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Re: A certain building has only 2-room and 3-room apartments to rent. If [#permalink]
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A certain building has only 2-room and 3-room apartments to rent. If the range of the rental fees of all the apartments in the building is $1,000 and the range of the rental fees for 3-room apartments is $600, what is the range of the rental fees for 2-room apartments?

(1) The lowest rental fee for a 3-room apartment in the building is $200 more than the highest rental fee for a 2-room apartment in the building.
(2) The lowest rental fee for a 2-room apartment is $800 in the building.

Please see the solution below in image.

IMO A
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A certain building has only 2-room and 3-room apartments to rent. If [#permalink]
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A certain building has only 2-room and 3-room apartments to rent. If the range of the rental fees of all the apartments in the building is $1,000 and the range of the rental fees for 3-room apartments is $600, what is the range of the rental fees for 2-room apartments?

I found it easy to solve by imagining highest and lowest rental fees of 2 and 3 room apartments to be points on a number line and RANGE as DISTANCE between 2 points.

A_____B______X______Y

A = LOWEST FEES (dont know 2 room or 3 room)
Y = HIGHEST FEES (dont know 2 room or 3 room)
B and X are Lowest or Highest of 2 room or 3 room, we dont know which is which.

Distance AY = 1000
Distance of 3 room highest and lowes is 600.... But we dont know which 2 points they are on the number line

(1) The lowest rental fee for a 3-room apartment in the building is $200 more than the highest rental fee for a 2-room apartment in the building.

Lowest of 3 room is higher than highest of 2 room.... SO ALL 2 ROOMS are LOWER than 3 rooms

A = Lowest 2 room
B = Highest 2 room
X = Lowest 3 room
Y = Highest 3 room

FIND AB

AY = 1000... because total range is 1000
BX = 200...... because lowest 3 room is 200 more than highest 2 room
XY = 600.... because 3 room range is 600

AB = 1000 - 600 - 200 = 200

(1) IS SUFFICIENT

(2) The lowest rental fee for a 2-room apartment is $800 in the building.

Lowest 2 room is 800, BUT, we dont know if 800 is A, or B, or X... it could be either of the 3.

We also dont know which one is Highest 2 room, so what do we find the distance between??

(2) IS NOT SUFFICIENT


ANSWER: A - 1 Alone is sufficient

Originally posted by Vinit1 on 23 Jul 2019, 09:21.
Last edited by Vinit1 on 23 Jul 2019, 21:45, edited 1 time in total.
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Re: A certain building has only 2-room and 3-room apartments to rent. If [#permalink]
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Re: A certain building has only 2-room and 3-room apartments to rent. If [#permalink]
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