Logical Reasoning set 8 ( Directions for Questions )

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.

Directions for Questions 1 and 2: 

These questions arc based on the situation given below:
 A, B, C, D, E and F are a group of friends from a club. There are two housewives, one lecturer, one architect, one accountant and one lawyer in the group. There are two married couples in the group. The lawyer is married to D who is a housewife. No lady in the group is either an architect or an accountant. C, the accountant, is married to F who is a lecturer. A is married to D and E is not a housewife.

---

1)What is the profession of E? 

A) Lawyer

wrong answer

B) Architect

right answer

C) Lecturer

wrong answer

D) Accountant

wrong answer

solution: B) Architect

explanation:

Basic information summary:
2 housewives, 1 lecturer, 1 architect (male), 1 accountant (male), 1 lawyer.

Also, since A is married to D and the lawyer is married to D, A is the lawyer.
Using the direct clues given in the question, we can reach the following conclusions:

A (lawyer—male)----------------> Married to D
B
C (accountant—male)------------> Married to F
D (housewife—female)-----------> Married to D
E
F (lecturer—female)------------> Married to C

At this point, we are left with one architect (male) and 1 housewife to place between B and E.
Since, it is given that E is not a housewife.
we may complete the above table as shown below:

A (lawyer—male)----------------> Married to D
B (housewife—female)
C (accountant—male)------------> Married to F
D (housewife—female)-----------> Married to D
E (architect—male)
F (lecturer—female)------------> Married to C

The answers can be read off this table:
E is an architect.

VIEW ANSWER

workspace

---

2) How many members of the group are male?

A) 2

wrong answer

B) 3

right answer

C) 4

wrong answer

D) None

wrong answer

solution: B) 3

explanation:

A,C and E are males.Thus, there are 3 males in the group.

VIEW ANSWER

workspace

---

Directions 3-6: 

The table below shows the number of people who responded to a survey about their favorite style of music. Use this information to answer the following questions to the nearest whole percentage.

---

3)What percentage of respondents under 31, indicated that blues in their favorite style?

A) 7.1

right answer

B) 7.6 

wrong answer

C) 8.3  

wrong answer

D) 7.2

wrong answer

solution: B) 7.6

explanation:

blues in their favorite style under 31 = 2+ 3=5
total people under 31 = 33 + 33 = 66
percentage of blues in their favorite style under 31 = (5/66)*100=7.57

VIEW ANSWER

workspace

---

4)What percentage of respondents aged 21-30 indicated a favorite style other than Rock music?

A) 64 % 

wrong answer

B) 60%

wrong answer

C) 75% 

right answer

D) 36% 

wrong answer

solution:  A) 64 %

explanation:

Rock music in their favorite style under 21-30 = 12
other than rock music = 33-12=21
total people under 20-31 = 33
percentage of blues in their favorite style under 20-31 = (21/33)*100=63.3

VIEW ANSWER

workspace

---

5)What percentage of the total sample indicated that Jazz is heir favorite style of music?

A) 6 %

wrong answer

B) 8%

wrong answer

C) 22%

wrong answer

D) 11%

right answer

solution:  D) 11%

explanation:

Jazz music in favorite style  = 1+4+11=16
total people  = 33 +33+68 = 134
percentage of blues in their favorite style under 20-31 = (16/134)*100=11.9%

VIEW ANSWER

workspace

---

6)What percentage of the total sample were aged 21-30?

A) 31 %

wrong answer

B) 23%

right answer

C) 25%

wrong answer

D) 14%

wrong answer

solution:  C) 25%

explanation:

total sample were aged 21-30  = 33
total people  = 33 +33+68 = 134
percentage of blues in their favorite style under 20-31 = (33/134)*100=24.6%

VIEW ANSWER

workspace

---

Directions 7-11: 

Gautam passes through seven lane to reach his school. He finds that YELLOW lane is betn his house and KAMA lane. The third lane from his school is APPLE lane. PEACOCK lane is immediately before the PARK lane. He passes ASH lane at the end. KAMA lane is betn YELLOW lane and PEACOCK lane. The sixth lane from his house is RAO lane.

---

7)How many lane are there betn KAMA lane and Rao lane?

A) 1

wrong answer

B) 2

wrong answer

C) 3

right answer

D) 4

wrong answer

solution:  C) 3

VIEW ANSWER

workspace

---

8) After passing the park lane how many lane does gautam cross to reach the school.

A) 4

wrong answer

B) 3

right answer

C) 2

wrong answer

D) 1

wrong answer

solution: B) 3

VIEW ANSWER

workspace

---

9) After passing the YELLOW lane how many lane does gautam cross to reach the school.

