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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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Manager
Joined: 12 Jun 2016
Posts: 224
Location: India
WE: Sales (Telecommunications)
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, 23:14
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75% (hard)

Question Stats:

52% (01:42) correct 48% (01:44) wrong based on 67 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. $$10x$$

[Reveal] Spoiler:
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!
[Reveal] Spoiler: OA

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Last edited by susheelh on 22 Oct 2017, 23:45, edited 1 time in total.
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Joined: 09 Aug 2017
Posts: 24
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
KUDOS
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?
Manager
Joined: 12 Jun 2016
Posts: 224
Location: India
WE: Sales (Telecommunications)
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
KUDOS
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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Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2116
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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Expert's post
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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. $$10x$$

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] 26 Oct 2017, 15:35
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