quantitative aptitude qa-10

QA-10

CLASS EXERCISE

1. Which number is exactly divisible by 99? (a) 135792 (b) 3572404

(c) 913464 (d) 114345

2. Which number is exactly divisible by 72? (a) 1161 (b) 1611

(c) 1152 (d) 1254

3. What will come in place of x and y respectively if 37x20y is exactly

divisible by 440?

(a) 2,3 (b) 3,2 (c) 6,0 (d) 4,0

4. What will come in place of x and y respectively if 268x51y is exactly

divisible by 72? (a) 2,3 (b) 3,2

(b) 5,1 (d) 1,5

5. What will come in place of x and y respectively if 653xy is exactly divisible

by 80?

(a) 2,0 (b) 0,2 (c) 5,1 (d) 6,0

6. Which of the following is the factor of 486486?

(a) 8 (b) 10 (c) 11 (d) 15

7. Which of the following is the factor of 616161? (a) 14 (b) 9

(c) 11 (d) 37

8. How many factors are there in 500? (a) 10 (b) 11

(c) 12 (d) 14

Quantitative Aptitude

Number System-1

QA-10

QA-10


(c) 24 (d) 48


(c) 24 (d) 48

11. If N = 9800, then find

(i) How many factors are there in N?

(ii) How many factors are odd? (iii) How many factors are even?

(iv) How many factors are prime?

(v) How many factors are composite?

(vi) How many factors end with zero?

12. How many distinct numbers divide 272727?

13. How many distinct numbers divide 456456?

14. How many numbers are divisible by 8 from 200 to 400. (a) 25 (b) 26

(c) 50 (d) 24

15. How many numbers are divisible by 8 between 200 to 400. (a) 25 (b) 26

(c) 50 (d) 24

16. How many numbers are divisible by 12 that lies from 200 to 400

(a) 15 (b) 17

(c) 16 (d) 33

17. How many numbers are divisible by 8 and 12 that lies from 200 to 400

(a) 8 (b) 16

(c) 26 (d) 50

18. How many numbers are divisible by 8 or 12 that lies from 200 to 400

(a) 24 (b) 25 (c) 26 (d) 35

QA-10

19. (i) How many numbers are not divisible by 8 or 12 in 200 to 400 (ii) How many numbers are not divisible by 8 and 12 in 200 to 400

20. Find the digit at unit’s place.

(i) 253 (ii) 6335

(iii) 58100

(iv) 5252 × 5353 (v) 365 × 659 × 771

(vii) 111 +122 + 133 + 144 + 155 + 166

QA-10

HOME EXERCISE

21. If 8A5146B is divisible by 88, then what is the value of A×B? (a) 4 (b) 16

(c) 8 (d) 12

22. How many numbers between 11 and 90 are divisible by 7?

(a) 10 (b) 11

(c) 9 (d) 12

23. If the number 357a25b is divisible by both 3 and 5, then find the value of a

and b respectively?

(a) 0,6 (b) 6,5 (c) 5,4 (d) 0,7

24. The sum of three consecutive odd numbers is always divisible by (a) 2 (b) 3

(c) 6 (d) Both 3 and 6

25. Which of the following number is divisible by 132? (a) 2392456 (b) 345345

(c) 369785 (d) 20,328

26. If N = 4800, then find

(i) How many factors are there in N?

(ii) How many factors are odd? (iii) How many factors are even?

(iv) How many factors are prime?

(v) How many factors are composite?

(vi) How many factors end with zero? (vii) How many factors are the multiple of 12?

