**Question 1 :**

Fill in the blanks in the following satisfying the given condition 2345 __ he number is divisible by 6.

(A) 3 (B) 8 (C) 4

**Solution :**

If the number is divisible by 6, then it must be divisible by 2 and 3.

= 2 + 3 + 4 + 5 + __

= 14 + __

If __ is 4, then we will get 18 and that is divisible by 3.

**Question 2 :**

Find the prime factors of 84.

(A) 12 ⋅ 7 (B) 2 ⋅ 2 ⋅ 3 ⋅ 7 (C) 14 ⋅ 6

**Solution :**

Prime factors of 84 are 2 ⋅ 2 ⋅ 3 ⋅ 7

**Question 3 :**

Multiply 46 by 99

(A) 4234 (B) 4554 (C) 3984

**Solution :**

46 x 99 = 46 x (100-1)

= 4600 - 46

= 4554

**Question 4 :**

Find the greatest number which divides 63 and 80 leaving the remainders 3 and 5 respectively.

(A) 12 (B) 15 (C) 8

**Solution :**

To find the greatest number which divides 63 and 80 leaving the remainders 3 and 5, let us subtract 3 and 5 from 63 and 80 respectively and find highest common factor.

63 - 3 = 60 ==> 5⋅2⋅2⋅3

80 - 5 = 75 ==> 5⋅5⋅3

HCF (60, 75) = 5⋅3 ==> 15

So, 15 is the greatest number.

**Question 5 :**

Find the L.C.M of 63, 105, 147.

(A) 2250 (B) 1600 (C) 1850

**Solution :**

Least common multiple = 7 ⋅ 3 ⋅ 3 ⋅ 5 ⋅ 7

= 2205

So, the answer is 2205.

**Question 6 :**

Convert 1.64 in to fraction and write in the simplest form.

(A) 18/27 (B) 41/25 (C) 15/21

**Solution :**

To convert a decimal as integer, we should follow the steps given below.

**Step 1 :**

In the given number, we have two digits after the decimal. So we should multiply and divide it by 100.

1.64 ⋅ (100/100)

**Step 2 :**

Multiplying the numerator, we get 164.

= 164/100

**Step 3 :**

If it is possible, we can simplify.

= 41/25

**Question 7 :**

Find the value of (75.384 + 64.963) - (35.562 + 42.027)

(A) 62.758 (B) 61.524 (C) 124.58

**Solution :**

(75.384 + 64.963) - (35.562 + 42.027)

75.384 + 64.963 = 140.347

35.562 + 42.027 = 77.589

= 140.347 - 77.589

= 62.758

**Question 8 :**

Multiply 8. 964 x 100

(A) 8.964 (B) 89.64 (C) 896.4

**Solution :**

8. 964 x 100

= 896.4

So, the product of 8. 964 x 100 is 896.4.

**Question 9 :**

Divide 172.8 by 100.

(A) 1.728 (B) 17.28 (C) 172.8

**Solution :**

To divide 172.8 by 100, we should move the decimal two digits to the left side. So,

172.8/100 = 1.728

**Question 10 :**

Simplify 3/4 ÷ 5/6

(A) 8/15 (B) 9/10 (C) 7/19

**Solution :**

3/4 ÷ 5/6 = (3/4) ⋅ (5/6)

= (3/4) ⋅ (6/5)

= 9/10

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