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Aptitude - Number series

Practice Q&A – Easy

1. The smallest 3 digit prime number is:

Answer:

101

Explanation :

The smallest 3-digit number is 100, which is divisible by 2.

∴ 100 is not a prime number.

√101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.

∴ 101 is a prime number.

Hence 101 is the smallest 3-digit prime number.

2. Which one of the following numbers is exactly divisible by 11?

Answer:

415624

Explanation :

(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

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3. (?) - 19657 - 33994 = 9999

Answer:

63650

Explanation :

19657+33994=53651

Let 𝑥 - 53651 = 9999

Then, 𝑥 = 9999 + 53651 = 63650

4. 753×753+247×247−753×247

753×753×753+247×247×247 = ?

Answer:

1

1000

Explanation :

Given Exp. = (𝑎2+𝑏2−𝑎𝑏)

(𝑎3+𝑏3)=

1

(𝑎+𝑏)=

1

(753+247)=

1

1000

5. (?) + 3699 + 1985 - 2047 = 31111

Answer:

27474

Explanation :

𝑥 + 3699 + 1985 - 2047 = 31111

⇒ 𝑥 + 3699 + 1985 = 31111 + 2047

⇒ 𝑥+ 5684 = 33158⇒ 𝑥= 33158 - 5684 = 27474.

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6. 107 x 107 + 93 x 93 = ?

Answer:

20098

Explanation :

107 x 107 + 93 x 93= (107)2 + (93)

= (100 + 7)2 + (100 − 7)2

= 2 x [(100)2 + (7)2] [Ref: (a + b)2 + (a − b)2 = 2(a2 + b2)]

= 20098

7. How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276

Answer:

6

Explanation :

Marking (/) those which are are divisible by 3 by not by 9 and the others by(𝑋) , by taking the sum of digits, we get:s

2133 → 9 (𝑋)

2343 → 12 (/)

3474 → 18 (𝑋)

4131 → 9 (𝑋)

5286 → 21 (/)

5340 → 12 (/)

6336 → 18 (𝑋)

7347→ 21 (/)

8115 → 15 (/)

9276 →24 (/) Required number of numbers = 6

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8 . (963+476)2+(963−476)2

(963×963+476×476) =?

Answer:

2

Explanation :

Given Exp. = (𝑎+𝑏)2+(𝑎−𝑏)2

(𝑎2+𝑏2) =

2(𝑎2+𝑏2)

(𝑎2+𝑏2) = 2

9. 8597 - ? = 7429 - 4358

Answer:

5526

Explanation :

7429 Let 8597 - x = 3071

-4358 Then, x = 8597 - 3071

——- = 5526

3071

-------

10. The smallest prime number is:

Answer:

2

Explanation :

The smallest prime number is 2.

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11. 12345679 x 72 = ?

Answer:

888888888

Explanation :

12345679 x 72= 12345679 x (70 +2)

= 12345679 x 70 + 12345679 x 2

= 864197530 + 24691358

= 888888888

12. Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ?

Answer:

(47 + 43)

Explanation :

When 𝑛 is odd, ( x 𝑛 + 𝑎𝑛 ) is always divisible by 𝑥 + 𝑎 .

∴ Each one of 4743 + 4343 and 4747 + 4347 is divisible by 47 + 43.

13. -84 x 29 + 65 = ?

Answer:

-2071

Explanation :

Given Exp.= -84 x (30 − 1)+ 365 = - (84 × 30) + 84 + 365

= -2520 + 449= -2071

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14. In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?

Answer:

5336

Explanation :

Divisor = 5 x 46 = 230

∴ 10 x Quotient = 230 ⇒ = 230

10 = 23

Dividend = [Divisor x Quotient] + Remainder

= [230 x 23] + 46 = 5290 + 46 = 5336.

15. 4500 x ? = 3375

Answer:

3

4

Explanation :

4500 x 𝑥 = 3375 ⇒ 𝑥 = 3375

4500 =

75

100 =

3

4

16. 9+ 3

4 +7+

2

17 - (9 +

1

15) = ?

Answer:

7 + 817

1020

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Explanation :

Given sum

= 9 + 3

4 + 7 +

2

17 - (9 +

1

15)

= (9 + 7 - 9) + (3

4+

2

17−

1

15)

= 7 + 765+120−68

1020 = 7 +

817

1020

17. How many prime numbers are less than 50 ?

Answer:

15

Explanation :

Prime numbers less than 50 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Their number is 15

18. (800 ÷ 64) x (1296 ÷ 36) = ?

a. 420

b. 460

c. 500

d. None of these

Answer:

None of these

Explanation :

Given Exp. = 800

64 x

1296

36 = 450

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19. Which natural number is nearest to 8485, which is completely divisible by 75 ?

Answer:

8475

Explanation :

On dividing, we get

75) 8485 (113

75 ----

98

75 ---- 235

225

---- 10 ----

Required number = (8485 - 10) // Because 10 < (75 - 10) = 8475.

20. Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?

Answer:

2079

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Explanation :

639 is not divisible by 7

2079 is divisible by each of 3, 7, 9, 11.

