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Consider the graph G0 with 3 components which are triangles. G0 has 9 vertices labeled
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If each vertex of G0 is assigned a red or a green color, then we say that an edge
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Ajai and Rekha color the vertices of G0 in the following manner. Ajai proposes a
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3

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IBM India recruitment paper

1. If a car starts from A towards B with some velocity. Due to some problem in the engine after traveling 30km, the car goes with 4/5 th of its actual velocity .The car reaches B 45 min later to the actual time. If the car engine fails after traveling 45km, the car reaches the destination B 36min late to the actual time What is the initial velocity of car and what is the distance between A and B in km
Ans. 20 & 130.

2. A person has Rs 100/- in his pocket, he can as 25 pencils or 15 books. He kept 15% of the money for traveling expenses and purchased 5 pencils. So how many books he can purchase with the remaining money.

3. The values of shares (in Rs).of A, B and C from January to June are as follows.
Month A B C
January 30 60 80
February 35 65 85
March 45 75 65
April 40 75 82
May 55 75 85
June 50 75 80

i) During this period which share has undergone maximium fluctuation?
ii) In which month it is possible to buy B and C selling A?
iii) In which month the share values are very low?
iv) By purchasing one share of A and 4 each of B and C in the beginning of the period,
when should these be sold to get maximum profit?
4. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Ans: 24

5. The value of [ (0.96)3 - (0.1)3 ] / [(0.96)2 + 0.096 + (0.1) 2]
ans: 0.86

6. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Ans: 21:22

7. find the next no in the series 15, 31, 63, 127, 255, (....)
Ans: 511

8. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per liter for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
Ans: 7.89

9. In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
Ans:67kg

10. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Ans:4:3

11. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
Ans:40

12. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
Ans:4

13. Find the odd one 11, 48, 100, 384, 768, 3072
Ans:100

14. If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
Ans:48 paise

15. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
Ans: 12

16. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
Ans:25

17. m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:
Ans:1000


18.a=2, b=3, c=6 Find the value of c/(a+b)-(a+b)/c
Ans. 11/30

19. What does the hexa number E78 in radix
(a) 12455
(b) 14153
(c) 14256
(d) 13541
(e) 131112
Ans. (d)

20. Q is not equal to zero and k = (Q x n - s)/2 What is n?
(a) (2 x k + s)/Q
(b) (2 x s x k)/Q (c) (2 x k - s)/Q
(d) (2 x k + s x Q)/Q (e) (k + s)/Q

Questions 21 - 25 are to be answered on the following data
A causes B or C, but not both
F occurs only if B occurs D occurs if B or C occurs E occurs only if C occurs
J occurs only if E or F occurs
D causes G,H or both H occurs if E occurs G occurs if F occurs


21. If A occurs which of the following must occurs?
I. F and G
II. E and H
III.D
(a) I only
(b) II only
(c) III only
(d) I,II, & III
(e) I & II (or) II & III but not both
Ans. (e)

22. If B occurs which must occur?
(a) D
(b) D and G
(c) G and H
(d) F and G
(e) J
Ans. (a)

23.If J occurs which must have occurred
(a) E
(b) either B or C
(c) both E & F
(d) B
(e) both B & C
Ans. (b)

24. Which may occurs as a result of cause not mentioned
I.D
II. A
III. F
(a) I only
(b) II only
(c) I & II
(d) II & III
(e) I,II & III
Ans. (c)

25. E occurs which one cannot occurs
(a) A
(b) F
(c) D
(d) C
(e) J
Ans. (b)

26.A 5 litre jug contains 4 litres of a salt water solution that is 15 percent salt. If 1.5 litres of the solution spills out of the jug, and the jug is then filled to capacity with water,approximately what percent of the resulting solution in the jug is salt?
(A)7.5% (B)9.5% (C) 10.5% (D)12% (E)15%

27. Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina Works independently at the job for 8 hours and then Ann.

