Logical Reasoning set 1

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) 3 members expect which will be the elected party among 4 parties namely A, B, C, D .
    X expects that either A or B will win.
    Y expects that either A or C will win
    Z expects that neither B nor C will win
One part of each members statement is correct. Which party will win?

i) A will win.

right answer

ii) B will win.

wrong answer

iii) C will win.

wrong answer

iv) D will win.

wrong answer

solution: A will win.

mathematical explanation :
x= A+B
Y= A+C
Z=( ~B)+( ~C)

X+Y+Z=A+B+A+C+(~B)+ (~ C)
X+Y+Z=A+A

X+Y+Z=A

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2)There are 11 more animals than birds in a pet shop. If there are as many birds as animals and if there are as many animals as birds the no. of legs is 4/5 of the original. How many birds and animals are there?

i) 15,11

wrong answer

ii) 22,18

wrong answer

iii) 11,22

right answer

iv) 22,11

wrong answer

solution: 11,22.

explanation:
let number of animal be A and birds be B.
so first condition we get A=B+11...(I)
Let X be no legs.
Animal(A) has 4 legs and Bird(B) has 2 legs
so total no of legs(x)
4A+2B=X
from (I)
4(11+B)+2B=X
6B+44=X.......(II)

If there are as many birds as animals and if there are as many animals as birds the no. of legs is 4/5 of the original.
4B+2(B+11)=4X/5
6B+22=4X/5....(III)

From (II) and (III) we get,
6B+22=(4/5)*(6B+44)
6B=4*44-5*22=66
B=11
substituting in eq(I)
A=22

Hence there is 11 birds and 22 animals.

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3)One soap can be made out of the scraps obtained while preparing 11 soaps. How many soaps can be prepared out of the scrap obtained out of 251 soaps. (Take all possibilities)

A) 23

wrong answer

B) 25

right answer

C) 24

wrong answer

D) 22

wrong answer

solution: 25

explanation:
The 251 scraps will be used to make 22 soaps with remaining 9 scraps.
But 22 soaps will produce 22 scraps.
so 22+9=31 scraps which makes 2 soaps with remaining 9 scraps.
Again the 2 soaps will produce 2 scraps. so we have 11 scraps which can be used to make 1 soap with 1 scrap as remaining.
Therefore totally,22+2+1=25 soaps.

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4)There is 66x33m rectangular area. Ram is 11/8 times faster than Krishna. Both of them started walking at opposite ends and they met at some point then, Ram said "See you in the other end" Then they continued walking. After some time Ram thought he will have tea so he turned back walked back 15 meters then he changed his mind again and continued walking. How much Krishna has traveled by the time they meet?

A) 90 m

wrong answer

B) 102 m

wrong answer

C) 108 m

wrong answer

D) 96m

right answer

solution: 96

explanation:

let x be the distance between the point they first met
Total time taken by the two willbe equal
so (x+30)*8/11 = (198-x)
x= 102m

distance travelled by krishna= 198-102 = 96m

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5)ship went on a voyage after 180 miles a plane statrted with 10 times speed  that of the ship.  Find the distance when they meet from starting point?

A.200 miles 

right answer

B.180 miles 

wrong answer

C.320 miles 

wrong answer

D.150 miles 

wrong answer

solution: 200

explanation:

if speed of ship=s then seaplane speed=10s
let distance of ship be x
then seaplane distance =180+x
because ships traveled 180 miles after that plane started it journey,so plan has to cover those 180 miles.
Therefore
x / s = (180 + x )/10s
x = 20
Hence total distance = 180+20=200 miles 

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6)A + B + C +D = D + E + F + G = G + H + I =17. If A = 4. What are the values of D and G. Each letter taken only one of the digit from 1 to 9.

A) d = 1 & g = 9

wrong answer

B) d = 1 & g = 5

wrong answer

C) d = 5 & g = 1

right answer

D) d = 2 & g = 6

wrong answer

solution:  d = 5 & g = 1

explanation:

Step 1:
a + b + c + d = d + e + f + g = g + h + i = 17

Means,
(a + b + c + d) + (d + e + f + g) + (g + h + i) = 17 +17+17
(a + b + c + d) + (d + e + f + g) + (g + h + i) = 51
i.e.
a + b + c + d + e + f + g + h + i + ( d + g ) = 51....(I)

