CTS - Analytical Reasoning - 3

CTS – Analytical Reasoning - 3

1.       X and Y live in North-South parallel streets. X travels 10 km towards North to reach the East-West Street. Y travels 6 km towards south to reach the East–West Street. X travels now 4km towards east and y travels 8km towards west and they met each other. What is the distance between the places X and Y live?

Ans: 20.77 km.

It’s an interesting question. The distance from X to his point of meeting Y is 10.77 km (approx.). The distance from Y to his point of meeting X is 10 km. Hence the distance between X and Y is 10.77 + 10 = 20.77 km. ( Use Pythagoras theorem)

2.       The houses are numbered 1,2,3,… and reach the end of the street and backtracks towards the starting point. The house numbered 10 is opposite to 23. There are even no of houses. Find the total no of houses.

Ans: 32 (Very simple. If house No 10 is opposite to house No 23, then there are 16 houses on either side of the street.)

3.       A seller has a set of apples out of which he sells one half of it and half an apple to his first customer. Then he sells half of the remaining apples and a half apple to his second customer. Then he sells half of the remaining apple and ½ apple to his third customer and so on. This is repeated upto 7th customer and after which no apple remains. How many apples he had initially?

Ans: 127 apples.

4.       A hollow cube of size 5cm is taken, with the thickness of 1cm. It is made of smaller cubes of size 1cm. If the outer surface of the cube is painted how many faces of the smaller cubes will remain unpainted?

Ans: 438 faces. (Note: This question was asked in TCS paper of 2012-13 also)

Assuming the cube to be a solid one of 5cm side then its volume is 125 cu.cm

When this cube is cut into small cubes of 1cm each then we will have 125 small cubes of side 1cm. If the outer surface of this cube is painted then we have 25*6 -> 150 faces of the small cubes painted.(Each surface would account to 25 small pieces)

This cube is hollow with 1 cm side. The inner side of the hollow will have dimensions of 5 – 2 -> 3cm all around. The volume of this is 27 cu.cm and this many numbers of cubes are less in the total cubes if it were to be solid.

Hence the actual number of 1cm cube now available is 125 – 27 = 98.

Each of these cubes have 6 sides and hence the total number of sides for these 98 cubes is 98 * 6 = 588 faces. Of these we know 150 faces are painted. Hence, the number of faces not painted is 588 – 150 = 438 faces.   

5.       If a 36 cm thread is used to wrap a book, lengthwise twice and breadthwise once, what is the size of the book?

Ans: 6cm x 6cm (length and breadth being equal. A square book)

6.       If 4 circles of equal radius are drawn with vertices of a square as the centre, the side of the square being 7 cm, find the area of the circles outside the square?

Ans: 105 sq.cm

Since the side of the square is 7 cm half of this will be the radius of each circle. Hence, the area of one circle is pir² -> (22*3.5*3.5)/7 -> 38.5 sq.cm. As there are 4 circles the total area of the circles 38.5 * 4 = 154 sq.cm. The area of the square falls within this total area. The area of the square is 7 * 7 = 49 sq.cm

Hence the area of the circles outside the square is 154 – 49 -> 105 sq.cm

7.       A bus has 40 seats and the passengers agree to share the total bus fare among them equally. If the total fair is Rs 80.67, find the total no of the seats unoccupied.

Ans: 10 seats

It’s a trial and error sum. The total fair is to be shared among group of passengers. Hence it has to be worked out at what figure the amount could be shared without extending fractions. 30 passengers fits into this and hence the number of vacant seats is 10. ( If one has patience to start working for different numbers you may get an alternate answer also.)

8.       A 4 digit no may consist of the digits 6,2,7,5 where none of the no’s is repeated. Find the possible no of combinations divisible by 36?

Ans: NIL (No combination is possible)

The sum of the four digits comes to 20 and the sum of the divisor is 9. Unless the sum of the digits works out to a multiple of 9 it cannot be divided by the devisor.

9.       If you are traveling from Mumbai to Bangalore and return back. To find the speed of the car which of the following are needed?

a) the distance between them.
b) time taken
c) average speed towards Mumbai and the average speed towards Bangalore.

1) (a) only.          2) (a) and (b)      3) (a,b,c)              4) (b) only          5) (c) only

Ans: (3) all the three are required.

10.   A son and father go for boating in river upstream. After rowing for 1 mile son notices the hat of his father falling in the river. After 5 min., he tells his father that his hat has fallen. So, they turn around and are able to pick the hat at the point from where they began boating after 5 min. Tell the speed of river.

Ans: 6 miles/hr

An old puzzle getting repeated frequently in many company’s papers. The hat falls after travelling one mile upstream and after turning round the father picks the same from where they started. In other words, the hat has travelled a distance of one mile. It has no momentum of its own and has moved along the river at the speed of the river.

The boy informs the father after 5 minutes of the hat falling into the river and the father takes another 5 minutes before picking up his hat.

Thus in 10 minutes the hat has moved one mile and hence the speed of the river is 6 miles per hour.