Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.2>Q 23

HARD

IOQM - PRMO and RMO

IMPORTANT

Earn 100

Consider the non-decreasing sequence of positive integers

$1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, \dots \dots .$ in which the $n^{th}$ positive integer appears $n$ times. The remainder when the $2019^{th}$ term is divided by $5$ is

50% studentsanswered this correctly

Important Questions on Number System

HARD

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.2>Q 24

Mary chose an even

4

-digit number

n .

She wrote down all the divisors of

n

in increasing order from left to right:

1, 2, \dots, \frac{n}{2}, n .

At some moment, Mary wrote

323

as a divisor of

n .

If the smallest possible value of the next divisor written to the right of

323

is

N .

Find the value of

\frac{N}{10} .

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.2>Q 25

The largest divisor of

2014000000

is itself. If its fifth largest divisor is

X .

Find sum of all the digits of

X .

HARD

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.2>Q 26

How many three-digit numbers are not divisible by

5,

have digits that sum to less than

20,

and have the first digit equal to the third digit?

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.2>Q 27

How many even integers are there between

200

and

700

whose digits are all different and come from the set

1, 2, 5, 7, 8, 9

?

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 1

The sum of the digits of the number

10^{n} - 1

is

3798 .

The value of

n

is

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 2

a, b, c, d

are natural numbers such that

a = b c, b = c d, c = d a

and

d = a b .

Then

(a + b) (b + c) (c + d) (d + a)

is equal to

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 3

A three-digit number with digits

A, B, C

in that order is divisible by

9 . A

is an odd digit and

C

is an even digit.

B

and

C

are non zero. The number of such three-digit numbers is

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 4

Nine numbers are written in ascending order. The middle number is also the average of the nine numbers. The average of the

5

larger numbers is

68

and the average of the

5

smaller numbers is

44 .

The sum of all the numbers is