Step 2: 
But Each letter taken only one of the digit from 1 to 9.
So, a + b + c + d + e + f + g + h + i = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

a + b + c + d + e + f + g + h + i =45....(II)
Step 3: 
From (I) and (II) we get,
( a + b + c + d + e + f + g + h + i + ( d + g ) ) - ( a + b + c + d + e + f + g + h + i )=51-45
d + g = 51 - 45 = 6

possible values of d & g are (1, 5), ( 5,1 ), (2,4) & (4, 2 )
( 2, 4 ) & ( 4 , 2 ) are not possible as "a = 4 "
We have to try with other values (1, 5 ) & ( 5 , 1 )

Step 4:

Case 1:
When d = 1 and g = 5
1. a + b + c + d = 4 + b +c + 1 = 17
b + c = 12
only possible values of b & c are ( 9, 3 ) or ( 3, 9 )

2.d + e + f + g = 1 + e + f + 5 = 17
e + f = 11

possible combinations for 11 are (2,9) ; (3,8) ; (4,7) & (5,6).
Out of the above four combinations nothing is possible because b & c takes values 3 & 9, g = 5 (assumed) and a = 4 (given).
So, d = 1 & g = 5 is not the solution.

Case 2: 
When d = 5 and g = 1
1. a + b + c + d = 4 + b + c + 5 = 17
b + c = 17 - 9 = 8
only possible combination is 2 & 6
a + b + c + d = 4 + ( 2 + 6 ) + 5 = 17
2. d + e + f + g = 5 + e + f + 1 = 17
e + f = 17 - 6 = 11
The only possible value is 3 & 8
d + e + f + g = 5 + ( 3 + 8 ) + 1 = 17
g + h + i = 1 + h + i = 17
h + i = 17 - 1 = 16
The only possible value for h & i are 7 & 9
g + ( h+ i ) = 1 + ( 7 + 9 ) = 17

So the values of d = 5 & g = 1

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7)Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ?

A) 16

wrong answer

B) 64

wrong answer

C) 24

wrong answer

D) 32

right answer

solution:  32

explanation:

First we have to arrange A,
there is 1 way for it.
for second person B,
there are 2 option one left and one right.
for third person C, 2 option are there same as for B similarly for others,
so total number of possibility = 1*2*2*2*2*2 = 32 

so all possible combination is:

A,B,C,D,E,F ; B,A,C,D,E,F ; C,A,B,D,E,F ; D,A,B,C,E,F ; E,A,B,C,D,F ; F,A,B,C,D,E

F,E,A,B,C,D ; E,D,A,B,C,F ; F,D,A,B,C,E ; D,C,A,B,E,F ; E,C,A,B,D,F ; F,C,A,B,D,E

C,B,A,D,E,F ; D,B,A,C,E,F ; F,B,A,C,D,E ; E,B,A,C,D,F ; F,E,D,A,B,C ; F,E,C,A,B,D 

E,D,C,A,B,F ; F,D,C,A,B,E ; E,D,B,A,C,F ; F,D,B,A,C,E ; D,C,B,A,E,F ; E,C,B,A,D,F

F,C,B,A,D,E ; F,E,D,C,A,B ; F,E,D,B,A,C ; F,E,B,A,C,D ; F,E,C,B,A,D ; E,D,C,B,A,F

F,D,C,B,A,E ; F,E,D,C,B,A 

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8)How can 1000000000 be written as a product of two factors neither of them containing zeros?

A.1953225 * 512

wrong answer

B.(2^9)*(5^9)

right answer

C.1952125 * 512

wrong answer

D.(2^8)*(5^9)

wrong answer

solution:  (2^9)*(5^9)= 1000000000

explanation:

1953125 * 512 = 1000000000
OR
(2^9)*(5^9)= 1000000000

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9)Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days ?

A) 18

wrong answer

B) 20

right answer

C) 15

wrong answer

D)21

wrong answer

solution:  20

explanation:

Let a be the initial quantity (in relevant units) of grass and b be the amount of grass grown per day.
Then, 60 x 30 = 1800 = a + 60b and 24*70= a + 24b.
Solving these equations, we get
36b = 120
b = 10/3, a = 1600
cows are needed to eat the grass in 96 days
x*96 = a+96b
x*96 = 1600+96(10/3)
x = 1920/96 = 20.

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10)X^(1/3) - X^(1/9) =60 then X ?

A)262144

right answer

B)4^8

wrong answer

C)262244

wrong answer

D)263144

wrong answer

solution:  x = 4^9=262144

explanation:

X^(1/3) - X^(1/9) =60.
let x^(1/9) =y
y^3-y =60
y^3-y-60=0
y=4
x^(1/9)= 4
x = 4^9=262144

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