A) 4

wrong answer

B) 6

wrong answer

C) 2

wrong answer

D) None

right answer

solution: D) None

VIEW ANSWER

workspace

---

10) Which lane is between PARK lane and RAO lane?

A) yellow lane

wrong answer

B) kama lane

wrong answer

C) apple lane

right answer

D) peacock lane

wrong answer

solution: C) apple lane

VIEW ANSWER

workspace

---

11)If the house of gautam,each lane and his school are equidistant and he takes 2 min to pass one lane then how long will he take to reach school from his house

A) 18 min

wrong answer

B) 14 min

wrong answer

C) 16 min

right answer

D) 12 min

wrong answer

solution: C) 16 min

req time=7*2+2=16mins

VIEW ANSWER

workspace

---

Directions 12-14: 

125 small but identical cubes are put together to form a large cube. This large cube is now painted on all six faces.

---

12)How many of the smaller cubes have no face painted at all.

A) 27

right answer

B) 64

wrong answer

C) 8

wrong answer

D) 36

wrong answer

solution:  A) 27

explanation:

click here for tricks to solve cube problem

0 sides painted = (n-2)^3  = (5-2)^3 = 3^3 = 27

VIEW ANSWER

workspace

---

13)How many of the smaller cubes have exactly three faces painted?

A) 4

wrong answer

B) 8

right answer

C) 9

wrong answer

D) 27

wrong answer

solution:  B) 8

explanation:

click here for tricks to solve cube problem

3 sides painted = 8 (eight painted cubes are the 8 corners )

VIEW ANSWER

workspace

---

14)How many of the smaller cubes have atleast one side painted?

A) 98

right answer

B) 100

wrong answer

C) 96

wrong answer

D) 95

wrong answer

solution:  A) 98

explanation:

click here for tricks to solve cube problem

cube have atleast one side painted = Cube with 1 face painted + cube with 2 side painted + cube with 3 side painted
 
1 sides painted = 6(n-2)^2 = 6(5-2)^2 = 6*(3^2) = 6*(9) = 54
2 sides painted = 12(n - 2) = 12(5-2) = 12*3    = 36
3 sides painted = 8 (eight painted cubes are the 8 corners )

cube have atleast one side painted = Cube with 1 face painted + cube with 2 side painted + cube with 3 side painted = 54+36+8=98

VIEW ANSWER

workspace

---

9)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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.

VIEW ANSWER

workspace

---

10)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

1) Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h?

A) A will win.

right answer

B) B will win.

wrong answer

C) C will win.

wrong answer

D) 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

VIEW ANSWER

workspace

---

2)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.?

A) 15,11

wrong answer

B) 22,18

wrong answer

C) 11,22

right answer

D) 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.

VIEW ANSWER

workspace

---

3)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

A) 23

wrong answer

B) 25

wrong answer

C) 24

wrong answer

D) 22

right 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.

VIEW ANSWER

workspace

---

4)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

5)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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 

VIEW ANSWER

workspace

---

6)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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:

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)

VIEW ANSWER

workspace

---

7)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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 

VIEW ANSWER

workspace

---

8)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

9)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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.

VIEW ANSWER

workspace

---

10)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

1) Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h?

A) A will win.

right answer

B) B will win.

wrong answer

C) C will win.

wrong answer

D) 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

VIEW ANSWER

workspace

---

2)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.?

A) 15,11

wrong answer

B) 22,18

wrong answer

C) 11,22

right answer

D) 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.

VIEW ANSWER

workspace

---

3)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

A) 23

wrong answer

B) 25

wrong answer

C) 24

wrong answer

D) 22

right 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.

VIEW ANSWER

workspace

---

4)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

5)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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 

VIEW ANSWER

workspace

---

6)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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:

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)

VIEW ANSWER

workspace

---

7)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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 

VIEW ANSWER

workspace

---

8)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

9)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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.

VIEW ANSWER

workspace

---

10)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

1) Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h?

A) A will win.

right answer

B) B will win.

wrong answer

C) C will win.

wrong answer

D) 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

VIEW ANSWER

workspace

---

2)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.?

A) 15,11

wrong answer

B) 22,18

wrong answer

C) 11,22

right answer

D) 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.

VIEW ANSWER

workspace

---

3)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

A) 23

wrong answer

B) 25

wrong answer

C) 24

wrong answer

D) 22

right 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.

VIEW ANSWER

workspace

---

4)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

5)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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 

VIEW ANSWER

workspace

---

6)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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:

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)

VIEW ANSWER

workspace

---

7)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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 

VIEW ANSWER

workspace

---

8)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---

9)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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.

VIEW ANSWER

workspace

---

10)Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.

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

VIEW ANSWER

workspace

---