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QOTD#19 A group of freshmen, juniors, and seniors are going
[#permalink]
03 Apr 2017, 03:40

1

Expert Reply

1

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Question Stats:

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?

Indicate all possible values.

A. 21

B. 22

C. 24

D. 25

E. 27

_________________

Indicate all possible values.

A. 21

B. 22

C. 24

D. 25

E. 27

Drill 3

Question: 10

Page: 320

Question: 10

Page: 320

_________________

Sandy

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Re: QOTD#19 A group of freshmen, juniors, and seniors are going
[#permalink]
17 Apr 2017, 09:35

1

Expert Reply

Explanation

To solve this question, plug in the answers as the number of seniors to see if the rest of the class adds up to 150.

Start with choice C. If S = 24, then \(\frac{60}{100}\) and J = 40; since 40 = 50% of F, then F = 80; since the sum of the students is 24 + 40 + 80 = 144, which is less than 150, try larger numbers and eliminate choices (A), (B), and (C).

For choice D, if S = 25, then \(25 = J \times \frac{60}{100}\), thus there are 41.67 juniors, which is incorrect since it is impossible to have a fraction of a student.

For choice (E), if S = 27, then \(J \times \frac{60}{100}\), thus J = 45; since 45 = 50% of F, then F = 90; since 27 + 45 + 90 = 162, which is at least 160, choice (E) is the only correct answer.

Hence option E is correct!

_________________

Sandy

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To solve this question, plug in the answers as the number of seniors to see if the rest of the class adds up to 150.

Start with choice C. If S = 24, then \(\frac{60}{100}\) and J = 40; since 40 = 50% of F, then F = 80; since the sum of the students is 24 + 40 + 80 = 144, which is less than 150, try larger numbers and eliminate choices (A), (B), and (C).

For choice D, if S = 25, then \(25 = J \times \frac{60}{100}\), thus there are 41.67 juniors, which is incorrect since it is impossible to have a fraction of a student.

For choice (E), if S = 27, then \(J \times \frac{60}{100}\), thus J = 45; since 45 = 50% of F, then F = 90; since 27 + 45 + 90 = 162, which is at least 160, choice (E) is the only correct answer.

Hence option E is correct!

_________________

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Re: QOTD#19 A group of freshmen, juniors, and seniors are going
[#permalink]
15 May 2017, 11:39

2

C is wrong

Re: QOTD#19 A group of freshmen, juniors, and seniors are going
[#permalink]
16 Jun 2018, 08:00

2

Hi, C would be wrong because the sum is 144 which is less than 150. Please confirm.

Thanks

Thanks

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Re: QOTD#19 A group of freshmen, juniors, and seniors are going
[#permalink]
17 Jun 2018, 02:38

1

Expert Reply

Kahani98 wrote:

Hi, C would be wrong because the sum is 144 which is less than 150. Please confirm.

Thanks

Thanks

You are correct, C is not a correct option.

Fixed, thanks!

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Re: QOTD#19 A group of freshmen, juniors, and seniors are going
[#permalink]
15 Aug 2022, 06:36

1

One way to approach this is to create proportions.

S------ J------ N

60% 100% 200%

3------5------ 10

Now, since the ratio of senior to junior is 3 to 5, we need numbers divisible by 3.

Option A, should be a good start: 21 - 35 - 70.

The proportion works, but the sum (126) is less than 150.

The only remaining multiple of 3 is 27 (Option E): 21 - 45 - 90. That works!

S------ J------ N

60% 100% 200%

3------5------ 10

Now, since the ratio of senior to junior is 3 to 5, we need numbers divisible by 3.

Option A, should be a good start: 21 - 35 - 70.

The proportion works, but the sum (126) is less than 150.

The only remaining multiple of 3 is 27 (Option E): 21 - 45 - 90. That works!

gmatclubot

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