27. The digit in the unit’s place of [(251)98 + (21)29– (106)100 + (705)35 – 164 + 259] is

(a) 1 (b) 4

(c) 5 (d) 6

QA-10

28. How many of the following numbers are completely divisible by 132? 264, 396, 462, 792, 968, 2178, 5184 and 6336

(a) 4 (b) 5

(c) 6 (d) 7

29. How many numbers between 11 and 90 are divisible by 9?

(a) 10 (b) 11

(c) 8 (d) 9

30. How many factors of 64800 are even?

(a) 70 (b)75 (c)80 (d)85

31. How many factors of 25 × 34 × 53 will end up with at least one zero?

(a) 72 (b) 80 (c) 85 (d) 75

32. How many number between 400 and 800 are divisible by 4 and 5 ? (a) 7 (b) 8

(c) 9 (d) 19

33. How many numbers between 400 and 800 are divisible by 4, 5 and 6?

(a) 7 (b) 8

(c) 9 (d) 10

34. How many numbers are divisible by 4 or 5 from 400 to 800?

(a) 160 (b) 161

(c) 171 (d) 132

35. How many numbers are not divisible by 4 or 5 from 400 to 800?

(a) 380 (b) 321

(c) 350 (d) None

36. The digit in unit’s place of the product 49237× 3995 × 738 × 83 × 9 is

(a) 0 (b) 7 (c) 5 (d) 6

37. What is the value of M and N respectively? If M39048458N is divisible by 8 and 11; where M and N are single digit integers?

(a) 7, 8 (b) 8, 6

(c) 6, 4 (d) 5, 4

QA-10

38. How many divisors does 7200 have? (a) 20 (b) 4

(c) 54 (d) 32

39. How many factors of 24 * 53 * 74 are odd numbers? (a) 100 (b) 99

(c) 20 (d) 24

40. The digit in the unit’s place of the product (2464)1793 × (515)317 × (131)491

is

(a) 0 (b) 2 (c) 3 (d) 5

QA-10 Page 1

Quantitative Ability-10

Number System-1

Answers and Explanations

CLASS EXERCISE

HOME EXERCISE

21 d 22 b 23 b 24 b 25 d 26i 42 ii 6 iii 36 iv 3 v 38

vi 24 vii 15 27 b 28 a 29 b 30 b 31 d 32 d 33 a 34 d

35 c 36 a 37 c 38 c 39 c 40 a

CLASS EXERCISE

1. d For a number to be divisible by 99, the number should be divisible by 11

and 9. 114345 is a number which is divisible by both 11 and 9

2. c For a number to be divisible by 72, the number should be divisible by 8

and 9. 1152 is a number which is divisible by both 8 and 9

3. c For a number to be divisible by 440, a number has to be divisible by 11, 8

and 5. If a number has to be divisible by 5 and 8 then last digit should be

either 0 or 5 and last three digits should be divisible by 8. With this logic, Y should be 0. And with the divisibility rule of 11,

9-(3+x) = 0

So, x=6

1 d 2 c 3 c 4 b 5 d 6 c 7 d 8 c 9 b 10 d

11(i) 36 (ii) 9 iii 27 iv 3 v 32 vi 18 12 40 13 128 14 b

15 d 16 b 17 a 18 d 19 (i) 193 ii 166

20 i 2 ii 7 iii 6 iv 8 v 4 vi 9

QA-10 Page 2

4. b If a number is divisible by 72, it has to be divisible by 8 and 9 both. For a number to be divisible by 8, the number formed by it’s last three digits

must be divisible by 8, with that logic Y is definitely 2. Now for a number

to be divisible by 9, sum of its digits must be divisible by 9. Sum of the

digits of given number is (22 + X + Y) that is (24 + X), for this sum to be divisible by 9 ‘X’ must be 3.

5. d If a number is divisible by 80, it has to be divisible by 16 and 5. For a number to be divisible by 5, last digit should be 0 or 5 and to be divisible

by 16, last 4 digits should be divisible by 16. So Y must be 0 and X must

be 6.

