CTS - Reasoning - 5

CTS – Reasoning - 5

1.       If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100 (both inclusive) varies by:

Ans: 330

2.       The total no. of numbers that are divisible by 2 or 3 between 100 and 200(both inclusive) are:

Ans: 67 (divisible by 2 – 51 Nos. Divisible by 3 – 16 Nos (excluding numbers already included under divisible by 2.)

3.       From a pack of cards Jack, Queen, King & Ace are removed. Then the algebraic sum of rest of the cards is:

Ans: 216

4.       The average temperature from Monday to Wednesday is 37 degree Celsius and that from Tuesday to Thursday is 34 degrees. The temperature of Thursday is 4/5th of Monday. Then the temperature of Thursday is:
Ans: 36 degrees

The Total Temperature from Monday to Wednesday = 37 * 3 = 111

The total Temperature from Tuesday to Thursday       = 34 * 3 = 102.

Let the temperature on Monday be ‘x’.

Then the temperature on Tuesday and Wednesday = 111 – x.

We are informed the temperature on Thursday was 4/5 of Monday -> 4x/5

So we have an equation. Total temperature from

Tuesday to Thursday =  111 – x + 4x/5 = 102.

Solving, we get the value of ‘x’ as 45.

Hence the temperature on Thursday -> 45 * 4/5 = 36 degrees.

5.       Swetha, Tina, Uma and Vidya are playing a game. In this different people lose in different games-in the reverse alphabetical order. The rule is that if one loses she should double the amount of others. At the end of 4th game each of them have same amount of money (Rs.32). Which one of them started with the least amount?

Ans: Vidya

6.       Which one of them started with the largest amount of money?

Ans: Swetha

7.       At the end of the 2nd game what is the amount of money with Uma?
Ans: Rs.8

( It’s a trial and error game. Better to start from the end and move upwards working out the various possibilities. The clue is losing in the reverse alphabetical order)

8.       A cube of 12 mm is painted on all its side. If it is cut into small cubes of size 3mm then the  number of small cubes that remain unpainted is:

Ans: 8
For Cube sums, remember the following formulae:

When a cube of size ‘n’ is cut into small cubes of equal dimension ( e.g.6 unit cube cut into 1 unit small cubes then you will have totally 6 * 6 * 6 = 216 small cubes.

If it is cut into 2 unit small cubes then 6/2 = 3 and the number of small cubes will be

3 * 3 * 3 = 27. If it is cut into small cubes of 3 units each then the number of small cubes will be 6/3 = 2 ->  2 * 2 * 2 = 8 small cubes.)

The total number of small cubes is given by n³ (where ‘n’ is the size of the main cube side divided by the unit into which it is cut)

No. of cubes coloured on three sides is always  ---- 8 (The top and bottom four corner pieces)

No of cubes coloured on 2 sides is given by ----  12(n-2)

No of cubes coloured on one side                 -----    6(n-2)²

No of cubes having no colour                         -----      (n-2)³

Using the above formula the answer to the question is -> (4 – 2)³ = 8

9.       B is 50% faster than A. If A starts at 9 A.M. and B starts at 10 A.M. A travels at a speed of 50 km/hr. If A and B are 300 km apart, at the start and travels towards each other, then at what time will they meet?  

Ans: 12 noon

The distance between A and B is 300 km and they travel towards each other.

A’ speed is 50kmph. B is 50% faster than A. Hence B’s speed is 75kmph.

A starts at 9 A.M. and B starts at 10 A.M.

A would have covered 50 km in the one hour time difference. Now the distance between A and B is reduced to 250 km.

The relative speed of A and B is (50 + 75) = 125 kmph (Pl note they travel in opposite direction)

Hence to cover the distance of 250km it would take 250/125 = 2 hours. Hence A and B will meet at 10 A. M plus 2 hours -> 12.00 noon.

10.   The ratio of white balls and black balls is 1:2. If 9 grey balls is added it becomes 2:4:3. Then what is number of black balls.

Ans: 12
The new ratio after 9 grey balls are added is W : B : G  =  2 : 4 : 3.

Now 3 parts of Grey is equal to 9 and hence one part is 3.

So, the number of Black balls is 3 * 4 = 12.  

11.   You are having 31kg of rice. You are provided with a 1kg stone for weighing. In how many weighing’s the 31kg of rice can be weighed.

Ans: 5

First Weighing – Weigh 1 kg and remove from the heap. Put the remaining 30 Kg on both the pans so that the weight is the same on both the pans. This equals 15 kg on either side.

Second weighing – Keep aside one 15 kg and weigh one kg from the remaining 15 kg and keep aside. This will leave 14 kg which split into two parts on the pans so that the weights are same. Now each pan has 7 kg rice.

Third weighing – Keep aside 7 kg and weigh one kg from the remaining 7 kg and keep the same aside. Now, we have 6 kg and this please put on both the pans so that the weight is equal. Now we have 3 kg rice on each pan.

Fourth weighing – Keep aside 3 kg and weigh 1 kg from the remaining 3kg. This will leave a balance of 2 kg rice.

Fifth weighing – Keep the remaining 2 kg rice on both the pans such that weight is equal. Now we have one kg rice on each pan.

12.   A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other.

Ans:  5.45 P. M.

A starts at 11.00 A. M. and travels at a speed of 4 kmph.

At 5.00 P. M. he will be at a distance of 24 km.

B starts at 1.00 p. M. with a speed of 1 kmph that doubles every hour.

B at 2 P. M. will be at a distance of 1 km.

B at 3 P. M. will be at a distance of  1 + 2 = 3 km

B at 4 P. M. will be at a distance of 3 + 4 = 7 km.

B at 5 P. M. will be at a distance of 7 + 8 = 15 km.

At 5 P. M. the difference is distance between A and B is 9 km and A is ahead.

At  P.M. B’s speed will be 16 kmph and A continues at 4 kmph.

Hence the Relative speed between A and B at 5.00 P. M. is 16 – 4 = 12 kmph.

At this relative speed to cover the difference in distance of 9 km would take 45 minutes.

Hence at 5.45 P. M. both A and B will meet.

13.   People near the sea shore are leading a healthy life as they eat fish. But people at other part of the city are also healthy. What inference you derive from this statement?

Ans: Healthy living has no bearing on eating fish.

14.   How will u find distance between Nagpur and Mumbai?
I took one hour more when I travel at 80 km/hr than at 90 km/hr.
Ans: 720 km.

Let D be the distance. Then we have an equation – D/80 – D/90 = 1.

Solving we get the value of D as 720 km.

15.   Two cars are 500 cm apart. Each car is moving forward for 100 cm at a speed of 50 cm/s and recedes back for 50 cm at 25 cm/s. At what time the two cars will collide with each other?
Ans: After 20 seconds the two cars will collide with each other.

Each car takes 2 seconds to move forward 100 cm and another 2 seconds to recede back 50 cm. Thus in 4 seconds the cars have actually moved forward 50 cm and the distance beween them gets reduced by 50 + 50 = 100 cm.

Thus after 4 seconds the two cars will be away at a distance of 500 – 100 = 400 cm.

          After 8 seconds they will be away at a distance of – 400 – 100 = 300 cm.

          After 12 seconds they will be away at a distance of  300 – 100 = 200 cm.

          After 16 seconds they will be away at a distance of  200 – 100 = 100 cm.

          After 20 seconds both the cars will collide with each other.