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) Look at this series: 31, 29, 24, 22, 17, ... What number should come next?
solution: 15
explanation :
1st number is 31
2nd number is 29 (31 -2)
3rd number is 24 (29 -5)
4th number is 22 (24 -2)
5th number is 17 (22 -5)
6th number is 15 (17 -2)
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2) The age of the grand lady is between 50-70 where each of her son has as many sons as many brothers he has. The grand lady's age is equal to the number of sons and grand sons. What is the age of the grand lady?
solution: 64
explanation:
The age of the grand lady is between 50-70 where each of her son has as many sons as many brothers he has.
The grand lady's age is equal to the number of sons and grand sons. What is the age of the grand lady
Assume the grand lady has x sons.
Each of her sons has x-1 brothers. Therefore they should each have x-1 sons.
Since there are x sons and each has x-1 sons, the total number of grandsons is: x(x-1)
The total number of grand lady sons and grandsons=x + x(x-1) = x + x^2 - x = x^2
it is given that grand lady age is between 50 and 70 and grand lady's age is equal to the number of sons and grand sons.
Now we have 50 <= x^2 <= 70
Take the square root and we get
sqrt(50) <= x <= sqrt(70)
The only natural number that satisfies these inequalities is x=8.
So grand lady has 8 sons. Each of them has 7 sons.
The total number of grandsons : 8x7=56
The total number of grandsons and sons: 64
grand Lady's age = 64
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3)A cube of volume 1000 cm^3 is divided into small cubes of 1 cm^3 & all the outer surfaces are painted how many cubes will be there with at least one side painted and no side painted ?
solution: 488,512
explanation:
click here for tricks to solve cube problem
0 sides painted = (n-2)^3 where n is number blocks on one row or column of the cube
here x =cube root of 1000=10
so ans is (10-2)^3=8^3=512
Number of cubes with atleast one side painted = 1000-512= 488
so
Number of cubes with No side painted = 512
Number of cubes with atleast one side painted = 1000-512= 488
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4)In a group of six women, there are four dancers, four vocal musicians, one actress and three violinists. Girija and Vanaja are among the violinists while Jalaja and Shailja do not know how to play on the vilion. Shailja and Tanuja are among the dancer. Jalaja, Vanaja, Shailja and Tanuja are all vocal musicians and two of them are also violinists. If Pooja is an actress, who among the following is both a dancer and a violinist ?
solution: Tanuja
explanation:
The four vocal musicians and one actress in the group are given. Two dancers are Shailja and Tanuja. Two violinists are Girija and Vanaja. Since Jalaja and Shailja cannot be violinists. so, remaining two violinists are Tanuja and Pooja.
Clearly, Tanuja is both a violinist andd a dancer.
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5) A sixth grade teacher asked her students to draw rectangles with positive integer length and a perimeter of 42.the difference between the largest and smallest possible ares of the rectangles that the students could have come up with is?
solution: 90
explanation:
sum of length and breadth will be 21 units .
2(l+b)=42
l+b=21
area will be max
when length=11 and breadth =10
area (lxb) = 11x10=110 sq units
area will be min
when length=20 and breadth =1
area (lxb) = 20x1=20 sq units
therefore difference between the largest and smallest possible areas of the rectangles that the students could have come up with= 110-20=90 sq units
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6) Find the number of 6 digit numbers consisting only of even digits
solution: 12500.
explanation:
even digits are 0,2,4,6,8... as we normally consider 0 as even number.
We can choose the 1st digit as 2,4,6, or 8. That's 4 ways. ( as first digit can not be zero.)
We can choose the 2nd digit as 0,2,4,6, or 8. That's 5 ways.
We can choose the 3rd digit as 0,2,4,6, or 8. That's 5 ways.
We can choose the 4th digit as 0,2,4,6, or 8. That's 5 ways.
We can choose the 5th digit as 0,2,4,6, or 8. That's 5 ways.
We can choose the 6th digit as 0,2,4,6, or 8. That's 5 ways.
number of 6 digit numbers consisting only of even digits= 4*5*5*5*5*5 = 4*3125 = 12500.
