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29 May 2020, 03:24
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E
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Difficulty:
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Question Stats:
50% (02:55) correct
50%
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wrong
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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.
Are You Up For the Challenge: 700 Level Questions
(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.
Are You Up For the Challenge: 700 Level Questions
29 May 2020, 03:49
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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
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
29 May 2020, 04:07
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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)
Add (1) and (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
Statement 1-
\(2A-\frac{B}{2} < 200\)
\(4A-B< 400\)
\(-4A+B > -400\).......(1)
Also, \(4A+4B >480\).....(2)
Add (1) and (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
