Dear Reader, below are three sample questions to prepare for CTS aptitude papers. These questions essentially deal with remainders and equation solving. Hope you find these useful.

Question 1

Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had?

a) 19 b) 17 c) 29 d) 23

Answer : d) 23

Solution:

Though there are many ways to solve these problems, the best and fastest approach would be to go by inspecting options one by one. Now lets get on to the solution :
Let x be the number. Let us take one option at a time and check if the conditions in question are satisfied.

Assume option a) is right :
If x=19, then 19/3 gives the remainder 1. This contradicts the statement that "he wants to give these books equally to 3 of his friends, then 2 books will remain"
Conclusion : Hence option a) is wrong.

Assume option b) is right :
If x=17, then 17/4 gives the remainder 1. This contradicts the statement that "he wants to give these books equally to 4 of his friends, then 3 books will remain"
Conclusion : Hence option b) is wrong.

Assume option c) is right :
If x=29, then 29/4 gives the remainder 1. This contradicts the statement that "he wants to give these books equally to 4 of his friends, then 3 books will remain"
Conclusion : Hence option c) is wrong.
Since we have ruled out first three options, the only possible correct answer would be (d) 23.

Question 2

In a Company, there are certain number of team members and certain number of team leaders. If five team members are assigned to each team leader, then one member is left out without team leader. If six members are assigned to each team leader, then one team leader has no member at all. Find the number of team leaders in that company?

a) 7 b) 36 c) 5 d) 8

Answer : a) 7

Solution:

Let the number of team members be x and the number of team leaders be y.
If 5 members are assigned to each team leader, then one member is left.
i.e. (x-1)/5 = y
=> x – 5y = 1 --------- (1)
If 6 members are assigned to each team leader, then one team leader is left out
i.e. x/6 = y -1
=> x – 6y = -6 -------- (2)
Solving (1) and (2), we get
x = 36 and y = 7
Hence, there are 7 team leaders in that company.

Question 3

In a street, there are certain number of houses. People in that street are decided to paint their houses with certain colours. If four houses are painted with each colour, then one house will be left without any colour. If five houses are painted with each colour, then one colour will remain. Find the number of houses in that street?

a) 6 b) 36 c) 25 d) 7

Answer : c) 25

Solution:

Let the number of houses in that street be x and the number of colours be y.
If 4 houses are painted with each colour, then one house will be left without any colour.
i.e. (x-1)/4 = y
=> x – 4y = 1 --------- (1)
If 5 houses are painted with each colour, then one colour will be left out
i.e. x/5 = y -1
=> x – 5y = -5 -------- (2)
Solving (1) and (2), we get
x = 25 and y = 6
Hence, there are 25 houses in that street.