## Problems on Numbers – Aptitude Questions and Answers

**Problems on Numbers aptitude questions and answers section with explanation. Practice online test for various interview, competitive and entrance exams.****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.

**Also Check:** **Aptitude Questions and Answers**