21. Which natural number is nearest to 9217, which is completely divisible by 88 ?

Answer:

9240

Explanation :

On dividing we get,

88) 9217 (104

88

---------------

417

352

--------------

65

--------------

Therefore, Required number = 9217 + (88 - 65) // Because (88 - 65) < 65.

= 9217 + 23 = 9240.

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22. 4300731 - ? = 2535618

Answer:

1765113

Explanation :

Let 4300731 – 𝑥 = 2535618

Then 𝑥 , = 4300731 - 2535618 = 1765113

23. (489+375)2−(489−375)2

(489×375) =?

Answer:

4

Explanation :

Given Exp. = (𝑎+𝑏)2−(𝑎−𝑏)2

𝑎𝑏 =

4𝑎𝑏

𝑎𝑏 = 4

24. 397 x 397 + 104 x 104 + 2 x 397 x 104 = ?

Answer:

251001

Explanation :

Given Exp.= (397)2 + (104)2

+ 2 x 397 x 104

= (397 + 104)2

= (501) 2

= (500 + 1)2

= (500)2 +(1)2 + (2 × 500 × 1)

= 250000 + 1 + 1000= 251001

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25. (35423 + 7164 + 41720) - (317 × 89) = ?

Answer:

28213

Explanation :

35423

• 7164

• 41720

-----------------

84307

• 28213

-----------------

56094

-----------------

317 x 89 = 317 x (90 − 1)

= (317 × 90 − 317)

= (28530 − 317)

= 28213

26. (xn - an) is completely divisible by (x - a), when

Answer:

n is any natural number

Explanation :

For every natural number 𝑛 , (xn - an) is completely divisible by (x - a).

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27. A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:

Answer:

3

Explanation :

Let 𝑥 = 6 𝑞 + 3.

Then, 𝑥2= (6q + 3)2

= 36 q2 + 36 𝑞 + 9

= 6(6 q2 + 6 𝑞 + 1) + 3

Thus, when 𝑥 2 is divided by 6, then remainder = 3.

28. What will be remainder when 17200 is divided by 18 ?

Answer:

1

Explanation :

When 𝑛 is even. (𝑥𝑛 − 𝑎𝑛)

is completely divisibly by ( x + a )

(17200 - 1200)is completely divisible by (17 + 1), i.e., 18.

⇒ (17200 - 1) is completely divisible by 18.

⇒ On dividing 17200 by 18, we get 1 as remainder.

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29. If 1400 x 𝑥 = 1050. Then, 𝑥 = ?

Answer:

3

4

Explanation :

1400 x 𝑥 = 1050 ⇒ 𝑥 = 1050

1400 =

3

4

30. Which one of the following numbers is completely divisible by 99?

Answer:

114345

Explanation :

99 = 11 x 9, where 11 and 9 are co-prime.

By hit and trial, we find that 114345 is divisible by 11 as well as 9. So, it is divisible by 99.

31. (51 + 52 + 53+. . . +100) = ?

Answer:

3775

Explanation :

This is an A.P. in which 𝑎 = 51, 𝑙 = 100 and 𝑛 = 50.

∴ Sum = 𝑛

2(𝑎 + 𝑙) =

50

2 x (51 + 100) = 25 x 151 = 3775.

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32. 1904 x 1904 = ?

Answer:

3625216

Explanation :

1904 x 1904= (1904)2 = (1900 + 4)2

= (1900)2 + (4)2 + (2 × 1900 × 4)

= 3610000 + 16 + 15200.= 3625216.

33. 1 + 2 + 3 + … + 40 = ?

Answer:

820

Explanation :

Sum of first n natural numbers = 𝑛×(𝑛+1)

2

Sum of first 40 natural numbers = 40×41

2

= 20 × 41 = 820

34. What is sum of first 17 natural numbers?

Answer:

153

Explanation :

Sum of first n natural numbers = 𝑛×(𝑛+1)

2

Sum of first 17 natural numbers = 17×18

2

= 17 × 9 = 153

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35. Find the sum of first 25 natural numbers.

Answer:

325

Explanation :

Sum of first n natural numbers = 𝒏×(𝒏+𝟏)

𝟐

Sum of first 25 natural numbers = 25×(25+1)

2

= 25×26

2 = 25 × 13 = 325

36. Find the sum of first 100 natural numbers.

Answer:

5050

Explanation :

Sum of first n natural numbers = 𝑛×(𝑛+1)

2

Sum of first 25 natural numbers = 100×(100+1)

2

= 100×101

2

= 50 × 101 = 5050

37. Find the sum of first 25 even numbers.

Answer: 650

Explanation :

Sum of first 25 even numbers = n × (n + 1) = 25 × 26 = 650

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38. Find the sum of first 100 even numbers.

Answer:

10100

Explanation :

Sum of first 100 even numbers = n × (n + 1) = 100 × 101 = 10100

39. Find the sum of first 20 odd numbers.

Answer:

400

Explanation :

Sum of first 20 odd numbers = 20 × 20 = 400

40. Find the sum of first 500 odd numbers.

Answer:

250000

Explanation :

Sum of first 500 odd numbers = 500 × 500 = 250000

More Questions at:: http://www.easytutorial.in/category/aptitude-number-series-practice-qa-46