Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 11

EASY

CAT

IMPORTANT

Earn 100

Digital sum of a number is obtained by adding all the digits of a number until a single digit is obtained. Find the digital sum of $19^{100}$ .

50% studentsanswered this correctly

Important Questions on Numbers and Their Properties

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 12

Find the HCF of

(2^{100} - 1)

and

((2^{120}) - 1)

.

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 13

Let S be the set of positive integers n for which

\frac{1}{n}

has the repeating decimal representation

0 . \bar{ab} = 0 . ababab \dots .

, with a and b as different digits. What is the sum of the elements of S?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 15

If

a, a + 2, and a + 4

are prime numbers, then the number of possible solutions for

a

is:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 16

Suppose N is an integer such that the sum of the digits of N is

2

, and

10^{9} < N < 10^{10}

. How many values of N are possible?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 17

Ten students solved a total of

35

questions in a Maths Olympiad. Each question was solved by exactly one student. There is at least one student who solved exactly one problem, at least one student who solved exactly two problems, and at least one student who solved exactly three problems. What is the minimum number of students who has/have solved at least five problems?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 18

N!

has

37

zeroes at its end. How many values of N is/are possible?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 19

In the abovementioned question, how many values of N will be odd?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - X+2 Maths>Practice Exercises>Q 30

An intelligence agency forms a code of two distinct digits selected from

0, 1, 2, . . . 9

, such that the first digit of the code is not zero. The code, handwritten on a slip, can however potentially create confusion when read upside down - for example, the code