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Analytical Reasoning Set 2
120 students are arranged by two teachers Baman and Chaman, in 'x' rows and 'y' columns such that each row has the same number of
students. Similarly, every column has same number of students. Each of the students hs 15 pencils initially. Every student gets extra
pencils from Baman. If he is in the m^{th} row, he gets 'm' pencils. Thereafter, each of the students gives away some pencils to
Chaman. If the student is in the n^{th} column, he gives away 'n' pencils. Finally, the total number with the students is
16 times the total number of students.

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Questions Set 2
Q1) What is the value of 'x'?1) 10
2) 12
3) 15
4) 20
Q2) How many pencils did students give away to Chaman?
1) 640
2) 660
3) 680
4) Cannot be Determined
Q3) How many pencils were given to the students by Baman?
1) 540
2) 660
3) 780
4) Cannot be Determined
SOLUTIONS:
Initially students had a total of 15xy pencils with them, where xy = 120.
Let the total number of pencils given to the students by Baman be 'J' and the total number of pencils given by the students to Chaman be 'M'.
J = (y + 2y +....+ xy), M = (x + 2x +...+ yx)
J = y(1 + 2 +...+ x), M = x(1 + 2 +...+ y)
15xy + J  M = 16xy where xy = 120.
J  M = xy = 120 i.e. x  y = 20
Therefore, x = 12, y = 10.
Pencils given to Chaman = M = 12(1 + 2 +...+ 10) = 660
Pencils given to the students by Baman = J = 120 + M = 780