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# Every student in a room is a junior or a senior, and there are no....

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Director
Joined: 12 Feb 2015
Posts: 875
Every student in a room is a junior or a senior, and there are no....  [#permalink]

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05 Aug 2018, 04:04
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Difficulty:

15% (low)

Question Stats:

93% (01:10) correct 7% (00:14) wrong based on 37 sessions

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Every student in a room is a junior or a senior, and there are no other people in the room. How many seniors are in the room?

(1) If 56 seniors were to leave the room, the ratio of seniors to juniors would be 18 to 5.

(2) There are a total of 677 students in the room.

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Manish

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Re: Every student in a room is a junior or a senior, and there are no....  [#permalink]

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05 Aug 2018, 05:07
CAMANISHPARMAR wrote:
Every student in a room is a junior or a senior, and there are no other people in the room. How many seniors are in the room?

(1) If 56 seniors were to leave the room, the ratio of seniors to juniors would be 18 to 5.

(2) There are a total of 677 students in the room.

Question stem:- To find the number of seniors

St1:-Total number of students in the room is not known.
Hence, insufficient.

St2:- Total number of students=677.
No information on number of Juniors or Seniors or any relationship between the number of seniors and juniors.
Hence, insufficient.

Combined, We have
$$S+J=677$$ and
$$\frac{S-56}{J}=\frac{18}{5}$$-----------(1)
Substituting J=677-S in (1),we can determine S.
Sufficient.

Ans. (C)
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Re: Every student in a room is a junior or a senior, and there are no....  [#permalink]

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05 Aug 2018, 19:24
CAMANISHPARMAR wrote:
Every student in a room is a junior or a senior, and there are no other people in the room. How many seniors are in the room?

(1) If 56 seniors were to leave the room, the ratio of seniors to juniors would be 18 to 5.

(2) There are a total of 677 students in the room.

Answered this in 16 seconds without doing any math.

Question: How many Seniors?

(1) No info on total number of students. Quantity could be very high or very low. Not Sufficient

(2) No info on how many are Juniors or Seniors. Could be 676 Seniors and 1 Junior or could be 675 Seniors and 2 Juniors... Not Sufficient

(1) + (2) We have the total number and the ratio. No need to work out the math, there can only be one quantity.

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Re: Every student in a room is a junior or a senior, and there are no....  [#permalink]

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06 Aug 2018, 03:23
Let S= Number of Seniors
....J= ................ Juniors

(1) $$\frac{S-56}{J}$$= $$\frac{18}{5}$$

(2) S+J= 677

(1) &(2)

No need to calculate. No of seniors can be found.

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Re: Every student in a room is a junior or a senior, and there are no....   [#permalink] 06 Aug 2018, 03:23
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