28.Directions to solve
Read the paragraph carefully and answer the qustions:

Six knights - P, Q,R,S,T and U - assemble for a long journey in Two ravelling parties. For security, each travelling party Consists of at least two knights. The two parties travel by separate routes, northern and southern. After one month, the routes of the northern and southern groups converge for a brief time and at that point the knights can, if they wish, rearrange their
travelling parties before continuing, again in two parties along separate northern and southern routes. Throughout the entire trip, the composition of traveling parties must be in accord with the following conditions P and R are deadly enemies and, although they may meet briefly,can never travel together. p must travel in the same party with sQ can’t travel by the southern route U can’t change

a. If one of the two parties of knights consists of P and U and two other knights and travels by the southern route,the other members of this party besides P and U must be
a) Q and S
b) Q and T
c) R and S
d) R and T
e) S and T
Ans: e

b.If each of the two parties of knights consists of exactly three members, which of the following is not a possible travelling party and route?
a) P,S,U by the northern route
b) P,S,T by the northern route
c) P,S,T by the southern route
d) P,S,U by the southern route
e) Q,R,T by the southern route
Ans: b

c. If one of the two parties of knights consists of U and two other knights and travels by the northern route, the other memnbers of this party besides U must be
a) P and S
b) P and T
c) Q and R
d) Q and T
e) R and T
Ans: c

d. If each of the two parties of knights consists of exactly three members of different parties, and R travels by the northern route,then T must travel by the
a) southern route with P and S
b) southern route with Q and R
c) southern route with R and U
d) northern route with Q and R
e) northern route with R and U
Ans: a

e. If, when the two parties of knights encounter one another after a month, exactly one knight changes from one travelling party to the other travelling party, that knight must be
a) P
b) Q
c) R
d) S
e) T
Ans: e

Questions 29 - 32:
A, B, C, D, E and F are six positive integers such that
B + C + D + E = 4A
C + F = 3A
C + D + E = 2F
F = 2D
E + F = 2C + 1
If A is a prime number between 12 and 20, then

29. The value of F is
(A) 14
(B) 16
(C) 20
(D) 24
(E) 28

30. Which of the following must be true?
(A) D is the lowest integer and D = 14
(B) C is the greatest integer and C = 23
(C) B is the lowest integer and B = 12
(D) F is the greatest integer and F = 24
(E) A is the lowest integer and A = 13


Please find the solution & send me!!

1. If a car starts from A towards B with some velocity. Due to some problem in the engine after traveling 30km, the car goes with 4/5 th of its actual velocity .The car reaches B 45 min later to the actual time. If the car engine fails after traveling 45km, the car reaches the destination B 36min late to the actual time What is the initial velocity of car and what is the distance between A and B in km
Ans. 20 & 130.

2. A person has Rs 100/- in his pocket, he can as 25 pencils or 15 books. He kept 15% of the money for traveling expenses and purchased 5 pencils. So how many books he can purchase with the remaining money.

3. The values of shares (in Rs).of A, B and C from January to June are as follows.
Month A B C
January 30 60 80
February 35 65 85
March 45 75 65
April 40 75 82
May 55 75 85
June 50 75 80

i) During this period which share has undergone maximium fluctuation?
ii) In which month it is possible to buy B and C selling A?
iii) In which month the share values are very low?
iv) By purchasing one share of A and 4 each of B and C in the beginning of the period,
when should these be sold to get maximum profit?
4. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Ans: 24

5. The value of [ (0.96)3 - (0.1)3 ] / [(0.96)2 + 0.096 + (0.1) 2]
ans: 0.86

6. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Ans: 21:22

7. find the next no in the series 15, 31, 63, 127, 255, (....)
Ans: 511

8. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per liter for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
Ans: 7.89

9. In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
Ans:67kg

10. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Ans:4:3

11. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
Ans:40

12. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
Ans:4

13. Find the odd one 11, 48, 100, 384, 768, 3072
Ans:100

14. If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
Ans:48 paise

15. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
Ans: 12

16. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
Ans:25

17. m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:
Ans:1000


18.a=2, b=3, c=6 Find the value of c/(a+b)-(a+b)/c
Ans. 11/30

19. What does the hexa number E78 in radix
(a) 12455
(b) 14153
(c) 14256
(d) 13541
(e) 131112
Ans. (d)

20. Q is not equal to zero and k = (Q x n - s)/2 What is n?
(a) (2 x k + s)/Q
(b) (2 x s x k)/Q (c) (2 x k - s)/Q
(d) (2 x k + s x Q)/Q (e) (k + s)/Q

