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A group of freshmen, juniors, and seniors are going on a school trip.

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Math Expert
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Joined: 02 Sep 2009
Posts: 59588
A group of freshmen, juniors, and seniors are going on a school trip.  [#permalink]

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New post 23 May 2019, 02:35
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (02:50) correct 51% (02:57) wrong based on 37 sessions

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A group of freshmen, juniors, and seniors are going on a school trip. The number of seniors is 60% of the number of juniors, which is 50% of the number of freshmen. If there are at least 150 students on the trip, then which of the following could be the number of seniors?

I. 24
II. 25
III. 27

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

_________________
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Joined: 26 Mar 2013
Posts: 2343
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Re: A group of freshmen, juniors, and seniors are going on a school trip.  [#permalink]

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New post 25 May 2019, 05:41
1
Bunuel wrote:
A group of freshmen, juniors, and seniors are going on a school trip. The number of seniors is 60% of the number of juniors, which is 50% of the number of freshmen. If there are at least 150 students on the trip, then which of the following could be the number of seniors?

I. 24
II. 25
III. 27

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


Let seniors = S, Juniors= J and Freshmen = F

S =0.6 J = 3/5 J

J =0.5 F= (1/2) F

Let's test III when S= 27

27 = 3/5 J.......... J=45

45 = 1/2 F..........F= 90

Total = 90 + 45 +27 = 162 > 150

Eliminate choices A & B

Let's Test I when s = 24

24 = 3/5 J...........J= 40

40 = 1/2 F...........F = 80

Total = 80 +40 + 24 = 144 <150

Eliminate choices D & E

Answer: C

Bunuel

Is the correct D? if so, how come s could be 24? Can you help please?

Thanks
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A group of freshmen, juniors, and seniors are going on a school trip.  [#permalink]

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New post 25 May 2019, 06:00
Mo2men wrote:
Bunuel wrote:
A group of freshmen, juniors, and seniors are going on a school trip. The number of seniors is 60% of the number of juniors, which is 50% of the number of freshmen. If there are at least 150 students on the trip, then which of the following could be the number of seniors?

I. 24
II. 25
III. 27

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


Let seniors = S, Juniors= J and Freshmen = F

S =0.6 J = 3/5 J

J =0.5 F= (1/2) F

Let's test III when S= 27

27 = 3/5 J.......... J=45

45 = 1/2 F..........F= 90

Total = 90 + 45 +27 = 162 > 150

Eliminate choices A & B

Let's Test I when s = 24

24 = 3/5 J...........J= 40

40 = 1/2 F...........F = 80

Total = 80 +40 + 24 = 144 <150

Eliminate choices D & E

Answer: C

Bunuel

Is the correct D? if so, how come s could be 24? Can you help please?

Thanks


Mo2men Bunuel, even I'm also getting only 27 C as the answer, kindly help.

Archit3110 please check once.
Math Expert
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Joined: 02 Sep 2009
Posts: 59588
Re: A group of freshmen, juniors, and seniors are going on a school trip.  [#permalink]

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New post 25 May 2019, 06:16
1
LeoN88 wrote:
Mo2men wrote:
Bunuel wrote:
A group of freshmen, juniors, and seniors are going on a school trip. The number of seniors is 60% of the number of juniors, which is 50% of the number of freshmen. If there are at least 150 students on the trip, then which of the following could be the number of seniors?

I. 24
II. 25
III. 27

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


Let seniors = S, Juniors= J and Freshmen = F

S =0.6 J = 3/5 J

J =0.5 F= (1/2) F

Let's test III when S= 27

27 = 3/5 J.......... J=45

45 = 1/2 F..........F= 90

Total = 90 + 45 +27 = 162 > 150

Eliminate choices A & B

Let's Test I when s = 24

24 = 3/5 J...........J= 40

40 = 1/2 F...........F = 80

Total = 80 +40 + 24 = 144 <150

Eliminate choices D & E

Answer: C

Bunuel

Is the correct D? if so, how come s could be 24? Can you help please?

Thanks


Mo2men Bunuel, even I'm also getting only 27 C as the answer, kindly help.

Archit3110 please check once.

________________________
The OA is C. Edited. Thank you.
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Re: A group of freshmen, juniors, and seniors are going on a school trip.  [#permalink]

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New post 25 May 2019, 20:39
1
s=0.6j
j=0.5f
So, s=0.3f

s+j+f ≥ 150

Substituting for s & j, 1.8f≥150

\(f≥\frac{150}{1.8}\) or \(s≥\frac{150*0.3}{1.8}\)

s≥25

When s=25, we don't get integer values for j or f and so s>25

Only III can be true

Answer is (C)

Hit Kudos if this helped!

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Re: A group of freshmen, juniors, and seniors are going on a school trip.   [#permalink] 25 May 2019, 20:39
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