#### Number properties

1)Find the greatest four digit number which is exactly divisible by 393.

Show Solution
The greatest four digit number is 9999. Dividing the number by 393, the remainder is 174. The required number = 9999 – 174 = 9825. Hence(A)

2) Which of the following numbers is divisible by 22?

Show Solution
For the number to be divisible by 22, it should be divisible by 2 and 11. Hence(b)

3) Find the LCM of 368 and 46.

Show Solution
Prime factors of 368 = 24 * 23
Prime factors of 46 = 2 * 23
LCM of 368 and 46 = 24 * 23 = 368. Hence(d)

4) LCM and HCF of two numbers are 504 and 8 respectively. If one of the numbers is 56, find the other number.

Show Solution
LCM * HCF = product of two numbers.
504 * 8 = 56 * x. à x= 72. Hence(c)

5) One-fifth of two-third of four-seventh of a number is 16. What is 35% of that number?

Show Solution
Let the number be x.
$${1 \over {5}}({2 \over {3}})$$ ($${4x \over {7}}$$) = 16, à x=210
35% of 210 = 73.5. Hence(b)

6) When a number is divided by 43 the remainder is 37. When the same number is divided by 29, what will be the remainder?

Show Solution
N = 43Q + 37, If Q = 0, N = 37
R(37/29) = 8. Hence(d)

7) When a number is successively divided by 9, 11 and 14, it leaves a remainder 4, 7 and 13 respectively. Find the smallest such number.

Show Solution
If N is the number and q1, q2, q3 are the successive quotients, then x =9q1 + 4
q1 = 11q2 + 7, q2 = 14q3 + 13. The smallest number will be if q3 = 0, N = 1354. Hence(a).

8) Find the unit digit of 8531327

Show Solution
The cyclicity of 3 is 4. Remainder when power divided by 4 => 3.
Unit digit of 8531327 = 33 = 27. Hence(c)

9) What is the unit digit of 3984191 + 4376297

Show Solution
The cyclicity of 4 is 2. If the power is odd number unit digit will be 4 and the power is even number unit digit will be 6.
The cyclicity of 6 is 1
Unit digit of 3984191 = 4
Unit digit of 4376297 = 6
Unit digit of 3984191 + 4376297 = 4 + 6 = 10. Hence(A)

10) How many factors are there in 548?

Show Solution
Prime factors of the number 546 = (2*3*7*13)
Number of factors = (1+1)*(1+1)*(1+1)*(1+1) = 16 factors. Hence(b).

11) Find the product of the factors of 1352.

Show Solution
Number of factors of 1352 = 23 *132 = (3+1) * (2+1) = 12 factors
Product of the factors = N(no of factors /2) = 1352(12/2) à13526. Hence (c).

12) Find the greatest number of 4 digits which when divided by 7, 9 and 11 leaves 4 as remainder in each case.

Show Solution
LCM of 7, 9 and 11 = 693
Greatest 4 digit number which is divisible by 693 = 9702
Required number = 9702 + 4 = 9706. Hence(d)

13) Convert binary to octal (101111011)2

Show Solution
1011110112 = 101 | 111 | 011
= (573)8. Hence(a)

14) Find the remainder of 1438157 when divided by 5.

Show Solution
Unit digit of 1438157 = 8
R(8/5) = 3. Hence (c).

15) Find the remainder when 7169 divided by 72.

Show Solution
R($${71{}{}{}{}{}{}{}{}{}{}{}{} \over {72}}$$) = R($${(72-1) \over {72}}$$)
= R($${72 \over {72}}$$) - R($${1 \over {72}}$$)
= 0 – 1 + 72 = 71. Hence(b).

#### Reach US

##### +91 9384058988

info@crampete.com