rate of Prof. Quin class ;
(1+0.2)*0.15 = 0.18.

There are 120 student at the end of the course, this means that 120 = X - 0.18X, where X is the total number of students at the beginning.
It is easy to find that the minimal starting number of students is ~146 .
Thus all the choice reporting a number greater than 146 are correct
IMO E


Hi Archit3110
Did you drive equation as 20% of dropout rate of taylor’s class + dropout rate of taylor’s Class?
I can’t seem to get my head around it. ?

Thanks
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Re: At least 15 percent of the students registered for Professor Tyler’s  [#permalink]

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New post 08 Mar 2019, 02:39
Doer01 wrote:
Archit3110 wrote:
Bunuel wrote:
At least 15 percent of the students registered for Professor Tyler’s course dropped out before the end of the course. The drop-out rate for Professor Quin’s course was 20 percent greater than that for Professor Tyler’s course. If 120 students remained on the last day of Professor Quin’s class, which of the following could be the number of students who signed up for Professor Quin’s class?

I. 147
II. 162
III. 185

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


If the drop out rate of prof. Tayler class is at least 15% and drop out rate of prof. Quin class is 20% greater, it means that the drop out rate of Prof. Quin class ;
(1+0.2)*0.15 = 0.18.

There are 120 student at the end of the course, this means that 120 = X - 0.18X, where X is the total number of students at the beginning.
It is easy to find that the minimal starting number of students is ~146 .
Thus all the choice reporting a number greater than 146 are correct
IMO E


Hi Archit3110
Did you drive equation as 20% of dropout rate of taylor’s class + dropout rate of taylor’s Class?
I can’t seem to get my head around it. ?

Thanks


Doer01
I have actually first determined the value of total drop rate of Quin class
given drop out rate of prof. Tayler class is at least 15% and drop out rate of prof. Quin class is 20% greater, it means that the drop out rate of Prof. Quin class ;
(1+0.2)*0.15 = 0.18
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At least 15 percent of the students registered for Professor Tyler’s  [#permalink]

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New post 09 Mar 2019, 08:25
Bunuel wrote:
At least 15 percent of the students registered for Professor Tyler’s course dropped out before the end of the course. The drop-out rate for Professor Quin’s course was 20 percent greater than that for Professor Tyler’s course. If 120 students remained on the last day of Professor Quin’s class, which of the following could be the number of students who signed up for Professor Quin’s class?

I. 147
II. 162
III. 185

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


Hi Bunuel,
Does "than that" in the question statement mean 20% of 15(just number) or 20% of 15%?

Thanks.
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At least 15 percent of the students registered for Professor Tyler’s   [#permalink] 09 Mar 2019, 08:25
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