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# There are two classrooms A and B. The sum of the number of students in

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There are two classrooms A and B. The sum of the number of students in  [#permalink]

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27 Nov 2018, 07:53
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Difficulty:

55% (hard)

Question Stats:

60% (02:25) correct 40% (02:33) wrong based on 34 sessions

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There are two classrooms A and B. The sum of the number of students in both classrooms is more than 120. Is the number of students in class B greater than 20?

(1) If number of students in classroom A are doubled and number of students in classroom B are halved, the difference between the number of students in classroom A and B is less than 200.
(2) If 20 students from each classroom leave the school, the sum of number of students in both classes would be more than 80.
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Joined: 08 Jan 2013
Posts: 106
There are two classrooms A and B. The sum of the number of students in  [#permalink]

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27 Nov 2018, 11:43
1
rencsee wrote:
There are two classrooms A and B. The sum of the number of students in both classrooms is more than 120. Is the number of students in class B greater than 20?

(1) If number of students in classroom A are doubled and number of students in classroom B are halved, the difference between the number of students in classroom A and B is less than 200.
(2) If 20 students from each classroom leave the school, the sum of number of students in both classes would be more than 80.

Let number of students in class A be x and number of students in class B be y

Given => x + y > 120 ............... (I)
Required => is y > 20?

St. I => 2x - 1/2y < 200
Multiplying both sides with -1 => -2x + 1/2y > -200
Multiplying both sides by 2 => -4x + y > -400 ............. (II)

Solving (I) and (II) =>

4x + 4y > 480
-4x + y > -400
------------------
5y > 80
y > 16 => Insufficient

St. II => x - 20 + y - 20 > 80
Adding 40 on both side => x+ y > 120 => is the same as (I) => Insufficient

Taking St. I and St. II together, y > 16 which is still insufficient.

There are two classrooms A and B. The sum of the number of students in   [#permalink] 27 Nov 2018, 11:43
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