Number Question Answers

Number Theory : Remainders, Finding Divisors

Remainders of division of different numbers by the same divisor

Question

A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

(1) 13
(2) 59
(3) 35
(4) 37

 

Number Theory : Test of Divisibility Question

Divisibility of a large number

Question

The largest number amongst the following that will perfectly divide 101¹⁰⁰ - 1 is

(1) 100
(2) 10,000
(3) 100¹⁰⁰
(4) 100,000

Correct Choice is (2) and Correct Answer is 10,000


 

Explanatory Answer

The easiest way to solve such problems for CAT puposes is trial and error or by back substituting answers in the choices given.

101² = 10201.
101² - 1 = 10200. This is divisible by 100.

Similarly try for 101³ - 1 = 1030301 - 1 = 1030300.

So you can safely conclude that (101¹ - 1) to (101⁹ - 1) will be divisible by 100.
(101¹⁰ - 1) to (101⁹⁹ - 1) will be divisible by 1000.
Therefore, (101¹⁰⁰ - 1) will be divisible by 10,000.

 

CAT Practice Questions and Answers : Listed Topicwise

Number Theory		Permutation & Probability		Data sufficiency		Inequalities
Geometry		Mensuration		Trigonometry		Coordinate Geometry
Percentages		Profit Loss		Ratio Proportion		Mixtures Alligation
Speed Time Distance		Pipes Cisterns		Linear Quadratic		Number Theory