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

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

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23 May 2019, 02:35
00:00

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

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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

Bunuel

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

Thanks
ISB School Moderator
Joined: 08 Dec 2013
Posts: 615
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
A group of freshmen, juniors, and seniors are going on a school trip.  [#permalink]

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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

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.

Math Expert
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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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

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.

________________________
The OA is C. Edited. Thank you.
_________________
Director
Joined: 16 Jan 2019
Posts: 507
Location: India
Concentration: General Management
WE: Sales (Other)
Re: A group of freshmen, juniors, and seniors are going on a school trip.  [#permalink]

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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

Hit Kudos if this helped!

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