H.C.F and L.C.M
Q21. The largest number that divides 210, 315 and 168 exactly is
(a) 13
(b) 16
(c) 21
(d) 27
Answer: (c) 21
1st term =
| 2|210 |
| 3|105 |
| 5|35 |
| 7 |
2nd term =
| 3|315 |
| 3|105 |
| 5|35 |
| 7 |
3rd term =
| 2|168 |
| 2|84 |
| 2|42 |
| 3|21 |
| 7 |
210 = 2 X 3 X 5 X 7
315 = 3 X 3 X 5 X 7
168 = 2 X 2 X 2 X 3 X 7
H.C.F = 3 X 7 = 21
∴ Required number = 21
Q22. A bell rings every 5 minutes. A second bell rings every 6 minutes and if two bells ring at 8 o'clock in the morning, then the next time they will ring together at
(a) 8.10 o'clock
(b) 8.15 o'clock
(c) 8.20 o'clock
(d) 8.30 o'clock
Answer: (d) 8.30 o'clock
L.C.M of 5 and 6 = 30
∴ Next time the bells will ring together at 8 o'clock + 30 min = 8.30 o'clock
Q23. Three different containers contain different quantities of mixtures of milk and water, whose measurements are 403 Kg, 434 Kg and 465 Kg. What biggest measure must be there to measure all the difefrent quantities exactly ?
(a) 26 Kg
(b) 31 Kg
(c) 35 Kg
(d) 37 Kg
Answer: (b) 31 Kg
403 ) 434 ( 1
403
31) 403 ( 13
31
93
93
Again 31 ) 465 ( 15
31
155
155
∴ H.C.F of 403 Kg, 434 Kg and 465 Kg = 31 Kg
Q24. A, B and C starts at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point ?
(a) 38 min 18 sec
(b) 46 min 12 sec
(c) 49 min 30 sec
(d) 52 min 22 sec
Answer: (b) 46 min 12 sec
| 2|252, 308, 198 |
| 2|126, 154, 99 |
| 3|63, 77, 99 |
| 3|21, 77, 33 |
| 7|7, 77, 11 |
| 11|1, 11, 11 |
| 1, 1, 1 |
∴ L.C.M = 2 X 2 X 3 X 3 X 7 X 11 = 2772 sec = 46 min 12 sec
Q25. Three sets of English, Mathematics and Science books containing 336, 240 and 96 books respectively have to be stacked in such a way that all the books are stored subject wise and the height of each stack in the same. Total number of stacks will be
(a) 14
(b) 17
(c) 21
(d) 25
Answer: (a) 14
240) 336 ( 1
240
96) 240 (2
192
48) 96 (2
96
48) 96 ( 2
96
∴ H.C.F of 336, 240, 96 = 48
∴ Number of stacks = (336/48) + (240/48) + (96/48) = 7 + 5 + 2 = 14
Q26. What is the least number which when diminished by 4 is divisible by each one of 20, 30, 36 ?
(a) 499
(b) 507
(c) 521
(d) 544
Answer: (d) 544
| 2|20, 27, 30, 36 |
| 3|10, 27, 15, 18 |
| 2|10, 9, 5, 6 |
| 3|5, 9, 5, 3 |
| 5|5, 3, 5, 1 |
| 1, 3, 1, 1 |
∴ L.C.M = 2 X 3 X 2 X 3 X 5 X 3 = 540
∴ Required number = 540 + 4 = 544
Q27. The H.C.F and L.C.M of two numbers are 21 and 4641 respectively. If one of the number lies between 200 and 300, then the two numbers are
(a) 251, 178
(b) 273, 357
(c) 323, 389
(d) 339, 421
Answer: (b) 273, 357
Let the numbers be 21x and 21y where x and y are co-prime
Now 21x X 21y = 21 X 4641
⇒ xy = (21 X 4641)/(21 X 21) = 221 = 13 X 17
∴ Numbers are (21 X 13, 21 X 17) = i.e 273, 357
Q28. Two 3 digit numbers have their H.C.F 29 and L.C.M 4147. The sum of the numbers is
(a) 635
(b) 696
(c) 733
(d) 749
Answer: (b) 696
Let, the numbers be 29a and 29b where a and b are co-primes
Then 29a X 29b = 29 X 4147
⇒ ab = (29 X 4147)/(29 X 29) = 143 = 11 X 13
∴ Numbers are (29 X 11, 29 X 13) = 319, 377
∴ Their Sum = 319 + 377 = 696
Q29. The L.C.M of two numbers is 12 times their H.C.F. The sum of the H.C.F and L.C.M is 403. If one number is 93, then the other is
(a) 124
(b) 139
(c) 156
(d) 177
Answer: (a) 124
Let L.C.M = x and H.C.F = y
then x = 12y and
x + y = 403
⇒ 12y + y = 403
⇒ 13y = 403
⇒ y = 403/13 = 31
∴ x = 12 X 31 = 372
Let, the other number be z, then
372 X 31 = 93 X z
⇒ z = (372 X 31)/93 = 124
Q30. The capacity of two pots is 120 liters and 56 liters respectively. The capacity of a container which can exactly measure the context of the two pots is
(a) 5000 cc
(b) 6000 cc
(c) 6500 cc
(d) 8000 cc
Answer: (d) 8000 cc
56) 120 ( 2
112
8) 56 (7
56
H.C.F of 120 liter and 56 liter = 8 liter
∴ Required capacity = 8 liter = 8000 cc
Practice Test Exam