*Q1. 944 – 307 + 119 is equal to*

(a) 886

(b) 756

(c) 556

(d) 686

*Q2. 2234 + 84 – 1273 = x + 123, then find the x.*

(a) 922

(b) 832

(c) 932

(d) 822

*Q3. The number which is to be added to 0.01 to get 1.1 is*

(a) 1.11

(b) 1.09

(c) 1

(d) 0.10

*Q4. On dividing 397246 by a certain number, the quotient is 865 and the remainder is 211. The divisor is*

(a) 435

(b) 432

(c) 459

(d) 482

*Q5. Find the value of 98375 × 9999.*

(a) 983656125

(b) 983651625

(c) 99573815

(d) None of these

**Q6. Which of the following numbers is divisible by 3?**

(a) 97632

(b) 88844

(c) 98765

(d) All of these

*Q7. By which of the following 555555 is divisible?*

(a) 11

(b) 7

(c) 13

(d) All of these

*Q8. By which of the following, 787878 is not divisible?*

(a) 7

(b) 11

(c) 13

(d) None of these

*Q9. A number 774958 N₁ 96 N₂ to be divisible by 8 and 9, the values of N₁ and N₂ will be*

(a) 7, 8

(b) 0, 8

(c) 5, 8

(d) 6, 7

**Q10. If x and y are different integers, both divisible by 5, then which of the following is not necessarily true?**

(a) x² + y² is divisible by 5

(b) (x – y) is divisible by 5

(c) xy is divisible by 25

(d) (x + y) is divisible by 10

**Solutions**

**S1. Ans.(b)**

**Sol**. 944 – 307 + 119 = (944 + 119) – 307

= 1063 – 307 = 756

**S2. Ans.(a)**

**Sol.** ∵ 2234 + 84 – 1273 = x + 123

⇒ 2234 + 84 – 1273 – 123 = x

∴ x = (2234 + 84) – (1273 + 123)

= 2318 – 1396 = 922

**S3. Ans.(b)**

**Sol.** Required number = 1.1 – 0.01 = 1.09

**S4. Ans.(c)**

**Sol**. We know that,

Divisor = (Dividend – Remainder) / Quotient

= (397246-211) /865 = 459

**S5. Ans.(b)**

**Sol.** Here, 98375 × 9999

= 98375 × (10000 – 1)

= 983750000 – 98375

= 983651625

**S6. Ans.(a)**

**Sol**. A number is divisible by 3 if the sum of all its digits is divisible by 3.

From the given options, only 97632 is divisible by 3 because

9 + 7 + 6 + 3 + 2 = 27,

which is divisible by 3.

**S7. Ans.(d)**

**Sol.** A number made by writing a digit 6 times is divisible by each of 7, 11 and 13.

So, 555555 is divisible by each of 7, 11 and 13.

**S8. Ans.(b)**

**Sol.** We know that a number which is made by writing a 2-digit number

3-times, then the number is divisible by 7 and 13.

Now, we are to check the divisibility of 11 only.

Sum of digits at odd places in 787878

= 7 + 7 + 7 = 21

Sum of digits at even places in 787878

= 8 + 8 + 8 = 24

Difference = 24 – 21 = 3, which is not divisible by 11.

Therefore, 787878 is not divisible by 11.

**S9. Ans.(b)**

**Sol.** First, we will check the divisibility by 9.

Sum of the digits of the given number

7 + 7 + 4 + 9 + 5 + 8 + N₁ + 9 + 6 + N₂

= 55 + N₁ + N₂

By taking option one-by-one, we take

1. 55 + 7 + 8 = 70 is not divisible by 9.

2. 55 + 0 + 8 = 63 which is divisible by 9.

Now, we will check the divisibility by 8.

For it, take last three digits 96N₂ = 968

Which is divisible by 8.

Hence, the number 7749580968 is divisible by both 8 and 9.

**S10. Ans.(d)**

**Sol.** Let x = 5 and y = 10

Then, x + y = 15 is not divisible by 10.

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