Learn and practice Problems on numbers with easy explaination and shortcut tricks. All questions and answers on numbers covered for various Competitive Exams

Solve Problems: 1) What is the difference in the place value of 5 in the numeral 754853?

49500 49950 45000 49940 Show Answer

The Correct answer is (B)

Answer with explanation:

The digit 5 has two place values in the numeral, 5 * 10^{5} = 50,000 and 5 * 10^{1} = 50.

∴Required difference = 50000 – 50 = 49950

2) What should be added to 1459 so that it is exactly divisible by 12?

4 3 5 6 Show Answer

The Correct answer is (C)

Answer with explanation:

On dividing 1459 by 12, the remainder is 7.

∴The number to be added would be = 12 – 7 = 5

3) If the number 467X4 is divisible by 9, find the value of the digit marked as X.

4 5 6 7 Show Answer

The Correct answer is(C)

Answer with explanation:

The number is divisible by 9 so the sum of its digits would be divisible by 9.

∴4 + 6 + 7 + X + 4 = 21+ X, must be divisible by 9.

X = 6, fulfills our requirement so the required digit is 6.

4) 7X2 is a three digit number and X is the missing digit. If the number is divisible by 6, the missing digit is

4 3 2 5 Show Answer

The Correct answer is (B)

Answer with explanation:

The given number is divisible by 6 so it would be divisible by 2 and 3. As the last digit is 2 whatever be the value of X, it would be divisible by 2.

Now, 7+X+2 = 9 + X, must be divisible by 3.

∴X = 3 makes the number divisible by 3, so 3 is the required digit.

5) What smallest number should be subtracted from 9805 so that it is divisible by 8?

3 4 5 7 Show Answer

The Correct answer is (C)

Answer with explanation:

On dividing 9805 by 8, the remainder is 5. So, 5 is the smallest number which should be subtracted from 9805 to make it divisible by 8.

Solve more problems on numbers.

6) Which of the following numbers is divisible by 9?

67578 56785 45678 65889 Show Answer

The Correct answer is (D)

Answer with explanation:

A number is divisible by 9 if the sum of its digits is divisible by 9.

Sum of the digits of the given numbers are;

6+7+5+7+8= 33

5+6+7+8+5= 31

4+5+6+7+8= 30

6+5+8+8+9= 36

The sum of the digits of the number 65889 is 36 which is divisible by 9, so the correct answer is 65889.

7) If (2^{p} + 1) is a prime number, which one of the following digits could be the value of p?

3 4 5 6 Show Answer

The Correct answer is (B)

Answer with explanation:

In such questions, each alternative should be tried.

So, if P = 3, we will get; 8 + 1= 9

If P = 4, we will get; 16 + 1 = 17

If P = 5, we will get; 32 + 1 = 33

If P= 6, we will get; 64 + 1= 65

Out of the four results, only 17 is the prime number. So, the required value of the P is 4.

8) Find the number of three-digit numbers which are divisible by 6.

150 130 120 110 Show Answer

The Correct answer is (A)

Answer with explanation:

The required three digit numbers would be 102, 108, 114, 120…990 and 996.

The sequence of numbers shows that it is an arithmetic progression, where ‘a’ = 102, ‘d’ = 6 and last number = 996

Let the number of terms = n

9) What is the sum of first 35 natural numbers?

610 630 645 660 Show Answer

The Correct answer is (B)

Answer with explanation:

First 35 natural numbers are 1, 2, 3, 4, 5…..35

Apply Formula; Sn=n(n+1)/2

=35(35+1)/2

=(35*36)/2

=630

10) Given that 1+2+3+.. +9 = 45, find the value of (11+12+13+..+19).

125 130 135 140 Show Answer

The Correct answer is (C)

Answer with explanation:

11+12+13+…+19 is an arithmetic progression with number of terms ‘n’ = 9, first term = 11 and last term = 19.

Apply formula; Sn = n/2 (first term + last term)

∴Required value or sum = 9/2 ( 11 + 19)

= 4.5 * 30 = 135