Problems on Numbers for Exam
Q11. 86 X 86 - 14 X 14
(a) 7020
(b) 7156
(c) 7200
(d) 7400
Answer: (c) 7200
=86 X 86 - 14 X 14
=(86)2 - (14)2
=(86+14) - (86-14) Formula [a2 - b2=(a+b)(a-b)]
=100 X 72
=7200
| (251 X 251 X 251) - (69 X 69 X 69) |
| (251 X 251 + 251 X 69 + 69 X 69) |
(a) 180
(b) 182
(c) 285
(d) 1081
Answer: (b) 182
=| (251 X 251 X 251) - (69 X 69 X 69) |
| (251 X 251 + 251 X 69 + 69 X 69) |
| (251)3 - (69)3 |
| (251)2 + (251 X 69) + (69)2 |
| (251 - 69) (2512 + 251 X 69 + 692) |
| (2512 + 251 X 69 + 692) |
=251 - 69
=182
Formula a3 - b3=(a-b)(a2+ab+b2)
| (407 + 315)2 - (407 - 315)2 |
| 407 X 315 |
(a) 41
(b) 401
(c) 4
(d) 104
Answer: (c) 4
=| (407 + 315)2 - (407 - 315)2 |
| 407 X 315 |
| 4 X 407 X 315 |
| 407 X 315 |
=4
Formula (a+b)2 - (a-b)2 = 4ab
| (215 + 102)2 + (215 - 102)2 |
| 215 X 215 + 102 X 102 |
(a) 2
(b) 12
(c) 102
(d) 215
Answer: (a) 2
=| (215 + 102)2 + (215 - 102)2 |
| 215 X 215 + 102 X 102 |
| 2(2152 + 1022) |
| 2152 + 1022 |
=2
Q15. 1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20 = ?
(a) 20
(b) 120
(c) 201
(d) 210
Answer: (d) 210
=1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20
=20 (20 + 1) ÷ 2
=10 X 21
=210
Formula 1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + n = n(n + 1) ÷ 2
Q16. 3 + 4 + 5 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20 = ?
(a) 205
(b) 206
(c) 207
(d) 208
Answer: (c) 207
=3 + 4 + 5 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20
=1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20 - (1 + 2)
=[20 (20 + 1) ÷ 2] - 3
=10 X 21 - 3
=210 -3
=207
Formula 1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + n = n(n + 1) ÷ 2
Q17. 12 + 22 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102 = ?
(a) 285
(b) 385
(c) 485
(d) 585
Answer: (b) 385
=12 + 22 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102
=[10 (10 + 1) (2 X 10 + 1)] ÷ 6
=(10 X 11 X 21) ÷ 6
=385
Formula 12 + 22 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + n2 = [n(n+1)(2n+1) ÷ 6
Q18. 32 + 42 + 52 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102 = ?
(a) 380
(b) 382
(c) 384
(d) 386
Answer: (a) 380
=32 + 42 + 52 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102
=12 + 22 + 32 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102 - (12 + 22)
=[10 (10 + 1) (2 X 10 + 1) ÷ 6] - (1+4)
=[10 X 11 X 21 ÷ 6] - 5
=385 - 5
=380
Q19. 13 + 23 + 33 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 103 = ?
(a) 2025
(b) 3025
(c) 3052
(d) 3205
Answer: (b) 3025
=13 + 23 + 33 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 103
=| 102(10 + 1)2 |
| 4 |
| 100 X 121 |
| 4 |
=3025
Formula [13 + 23 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + n3] =[n2(n + 1)2] ÷ 4
Q20. The difference between the place value and face value of 5 in the number 835422 is
(a) 4995
(b) 5000
(c) 5005
(d) 5995
Answer: (a) 4995
Place value of 5 = 5000
Face value of 5 = 5
Diference = 4995
Practice Test Exam