Questions 21 - 25 are to be answered on the following data
A causes B or C, but not both
F occurs only if B occurs D occurs if B or C occurs E occurs only if C occurs
J occurs only if E or F occurs
D causes G,H or both H occurs if E occurs G occurs if F occurs


21. If A occurs which of the following must occurs?
I. F and G
II. E and H
III.D
(a) I only
(b) II only
(c) III only
(d) I,II, & III
(e) I & II (or) II & III but not both
Ans. (e)

22. If B occurs which must occur?
(a) D
(b) D and G
(c) G and H
(d) F and G
(e) J
Ans. (a)

23.If J occurs which must have occurred
(a) E
(b) either B or C
(c) both E & F
(d) B
(e) both B & C
Ans. (b)

24. Which may occurs as a result of cause not mentioned
I.D
II. A
III. F
(a) I only
(b) II only
(c) I & II
(d) II & III
(e) I,II & III
Ans. (c)

25. E occurs which one cannot occurs
(a) A
(b) F
(c) D
(d) C
(e) J
Ans. (b)

26.A 5 litre jug contains 4 litres of a salt water solution that is 15 percent salt. If 1.5 litres of the solution spills out of the jug, and the jug is then filled to capacity with water,approximately what percent of the resulting solution in the jug is salt?
(A)7.5% (B)9.5% (C) 10.5% (D)12% (E)15%

27. Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina Works independently at the job for 8 hours and then Ann.

28.Directions to solve
Read the paragraph carefully and answer the qustions:

Six knights - P, Q,R,S,T and U - assemble for a long journey in Two ravelling parties. For security, each travelling party Consists of at least two knights. The two parties travel by separate routes, northern and southern. After one month, the routes of the northern and southern groups converge for a brief time and at that point the knights can, if they wish, rearrange their
travelling parties before continuing, again in two parties along separate northern and southern routes. Throughout the entire trip, the composition of traveling parties must be in accord with the following conditions P and R are deadly enemies and, although they may meet briefly,can never travel together. p must travel in the same party with sQ can’t travel by the southern route U can’t change

a. If one of the two parties of knights consists of P and U and two other knights and travels by the southern route,the other members of this party besides P and U must be
a) Q and S
b) Q and T
c) R and S
d) R and T
e) S and T
Ans: e

b.If each of the two parties of knights consists of exactly three members, which of the following is not a possible travelling party and route?
a) P,S,U by the northern route
b) P,S,T by the northern route
c) P,S,T by the southern route
d) P,S,U by the southern route
e) Q,R,T by the southern route
Ans: b

c. If one of the two parties of knights consists of U and two other knights and travels by the northern route, the other memnbers of this party besides U must be
a) P and S
b) P and T
c) Q and R
d) Q and T
e) R and T
Ans: c

d. If each of the two parties of knights consists of exactly three members of different parties, and R travels by the northern route,then T must travel by the
a) southern route with P and S
b) southern route with Q and R
c) southern route with R and U
d) northern route with Q and R
e) northern route with R and U
Ans: a

e. If, when the two parties of knights encounter one another after a month, exactly one knight changes from one travelling party to the other travelling party, that knight must be
a) P
b) Q
c) R
d) S
e) T
Ans: e

Questions 29 - 32:
A, B, C, D, E and F are six positive integers such that
B + C + D + E = 4A
C + F = 3A
C + D + E = 2F
F = 2D
E + F = 2C + 1
If A is a prime number between 12 and 20, then

29. The value of F is
(A) 14
(B) 16
(C) 20
(D) 24
(E) 28

30. Which of the following must be true?
(A) D is the lowest integer and D = 14
(B) C is the greatest integer and C = 23
(C) B is the lowest integer and B = 12
(D) F is the greatest integer and F = 24
(E) A is the lowest integer and A = 13



Please find the solution & post

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