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

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Joined: 02 Sep 2009
Posts: 65014
There are two classrooms A and B. The sum of the number of students in  [#permalink]

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29 May 2020, 02:24
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Difficulty:

85% (hard)

Question Stats:

47% (02:38) correct 53% (02:30) wrong based on 57 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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Re: There are two classrooms A and B. The sum of the number of students in  [#permalink]

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29 May 2020, 02:49
1
I tried solving this question by taking values,
As ques is asking whether B > 20, Let us consider B =20 so that we can check if value satisfies if not then would be sufficient or insufficient accordingly
Now A+B > 120

Statement 1 :
(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.
Min No of students considered in B =20, A : 101 == > A+B =121
Now A is doubled: 202, B is halved, B= 10
A- B :192 : less than 200 as required,
Now if we go less than 20, all values will satisfy , Now let us check if B> 20 also satisfy this
b= 22, A =102 : A+ B =124
Doubling A = 204, B = 1/2 *22 =11
A- B = 193,
Still satisfies equation,
Thus B < 20 and B> 20 both possible,
Insufficient

Statement 2 :
(2) If 20 students from each classroom leave the school, the sum of number of students in both classes would be more than 80.

So min no of Students in B = 20 , Because they leave school .
Now A+ B > 120 from initial stem
A+B- 40 > 80
A+B > 120
It can be that A has all the students and B has 20 or B can have more than 20 also.
So B > 20

In sufficient

Combining we know that Min no of students B has is 20, But as we checked 20 also satisfies statement 1 and statement 2 and B > 20 also satisfies,
Still Insufficient.

IMO E

i know this might not be correct algebric method, but tried using numbers
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Re: There are two classrooms A and B. The sum of the number of students in  [#permalink]

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29 May 2020, 03:07
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A+B>120

Statement 1-

$$2A-\frac{B}{2} < 200$$

$$4A-B< 400$$

$$-4A+B > -400$$.......(1)

Also, $$4A+4B >480$$.....(2)

$$5B > 80$$
$$B>16$$

B can be 17 or 21

Insufficient

Statement 2-

A, B > 20

B can be 20 or 21

Insufficient

Combining both statements

B > 20

Insufficient

Bunuel 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.

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Joined: 05 Aug 2019
Posts: 298
Location: India
GMAT 1: 600 Q50 V22
GPA: 4
There are two classrooms A and B. The sum of the number of students in  [#permalink]

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Updated on: 01 Jun 2020, 03:41
See the attachment.

Thanks aka007 for making me realize the mistake

Given a+b > 120 or a> 120 -b

Statement 1=>
2a - b/2 < 200
4a-b < 400
b> 4a-400

Combining given equation
b> 4a-400 > 4(120-b) -400
b> 480 -4b -400
5b> 80
b> 16

Insufficient
Attachments

1.PNG [ 34.76 KiB | Viewed 400 times ]

Originally posted by sambitspm on 29 May 2020, 10:09.
Last edited by sambitspm on 01 Jun 2020, 03:41, edited 1 time in total.
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Joined: 15 Nov 2019
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There are two classrooms A and B. The sum of the number of students in  [#permalink]

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29 May 2020, 23:45
1
sambitspm wrote:
See the attachment.

Hi,

You read the question wrong. Firstly the sum is greater than 120, not greater than equal to.
secondly, the statement 1 says less than 200, not 20.

Statement 1 gives you that B>16.
Statement 2 gives nothing new.

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

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01 Jun 2020, 02:57
aka007 thanks for letting me know. I will update my response by today.

Posted from my mobile device
Re: There are two classrooms A and B. The sum of the number of students in   [#permalink] 01 Jun 2020, 02:57