1. Find the greatest number which divides 83, 125 and 209 leaving the same remainder in each case.
A.19 B.17 C.42 D.23 E.None of these
Answer: C
Explanation:
The greatest number which divides three dividends p, q and r leaving the same remainder in each case is given by H.C.F(any two of (q - p), (r - p) and (r - q)).
For the given problem, p = 83, q = 125 and r = 209.
Hence the greatest number which divides these three leaving the same remainder in each case is H.C.F(any two of (125 - 83, 209 - 83, 209 - 125) = 42.
2. Two numbers have a H.C.F of 16 and a product of two numbers is 2560. Find the L.C.M of the two numbers?
A.140 B.150 C.160 D.170 E.None of these
Answer: C
Explanation:
L.C.M of two numbers is given by
(Product of the two numbers) / (H.C.F of the two numbers) = 2560/16 = 160.
3. Find the greatest four digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24.
A.9974 B.9125 C.9565 D.9997 E.None of these
Answer: E
Explanation:
Since the difference between the divisors and the respective remainders is not constant, back substitution is the convenient method. None of the given numbers is satisfying the condition.
4. Find the greatest number which leaves the same remainder when it divides 25, 57 and 105.
A.18 B.8 C.12 D.16 E.None of these
Answer: D
Explanation:
105 - 57 = 48
57 - 25 = 32
105 - 25 = 80
The H.C.F of 32, 48 and 80 is 16.
5. What is the remainder when 263251 is divided by 9?
A.8 B.3 C.6 D.1 E.None of these
Answer: D
Explanation:
If the sum of the digits of a number is divisible by 9, the number will be divisible by 9.
2 + 6 + 3 + 2 + 5 + 1 = 19
The nearest multiple of 9 is 18.
19 - 18 = 1.
6.If the L.C.M of two numbers is 750 and their product is 18750, find the H.C.F of the numbers.
A.50 B.30 C.125 D.25 E.None of these
Answer: D
Explanation:
H.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750 = 25.
7. Find the smallest four-digit number which is a multiple of 112.
A.896 B.1008 C.1120 D.1024 E.None of these
Answer: B
Explanation:
The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104.
112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112.
8. A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 4 rows or 5 rows or 6 rows, then no tree will be left. Find the least number of trees required.
A.30 B.60 C.120 D.240 E.None of these
Answer: B
Explanation:
The least number of trees that are required = LCM(4, 5, 6) = 60.
9. Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case.
A.384 B.391 C.388 D.397 E.386
Answer: E
Explanation:
The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(35, 11) + 1 = 386.
10. Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5.
A.187 B.197 C.207 D.219 E.None of these
Answer: B
Explanation:
Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5.
Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197.
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