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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 73

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IMPORTANT

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Let $F (x)$ denote the sum of the digits of the positive integer $x .$ For example, $F (8) = 8$ and $F (123) = 1 + 2 + 3 = 6 .$ For how many two-digit values of $x$ is $F (F (x)) = 3$ ?

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Important Questions on Number System

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IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 74

Given that

3^{8} \cdot 5^{2} = a^{b},

where both a and

b

are positive integers, find the smallest possible value for

(\frac{a + b + 93}{25})

.

EASY

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IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 75

What is the largest integer that is a divisor of

(n + 1) (n + 3) (n + 5) (n + 7) (n + 9)

for all positive even integers

n

?

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 76

The product of three consecutive positive integers is

8

times their sum. What is the sum of their squares?

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 77

Let

P (n)

and

S (n)

denote the product and the sum, respectively, of the digits of the integer

n .

For example,

P (23) = 6

and

S (23) = 5 .

Suppose

N

is a two-digit number such that

N = P (N) + S (N) .

What is the units' digit of

N

?

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 78

The mean of three numbers is

10

more than the least of the numbers and

15

less than the greatest. The median of the three numbers is

5 .

What is their sum?

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 79

Two non-zero real numbers,

a

and

b,

satisfy

a b = a - b

. Then find the possible value of

\frac{a}{b} + \frac{b}{a} - a b

?

HARD

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IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 80

There are

N

number of positive integers not exceeding

2001

are multiples of

3

or

4

but not

5

. Then find the value of

(\frac{N - 1}{50})

EASY

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IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 81

In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by $v, w, x, y,$ and $z .$ Find $y + z$

$v$	$24$	$w$
$18$	$x$	$y$
$25$	$z$	$21$

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Let Fx denote the sum of the digits of the positive integer x. For example, F8=8 and F123=1+2+3=6. For how many two-digit values of x is FFx=3 ?

Important Questions on Number System

Learn and Prepare for any exam you want !

Let $F (x)$ denote the sum of the digits of the positive integer $x .$ For example, $F (8) = 8$ and $F (123) = 1 + 2 + 3 = 6 .$ For how many two-digit values of $x$ is $F (F (x)) = 3$ ?