6. c

7. d

8. c 500 = 53×22

= 4×3

=12

9. b 4500 = 53×32×22

= 4×3×3

=36

10. d 6600 = 11×3×23×52 = 2×2×4×3 = 48 11. i 9800 = 72×23×52

= 3×4×3 = 36 ii. Odd factors = 3×3 = 9 iii. Even factors = 36-9 =27 iv. Prime factors = 3 v. Composite factors = 36-3-1 = 32 vi. Multiples of 10 =21-3×51-2×70-2

= 3×3×2 = 18

12. 272727 = 27 × 10101

= 34×37×13×7 = 5×2×2×2

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= 40 13. 456456 = 456 × 1001 = 23×3×19×7×11×13 = 4×2×2×2×2×2 =128

14. b = 400

8 -

199

8

= 50-24 = 26

15. d = 399

8 -

200

8

= 49-25 = 24

16. b = 400

12 -

199

12

= 33-16 = 17 17. a Numbers divisible by 8 and 12 means the numbers that are divisible

by both 8 and 12. So, in this case, we will take the LCM(8,12)=24

= 400

24 -

199

24

= 16-8 = 8 18. d Numbers divisible by 8 or 12 means the numbers that are divisible by

either 8 or 12. So, in this case, =m(8) + m(12) – m(24) =26+17-8 = 43-8 =35 19.i Total – m(8 and 12) = 201-8 = 193 ii. Total- m(8 or 12) = 201-35 = 166 20. i 53 when divided by 4, remainder is 1 So 21=2 ii 35 when divided by 4, remainder is 3 So, 633 = 33 = 27. Unit digit is 7 iii. 100 when divided by 4, remainder is 0. We will replace it with 4. So, 584= 84 = 6 iv. 524×531

QA-10 Page 4

=24×31 =6×3 =8 v. 31×63×73 =3×6×3 =8×3 =4 vi. 11+22+33+44+55+66 =1+4+7+6+5+6 =9

HOME EXERCISE 21. d If a number is divisible by 88, then it has to be divisible by 11 and 8.

For a number to be divisible by 8, the number formed by it’s last three

digits must be divisible by 8, with that logic B is definitely 4. Now for a number to be divisible by 11,

21-(7+A)=11

A=3

A×B = 3×4 = 12

22. b = 89

7 -

11

7

= 12-1 = 11 23. b If a number is divisible by 5, last digit should be either 0 or 5.

Therefore, according to options b is the only possible answer. 24. b 25. d For a number to be divisible by 132, the number should be divisible by 11

4 and 3. 20,328 is a number which is divisible by both 11 and 9.

26. i 4800 = 3×26×52

= 2×7×3 = 42 ii. Odd factors = 3×2 = 6 iii. Even factors = 42-6 =36 iv. Prime factors = 3 v. Composite factors = 42-3-1 = 38

QA-10 Page 5

vi. Multiples of 10 =21-6×51-2×30-1

= 6×2×2 = 24 vii. Multiples of 12 =22-6×50-2×31

= 5×3×1 = 15 27. b Unit Digit will be = 1+1-6+5-6+9 = 4 28. a There are 4 numbers which are divisible by 11, 4 and 3

29. b = 89

7 -

11

7

= 12-1 = 11 30. b 64800= 25×52×34

Total factors = 6×3×5 = 90 Odd factors = 3×5 = 15 Even factors = 90-15=75 31. d 21-5×51-3×30-4 =5×3×5 =75

32. d = 799

20 -

400

20

= 39-20 = 19

33. a = 799

60 -

400

60

= 13-6 = 7 34. d m(4) + m(5) – m(20)

= 800

4 -

399

4 +

800

5 -

399

5 - 800

20 +

399

20

= 200-99+160-79-101+81 = 182 35. a Total factors – m(4 and5) 401-21 = 380 36. a 7×5×8×3×9 =0 (unit digit)

QA-10 Page 6

37. c For a number to be divisible by 8, the number formed by it’s last three

digits must be divisible by 8, with that logic N is definitely 4. Now for a

number to be divisible by 11,

20 – (25+M) = 11 M= 6

38. c 7200 = 32×25×52 = 3×6×3 =54 39. c Odd factors = 4×5 = 20 40. a 41×51×13 = 4×5×1 = 0 (unit digit)

quantitative aptitude qa-10

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