The logical reasoning, also known as critical thinking or analytic reasoning, involves one's ability to isolate and identify the various components of any given argument.So, it is not a surprise that the logical reasoning questions commonly appear in any placement tests, competitive exams or entrance exams.
1) The Master says to his grandmaster that me and my three cousins have ages in prime nos. only. Summation of our ages is 50. Grandmaster who knows the age of the master instantly tells the ages of the three cousins. Tell the ages of three cousins.( 1 is not considered as prime no.)
solution: 43,3,2,2 or 3,5,11,31
mathematical explanation :
sum of ages of all 4 cousin is 50
2+2+3+43=50
ages can be 2,2,3,43 yrs
OR
5+3+11+31=50
ages can be 3,5,11,31 yrs
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2)What is the maximum number of slices can you obtain by cutting a cake with only 4 cuts?
solution: 11 (answer can be 16 if after each slice cut we can put all slice on top of each other )
explanation:
A maximum number of 11 slices is attainable with 4 straight cuts.Assuming that after each slice cut we can
not put all slice on top of each other.
A maximum number of 16 slices is attainable with 4 straight cuts.Assuming that after each slice cut we can put all slice on top of each other.
solution 1: (Assuming that after each slice cut we
can not put all slice on top of each other.)
If you cut cake in traditional way like pizza.(Cutting through the center would give you 8 slices )
However, even more slices are possible if the cuts do not all intersect.
look at
lazy caterer’s sequence
The lazy caterer’s sequence describes the maximum number of pieces of a circle that can be made with a given number of straight cuts. The maximum number of pieces, p, that can be created with n cuts is given by the formula:
p = 1/2(n^2 + n + 2)
Therefore, for 4 cuts of the cake:
p(4) = 1/2(4^2 + 4 + 2) = 11
cut will look like:
solution 2: (Assuming that after each slice cut we
can put all slice on top of each other.)
2^4= 16
step 1: cut the cake from middle in two equal pieces. this is the first cut and we get two pieces.
step 2: put one piece on the other piece vertically and cut them from top to bottom. this is the 2nd cut and we have 4 piece.
step 3: again put the 4 pieces on each other vertically and cut from top to bottom. this is 3rd cut and we have 8 piece.
step 4: again put all the 8 pieces on each other vertically and cut from top to bottom. this is the 4th cut and we have 16 equal piece.
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3)If the digits of my present age are reversed then i get the age of my son.If 1 year ago my age was twice as that of my son.Find my present age.
A) Father - 72, Son - 38
wrong answer
B) Father - 71, Son - 39
wrong answer
C) Father - 73, Son - 37
right answer
D) Father - 73, Son - 38
wrong answer
solution: Father - 73, Son - 37
explanation:
Digits of my present age are reversed then i get the age of my son.
My age : 10x+y
Son age : 10y+x
If 1 year ago my age was twice as that of my son.
10x+y-1 = 2(10y+x-1)
x = (19y-1)/8
For y=3 (19y-1) is completely divisible by 8
So x = 7
So my present age : 10*7+3 = 73
Son's age : 10*3+7 = 37
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4) Every day a cyclist meets a train at a particular crossing. The road is straight before the crossing and both are travelling in the same direction. Cyclist travels with a speed of 10 Kmph. One day the cyclist comes late by 25 min. and meets the train 5km before the crossing. What is the speed of the train.
solution: 60
explanation:
first part:
when the cyclist meets the train, he has 5 km to go
so for the cyclist Time require to travel 5km is
Distance = Speed * Time
Cyclist:
Speed = 10 km/h
Distance = 5 km
Time = 5/10 h = 1/2 h = 30 min
The cyclist takes 30 min to travel 5 km.
second part:
The cyclist is already 25 minutes late, so it takes the train t=30-25= 5 minutes to travel 5 km.
So the speed should have been 60 km/h
Hence, the speed of the train is 60 km/hr.
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5)A big cube painted red on all the sides. It was cut into 27 smaller cubes by 6 straight lines. How many of the smaller cubes painted on all 3 sides, on 2 sides, on 1 side and no faces painted?
solution: 8,12,6,1
explanation:
click here for tricks to solve cube problem
here n is 3.
0 sides painted = (n-2)^3 =(3-2)^3=1
1 sides painted = 6(n - 2)^2 =6(3-2)^3=6
2 sides painted = 12(n - 2) =12(3-2)^3=12
3 sides painted = 8 (eight painted cubes are the 8 corners )
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6)Ramesh starting from a fixed point goes 15 m towards North and then after turning to his right he goes 15 m. then he goes 10, 15 and 15 m after turning to his left each time. How far is he from his starting point?
solution: 10m
explanation:
He will be 10m away from his starting point.
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7)Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point?
A) 7 km East
wrong answer
B) 5 km West
wrong answer
C) 7 km West
wrong answer
D) 5 km North-East
right answer
solution: 5 km North-East
explanation:
Sonalika is 5 km North-East from Starting point
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8)Laxman went 15kms to the west from my house, then turned left and walked 20 kms.He then turned east and walked 25kms and finally turning left covered 20kms. how far was he from my house?
solution: 10
explanation:
Distance from house=25-15=10
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9)find the angle between hour hand and minute hand when time is 12:40?
solution: 220 degree OR 140 degree
explanation:
For hour hand:
12 hrs=360 degree
1hr=30degree
60min=30 degree
1min=0.5 degree
therefore 40min=20 degree
For minute hand:
60min =360 degree
1min =6 degree
therefore 40min=240 degree
Angle between hour hand and minute hand =240-20=220 degree
or 360-220=140
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10)Three customers want haircut and a shave. In a saloon, two barbers operate at same speed. They take quarter of an hour for the haircut and 5 mins for the shave. How quickly can they finish the haircut and shave of these three customers?
A) 30 minutes
right answer
B) 25 minutes
wrong answer
C) 35 minutes
wrong answer
D) 28.75 minutes
wrong answer
solution: 30 minutes
explanation:
Suppose the time is 12:00.
for the customers 1,his haircut and shave can be done at the same time.
After 5 minutes,the shaving barber2 moves to the customers 2 after 5 minuts to the customers 3.
now time left after the shaving of the 3 men will be 15 minutes(12:15 is going),
so he will moves quickly to the customers 2 for his haircut(12:15 to 12:30)
and for the customers 3,the barbers 1 has moves already for his haircut.
So 12:15 to 12:30,the haircutting of 2nd and 3rd is done.
Hence total time require is 30 min
barbers 1:
customers 1(haircut)------->15m
customers 3(haircut)------->15m
and same time
barbers 2:
Jobs
time taken
customers 1(Shave)--------->5m
customers 2(shave)--------->5m
customers 3(shave)--------->5m
customers 2(haircut)------->15m
Total time taken is 30 minutes.
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