Many competitive exams test your ability to solve math puzzles and brain teasers. Most of them are number puzzles, based on the concepts of arithmetic, algebra, ratio & proportion, set theory, probability, permutations, etc. Here, we have compiled various types of mathematical puzzles in the order of difficulty. This article contains a set of 10 simple mathematical puzzles along with answers and explanations. Solve the given maths puzzle questions and check your mental aptitude:

Q.1.The front wheel of a car has a circumference of 24 ft and that of the back wheel is 30 ft long. What is the distance traveled by the car, when the front wheel has done six more revolutions than the rear wheel?

The circumference of the front wheel is 24 ft and that of the rear wheel is 30 feet. Let the rear wheel make n revolutions. At this time, the front wheel should have made n+6 revolutions. As both the wheels would have covered the same distance, n*30 = (n+6)*24⇒ 30n = 24n + 144,6n = 144 or n = 24. Distance covered = 24*30 = 720 ft.

Q.2.There are 3 bag labeled as bag P, bag Q, and bag R. Only one bag has the gift you wanted, the other 2 are empty. Assume you pick the bag P, you will have one third (1/3) of chance to win the gift. If I open the bag Q and show you the bag Q is empty, do you want to exchange your bag P for bag R in order to get a better chance to win?

No, because originally the possibility to win by picking the bag r was one third (1/3). By knowing the fact the bag Q is empty its chance of having gift is transferred to bag R, so the chance to win gets increased to (1/2).

Q.3.When the number 153,810 is divided by n, for which n is the remainder largest ?

A. 2

B. 5

C. 6

D. 8

E. 9

The correct answer is (D). 153, 810 is divisible by all the numbers in the list except 8. Hence, 8 must give the largest remainder.

Q.4.Which of the following is a common factor of both x^{2} – 4x – 5 and x^{2} – 6x – 7?

A. x-5

B. x-7

C. x-1

D. x+5

E. x+1

x^{2} – 4x – 5 = (x – 5)(x + 1), and x^{2} – 6x – 7 = (x – 7)(x + 1). The common factor is x + 1, choice (E).

Q.5.If log 3 = 0. 4771, then find how many digits are contained in the number 3^{64}.

To find the number of digits contained in the number, increase the characteristic (integral part) of the logarithmic value of the number by one.
Taking log of the given number, we get log 3^{64} = 64* log 3 = 64 * 0. 4771 = 30.535.
Here the characteristic (integral part) = 30. Therefore, number of digits contained in the number 3^{64} is 30 + 1 = 31.

Q.6.If two similar triangles have bases in the ratio of 3:4, what is the ratio of their areas?

A. 1:1.67

B. 3:4

C. 9:16

D. 6:8

Correct answer is (C). Area is proportional to square of the sides.

Q.7.A yellow light flashes 4 times per minute and a green light flashes 6 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?

Yellow light flashes every 15 seconds, Green light flashes every 20 seconds. Therefore, they will flash together after LCM of 20 and 15 i.e. every 60 seconds. In every hour they will flash 3600/60 = 60 times.

Q.8.S = { 1,3,5,7……100 elements}. How many ways are there to choose exactly 8 elements from S such that their sum is 71?

0 ways, because the sum of 8 odd numbers can never be odd.

Q.9.There are 2 sisters among a group of 15 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two sisters?

13 people can be arranged around a circle in 12! ways. There are exactly 13 places where the two sisters can be arranged. The sisters can be arranged in 2! ways. Therefore, the total number of ways 12! * 2 * 13 = 2 * 13!

Q.10.The square of a 3-digit number is a 6-digit number. If the two numbers together use all of the digits from 0 to 9 except 3, what is the 3-digit number?

(807)^{2} = 651249; Therefore, the 3-digit number is 807.