Q 1-Which f the following numbers is exactly divisible by 11?

A - 499774

B - 47554

C - 466654

D - 4646652

```Answer - A

Explanation

"Reference : Divisibility by 11 Rule

Take 47554

4 + 5 + 4 = 13

7 + 5 = 12

13 - 12 = 1

1 is not divisible by 11

Hence 47554 is not divisible by 11

Take 466654

4 + 6 + 4 = 14

6 + 5 = 11

14 - 11 = 3

3 is not divisible by 11

Hence 466654 is not divisible by 11

Take 4646652

4 + 4 + 6 + 2 = 16

6 + 6 + 5 = 17

17 - 16 = 1

1 is not divisible by 11

Hence 4646652 is not divisible by 11

Take 499774

4 + 9 + 7 = 20

9 + 7 + 4 = 20

20 - 20 = 0

We got the difference as 0.

Hence 499774 is divisible by 11
"
```

Q 2-What is the sum all even natural numbers between 1 and 101?

A - 5050

B - 2550

C - 5040

D - 2540

```Answer - B

Explanation

"Reference 1: Natural Numbers

Reference 2: Arithmetic Progression (AP) and Related Formulas

Required sum = 2 + 4 + 6+ . . . + 100

This is an arithmetic progression with

a = 2

d = (4 - 2) = 2

n=( l − a ) / d+1

=(100−2)/2+1

=98/2+1

=49+1

=50

2+4+6+⋯+100

= n/2 (a+l)

=50/2(2+100)

=50×51

=2550
"
```

Q 3-A boy multiplies 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong , but the other digits are correct, then what will be the correct answer?

A - 556581

B - 555681

C - 555181

D - 553681

```Answer - B

Explanation

"The answer is divisible by 987. So we can use hit and trial method to find out

the number divisible by 987 from the given choices.

553681 ÷ 987 gives a remainder not equal to 0

555181 ÷ 987 gives a remainder not equal to 0

556581 ÷ 987 gives a remainder not equal to 0

But 555681 ÷ 987 gives 0 as remainder. Hence this is the answer
"
```

Q 4-Which one of the following cannot be the square of a natural number ?

A - 15186125824

B - 49873162329

C - 14936506225

D - 60625273287

```Answer - D

Explanation

"Square of a natural number cannot end with 7.
```

Q 5-7128+1252=1202+?

A - 6028

B - 1248

C - 2348

D - 7178

```Answer - D

Explanation

"?=7128+1252−1202

=7128+50

=7178
"
```

Q 6-73411×9999=?

A - 724836589

B - 724036589

C - 734036589

D - 734036129

```Answer - C

Explanation

"73411×9999

=73411(10000−1)

=734110000−73411

=734036589
"
```

Q 7-32+33+34+⋯+42=?

A - 397

B - 407

C - 417

D - 427

```Answer - B

Explanation

"1+2+3+⋯+n =∑n=n(n+1)/2

(Reference: Power Series)

32+33+34+⋯+42

=(1+2+3+⋯+42)  − (1+2+3+⋯+31)

=(42×43/2)−(31×32/2)  = 21×43−31 × 16

=903−496

=407
"
```

Q 8-1234+123+12−?=1221

A - 148

B - 158

C - 168

D - 178

```Answer - A

Explanation

? = 1234+123+12−1221=148
```

Q 9-9312×9999=?

A - 93110688

B - 93010688

C - 93110678

D - 83110688

```Answer - A

Explanation

"9312×9999

=9312(10000−1)

=93120000−9312

=93110688
"
```

Q 10-A three-digit number 4a3 is added to another three-digit number 984 to give a four digit number 13b7, which is divisible by 11. What is the value of (a + b)?

A - 9

B - 10

C - 11

D - 12

```Answer - B

Explanation

"(Reference : Divisibility by 11 rule)

4  a  3

9  8  4

13  b  7

=> a + 8 = b ...(1)

13b7 is divisible by 11

=> (1 + b) - (3 + 7) is 0 or divisible by 11

=> (b - 9) is 0 or divisible by 11 ...(2)

Assume that (b - 9) = 0

=> b = 9

Substituting the value of b in (1),

a + 8 = b

a + 8 = 9

=> a = 9 - 8 = 1

If a = 1 and b= 9,

(a + b) = 1 + 9 = 10

10 is there in the given choices. Hence this is the answer.
"
```

Q 11-The sum of the two numbers is 11 and their product is 24. What is the sum of the reciprocals of these numbers ?

A - 42563

B - 42686

C - 42698

D - 42559

```Answer - C

Explanation

"Let the numbers be xx and y Then

x+y=11

xy=24

Hence,

x+y/xy=11/24

⇒1/y+1/x=11/24
"
```

Q 12-What is the difference between the place values of two sevens in the numeral 54709479 ?

A - 699930

B - 699990

C - 99990

D - None of these

```Answer - A

Explanation

"Required Difference

= 700000 - 70 = 699930
"
```

Q 13-A number when divided by 75 leaves 34 as remainder. What will be the remainder if the same number is divided by 65?

A - 1/2

B - 12/31

C - 1/5

D - 1/8

```Answer - D

Explanation

"Let the number be x

Let x÷75 =p and remainder = 34

⇒x=75p+34

⇒x=(25p×3)+25+9

⇒x=25(3p+1)+9

Hence, if the number is divided by 25, we will get 9 as remainder
"
```

Q 14-The number 7490xy7490xy is divisible by 90. Find out (x+y)(x+y)

A - 4

B - 5

C - 6

D - 7

```Answer - D

Explanation

"If a number is divisible by two co-prime numbers, then the number is divisible

by their product also.

A number is divisible by 10 if the last digit is 0.

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

10×9=90 where 10 and 9 are co-prime numbers. Hence, if 7490xy is

divisible by 9 and 10, it will also be divisible by 90

Suppose 7490xy is divisible by 10. We know that a number is divisible by

10 if the last digit is 0.

Hence y=0y=0

Thus we have the number 7490x0. If this is divisible by 9,

7+4+9+0+x+0   is divisible by 9

=> 20+x is divisible by 9  (where x is a digit)

=> x=7

Hence, (x+y)=(7+0)=7
"
```

Q 15-What is the smallest 3 digit prime number?

A - 107

B - 100

C - 102

D - 101

```Answer - D

Explanation

". Prime Numbers

. Divisibility Rules

102 is divisible by 2

=> 102 is not a prime number

100 is divisible by 2

=> 100 is not a prime number.

√101<11

101 is not divisible by the prime numbers 2, 3, 5, 7

Hence 101 is a prime number.

Since 100 is not a prime number, 101 is the smallest 3 digit prime number.

√107<11

107 is also not divisible by the prime numbers 2,3,5,7

Hence 107 is also a prime number.

But the smallest 3 digit prime number is 101
"
```