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If 3/7 of the students in a room are seniors and 7/25 of the other stu

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Joined: 12 Jun 2016
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If 3/7 of the students in a room are seniors and 7/25 of the other stu  [#permalink]

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Updated on: 22 Oct 2017, 23:45
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65% (hard)

Question Stats:

62% (02:39) correct 38% (02:44) wrong based on 119 sessions

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If $$\frac{3}{7}$$ of the students in a room are seniors and $$\frac{7}{25}$$ of the other students are juniors, and there are $$x$$ students in the room who are not juniors or seniors, how many students are in the room?

A. $$\frac{175}{72} x$$

B $$\frac{175}{51}x$$

C. $$\frac{25}{7}x$$

D. $$\frac{25}{3}x$$

E. $$10x$$

I tried searching for this question and could not find in the Forum. Please merge/delete if this has already been posted before in the forum. Thanks in advance!

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Originally posted by susheelh on 22 Oct 2017, 23:14.
Last edited by susheelh on 22 Oct 2017, 23:45, edited 1 time in total.
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Re: If 3/7 of the students in a room are seniors and 7/25 of the other stu  [#permalink]

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22 Oct 2017, 23:42
1
total students in room are T.
Seniors are 3/7th so Seniors =3/7*T
Juniors are 7/25 of other students=7/25*(T-3/7*T)=4/25*T
x is neither seniors nor juniors= (T-3/7*T-4/25*T)=72/175*T
Hence total students are T=175/72*x

Plz explain where I am wrong?
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Re: If 3/7 of the students in a room are seniors and 7/25 of the other stu  [#permalink]

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22 Oct 2017, 23:47
1
Hello gvij2017,

Thanks for pointing this out. There was a Typo in the question. Your answer and approach are correct. I have edited the question and fixed the typo. +1 to you.

gvij2017 wrote:
total students in room are T.
Seniors are 3/7th so Seniors =3/7*T
Juniors are 7/25 of other students=7/25*(T-3/7*T)=4/25*T
x is neither seniors nor juniors= (T-3/7*T-4/25*T)=72/175*T
Hence total students are T=175/72*x

Plz explain where I am wrong?

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Re: If 3/7 of the students in a room are seniors and 7/25 of the other stu  [#permalink]

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26 Oct 2017, 15:35
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1
susheelh wrote:
If $$\frac{3}{7}$$ of the students in a room are seniors and $$\frac{7}{25}$$ of the other students are juniors, and there are $$x$$ students in the room who are not juniors or seniors, how many students are in the room?

A. $$\frac{175}{72} x$$

B $$\frac{175}{51}x$$

C. $$\frac{25}{7}x$$

D. $$\frac{25}{3}x$$

E. $$10x$$

We see that 3/7 of the total students are seniors, and thus 4/7 of the students are not seniors (or are the other students). Hence, 7/25(4/7) = 4/25 of the students are juniors.

If we let t = the total number of students, then we have:

(3/7)t + (4/25)t + x = t

(75/175)t + (28/175)t + x = t

(103/175)t + x = (175/175)t

x = (72/175)t

t = (175/72)x

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Re: If 3/7 of the students in a room are seniors and 7/25 of the other stu  [#permalink]

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23 Dec 2018, 10:18
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susheelh wrote:
If $$\frac{3}{7}$$ of the students in a room are seniors and $$\frac{7}{25}$$ of the other students are juniors, and there are $$x$$ students in the room who are not juniors or seniors, how many students are in the room?

A. $$\frac{175}{72} x$$

B $$\frac{175}{51}x$$

C. $$\frac{25}{7}x$$

D. $$\frac{25}{3}x$$

E. $$10x$$

Let T = Total number of students in room
So, T = (# of seniors) + (# of juniors) + (others)

3/7 of the students in a room are seniors
So, the # of seniors = (3/7)T

IMPORTANT: We've already accounted for 3/7 of the students. So, 4/7 of the students are not yet accounted for. So, the number of remaining (unaccounted for) students = (4/7)T

7/25 of the remaining students are juniors
So, # of juniors = (7/25)(4/7)T
= (4/25)T

There are x students in the room who are neither juniors nor seniors
So, # of others = x

We're now ready . . .
T = (# of seniors) + (# of juniors) + (others)
T = (3/7)T + (4/25)T + x
Get common denominator: T = (75/175)T + (28/175)T + x
Simplify: T = (103/175)T + x
Subtract (103/175)T from both sides to get: (72/175)T = x
Multiply both sides by (175/72) to get: T = (175/72)x

Cheers,
Brent

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Re: If 3/7 of the students in a room are seniors and 7/25 of the other stu   [#permalink] 23 Dec 2018, 10:18
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