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
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
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:
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.
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.
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.
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.