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

Question

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

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

Mo2men · Answer

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

LeoN88 · Answer

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

Archit3110  please check once.

Bunuel · Answer

________________________
The OA is C. Edited. Thank you.

firas92 · Answer

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!

Posted from my mobile device

JavRam · Answer

S = 0.6J
J = 0.5F

S:J:F = 0.6:1:2 
People cannot be cut, therefore (multiply everything by 5 to get an integer of S) --> 3:5:10

Senior must be a multiple of 3, therefore II) 25 is out.

There are at least 150 people

I) S=24 --> 24:40:8 --> 24+40+80<150 NOT VALID

III) S=27 --> 27:45:90 --> 27+45+90>150 VALID

Answer: C (III only)

bumpbot · Answer

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

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