1. Find the greatest number of four digits which must be added to 5,231 so that the final number becomes exactly divisible
by 12, 15, 27, 32 and 40.
(a) 7,729 (b) 7,829 (c) 7,929 (d) 9,729
2. Find the greatest number of six digits, which on being divided by 6, 7, 8, 9 and 10 leaves 4, 5, 6, 7 and 8 as remainder,
respectively.
(a) 9,97,920 (b) 9,97,918 (c) 9,98,918 (d) 9,99,918
3. A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45, there are 3 stones
left in each case. How many least stones can there be in the heap?
(a) 2,403 (b) 3,603 (c) 4,803 (d) 7,203
4. What is the least number of pieces of equal length that can be cut out of two lengths, 10 m, 857 mm and 15 m 87 mm?
(a) 174 (b) 172 (c) 164 (d) 184.
5. The HCF  of two numbers is 11 and their LCM is 693. If one of the numbers is 77, find the other.
(a) 66 (b) 99 (c) 1,119 (d) 909
6. What is the least multiple of 17, which leaves a remainder of 1 when divided by each of the first twelve integers excepting
unity?
(a) 1,38,599 (b) 1,38,601 (c) 27,719 (d) 27,720
7. The LCM and GCM of two numbers are 1,530 and 51, respectively. Find how many such pairs are possible:
(a) 4 (b) 3 (c) 2 (d) 1
8. Find the greatest four-digit number which, when divided by 12, 18, 21 and 28 leaves a remainder 3 in each case.
(a) 9,830 (b) 9,831 (c) 9,835 (d) 9,836
9. The LCM of 54, 90 and a third number is 1,890 and their GCM is 18. What is the third number?
(a) 36 (b) 126 (c) 108 (d) 180
10. Find the least number which on being divided by 5, 6, 8, 9, 12 leaves in each case a remainder 1, but when divided by
13 leaves no remainder.
(a) 3,595 (b) 3,600 (c) 3,601 (d) 3,602
11. Three men start together to travel the same way around a circular track of 11 km circumference. Their speeds are 4, 5
and 8 km/h, respectively. When will they meet at the starting point?
(a) 11 h (b) 12 h (c) 22 h (d) 220 h
12. When 5 or 6 dozens of oranges were packed in each box, three dozens were remaining. Therefore, bigger boxes were
taken to pack 8 or 9 dozens of oranges. However, still three dozens of oranges remained. What was the least number of
dozens of oranges to be packed?
(a) 216 (b) 243 (c) 363 (d) 435
13. Four bells toll at intervals of 6, 8, 12 and 18 minutes, respectively. If they start tolling together at 12 a.m., after what
interval will they toll together again and how many times will they toll together in 6 hours?
(a) 6 times (b) 5 times (c) 4 times (d) Data inadequate
14. Which of the following is a pair of co-primes?
(a) (14, 35) (b) (18, 25) (c) (32, 62) (d) (31, 93)
15. The GCM of two numbers is 38 and their LCM is 98,154. If one of the numbers is 1,558, the other number is
(a) 3,450 (b) 2,395 (c) 2,394 (d) 1,260

July 6, 2023

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## Fast Track Practice-MATH

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