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7) There are 15 stepping stones numbered from 1 to 15. A frog jumps from the 1st stone as follows; Every minute it jumps to the 5th stone from where it started - that is from 1st it would go to 6th and from 6th it would go to 11th and from 11th it would go to 16th etc. And another frog jumps from 1st stone in the same manner but it takes 4 minutes for each jump. What would be the number of stepping stones between the two frogs at the 60th minute if they start at 1st step?
solution: 0
explanation:
To find the position of the 1st frog at 60 minute:
1st minute : 1 + 5 = 6th step
2nd minute : 6 + 5 = 11th step
3rd minute : 11 + 5 = 15 + 1 = 1st step
(next step was 11+ 5=16 but we have only 15 stones so it will start back to 1st for remaining steps)
4th minute : 1 + 5 = 6th step
5th minute : 6 + 5 = 11th step
6th minute : 11 + 5 = 15 + 1 = 1st step
The same process is repeated 20 x 3 times.
Then, the jumping positions are
1 6 11
1 6 11
1 6 11 and so on.
after 20th cycle it will be in the 1st position
i.e., at 60th minute it will be in the step numbered 1.
Now, to find the position of the 2nd frog at 60 minute:
It takes 4 minutes for each jump.
End of 4 minutes : 1 + 5 = 6th step
End of 8 minutes : 6 + 5 = 11th step
End of 12 minutes : 11 + 5 = 15 + 1 = 1st step
End of 16 minutes : 1 + 5 = 6th step
End of 20 minute : 6 + 5 = 11th step
To make it easy we have written the above pattern again as follows:
Minutes : 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Steps : 6 11 1 6 11 1 6 11 1 6 11 1 6 11 1
At 60th minute the 2nd frog will be in 1st step.
Thus, the two frogs are in same position in 60th minute.
Then the number of stepping stones between them is 0.
Hence, the answer is 0.
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8) The average price of 14 different dolls is Rs 18 while the average price of 20 of these dolls is Rs 18.20. Of the remaining two dolls if the price of one is 50% more than the price of the other. What is the price of these two dolls?
A) 44.8 & 67.2
right answer
B) 67.2 & 44.8
wrong answer
C) 54.8 & 37.4
wrong answer
D) 47.2 & 64.8
wrong answer
solution: (A) 44.8 & 67.2
explanation:
18 dolls price= 18*14=252
20 dolls price = 20*18.20 = 364
remaining (20-18)=2 dolls price = (364-252)=112
let price of 1 doll be 'X'
price of 2nd doll is 50% more than the price of doll 1
price of 2nd doll = X + (50/100)X=x+x
so total price of the dolls =X + X/2 + X = 112
X=44.8
price of 1st doll = 44.8
price of 2nd doll = x+x/2= 44.8 + 44.8/2=67.2
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9) There are 3 temples and river.location of river and temple is alternative.(such as river, temple, river, temple, river, temple) A person having some flowers and when that person moves in river the flower got doubled and person put equal no of flowers in each temple.At the end no flower is left with him then how many flowers initially person carried and how many flowers he put in each temple ?
solution: 7
explanation:
Let m be initial number of flowers and n be the flowers offered at each temple by the person.
Initial flowers = m
After stepping into the first temple = 2m
Flowers offered at the first temple = n
Remaining flowers = 2m – n
After stepping into the second temple = 2*(2m – n) = 4m – 2n
Flowers offered at the second temple = n
Remaining flowers = 4m – 3n
After stepping into the third temple = 2*(4m – 3n) = 8m – 6n
Flowers offered at the third temple = n
Remaining flowers = 8m – 7n
Now as per the question (8m – 7n) must be equal to 0.
i.e. 8m – 7 n = 0
8m = 7n
m/n = 7/8
Thus m = 7; n = 8
Which means, the person had 7 flowers in the beginning and he offered 8 flowers at each temple.
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10) I have to catch a train by 6 AM. there is still time remaining to catch the train. My friend told me that 50 min ago the time remaining was 3 times as much time as that after 3 AM. How much time is remaining for my train?
A) 8 hrs 10 mins
right answer
B) 4 hrs 50 mins
wrong answer
C) 6 hrs 50mins
wrong answer
D) 7 hrs 10mins
wrong answer
solution: 8 hrs 10 mins
explanation:
t2----t1---6AM
At t1 it was told 50 mins ago
At t2 time left is 3 times a left at 3AM which is 3 hrs.
So time at t2 is 3*3=9 hrs
so t1=9hrs- 50 mins=8hrs 10mins
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