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Number System and Number Theory Question Bank
Number system and Number Theory questions that appear in PGSEM, XAT, CAT, TANCET
A collection of questions that typically appear in the Common Admission Test (CAT) from the topic Number Theory. These questions will guide you through your CAT and other MBA entrance exam preparation.
 Question 1 » If both 11^{2} and 3^{3} are factors of the number a * 4^{3} * 6^{2} * 13^{11}, then what is the smallest possible value of 'a'?
Solution »
 Question 2 » Find the largest five digit number that is exactly divisible by 7, 10, 15, 21 and 28.
Correct Answer and Solution »
 Question 3 » Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?
Solution »
 Question 4 » Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?
Explanatory Answer »
 Question 5 » When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?
Solution »
 Question 6 » The sum of the first 100 natural numbers, 1 to 100 is divisible by
Correct Answer and Explanation »
 Question 7 » How many different factors does 48 have, excluding 1 and 48?
Solution »
 Question 8 » 10^{25}  7 is divisible by
Solution »
 Question 9 » Find the G.C.D of 12x^{2}y^{3}z^{2}, 18x^{3}y^{2}z^{4}, and 24xy^{4}z^{3}
Solution »
 Question 10 » What is the value of M and N respectively? If M39048458N is divisible by 8 & 11;
Where M & N are single digit integers?
Solution »
 Question 11 » 48 students have to be seated such that each row has the same number of students as the others. If at least 3 students are to be seated per row and at least 2 rows have to be there, how many arrangements are possible?
Solution »
 Question 12 » If two fractions, each of which has a value between 0 and 1, are multiplied together, the product will be:
TANCET 2008 : Solution »
 Question 13 » Three Vice Presidents (VP) regularly visit the plant on different days. Due to labour unrest, VP (HR) regularly visits the plant after a gap of 2 days. VP (Operations) regularly visits the plant after a gap of 3 days. VP (sales) regularly visits the plant after a gap of 5 days. The VPs do not deviate from their individual schedules. CEO of the company meets the VPs when all the three VPs come to the plant together. CEO is on leave from January 5^{th} to January 28^{th}, 2012. Last time CEO met the VPs on January 3, 2012. When is the next time CEO will meet all the VPs?
XAT 2012  1 Mark : Solution »
 Question 14 » How many divisors does 7200 have?
Solution »
 Question 15 » What is the highest power of 7 that can divide 5000! without leaving a remainder? (5000! means factorial 5000)
Solution »
 Question 16 » 'a' and 'b' are the lengths of the base and height of a right angled triangle whose hypotenuse is 'h'. If the values of 'a' and 'b' are positive integers, which of the following cannot be a value of the square of the hypotenuse?
Solution »
 Question 17 » If x, y, z are chosen from the three numbers, 3, and 2, what is the largest possible value of the expression z^{2}?
TANCET 2008 : Explanatory Answer »
CAT, XAT, TANCET Practice Questions and Answers : Listed Topicwise
