EngiGuide

Five houses lettered A,B,C,D, & E are built in a row next to each other. The houses are lined up in the order A,B,C,D, & E. Each of the five houses has a colored chimney. The roof and chimney of each housemust be painted as follows.
i. The roof must be painted either green,red ,or yellow.
ii. The chimney must be painted either white, black, or red.
iii. No house may have the same color chimney as the color of roof.
iv. No house may use any of the same colors that the every next house uses.
v. House E has a green roof.
vi. House B has a red roof and a black chimney
1. Which of the following is true ?
(a) At least two houses have black chimney.
(b) At least two houses have red roofs.
(c) At least two houses have white chimneys
(d) At least two houses have green roofs
(e) At least two houses have yellow roofs
Ans: (c)

2. Which must be false ?
(a) House A has a yellow roof
(b) House A & C have different color chimney
(c) House D has a black chimney
(d) House E has a white chimney
(e) House B&D have the same color roof.

Ans: (b)

3. If house C has a yellow roof. Which must be true.
(a) House E has a white chimney
(b) House E has a black chimney
(c) House E has a red chimney
(d) House D has a red chimney
(e) House C has a black chimney

Ans: (a)

4. Which possible combinations of roof & chimney can house
I. A red roof 7 a black chimney
II. A yellow roof & a red chimney
III. A yellow roof & a black chimney

(a) I only
(b) II only
(c) III only
(d) I & II only
(e) I&II&III

Ans: (e)

Find x+2y
(i). x+y=10
(ii). 2x+4y=20

Ans: (b)

Is angle BAC is a right angle
(i) AB=2BC
(2) BC=1.5AC

Ans: (e)

Is x greater than y
(i) x=2k
(ii) k=2y

Ans: (e)

QUE 1:
In a certain society, there are two marriage groups, red and brown. No marriage is permitted within a group. On marriage, males become part of their wives groups; women remain in their own group. Children belong to the same group as their parents. Widowers and divorced males revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendant are forbidden
1. A brown female could have had
I. A grandfather born Red
II. A grandmother born Red
III Two grandfathers born Brown
(A) I only
(B) III only
(C) I, II and III
(D) I and II only
Ans. D

Q2. A male born into the brown group may have

(A) An uncle in either group
(B) A brown daughter
(C) A brown son
(D) A son-in-law born into red group

Ans. A

Q3. Which of the following is not permitted under the rules as stated.

(A) A brown male marrying his father’s sister
(B) A red female marrying her mother’s brother
(C) A widower marrying his wife’s sister
(D) A widow marrying her divorced daughter’s ex-husband

Ans. B

Q4. If widowers and divorced males retained their group they had upon marrying which of the following would be permissible ( Assume that no previous marriage occurred)

(A) A woman marrying her dead sister’s husband
(B) A woman marrying her divorced daughter’s ex-husband
(C) A widower marrying his brother’s daughter
(D) A woman marrying her mother’s brother who is a widower.

Ans. D

QUE 2:

There are six steps that lead from the first to the second floor. No two people can be on the same step
Mr. A is two steps below Mr. C
Mr. B is a step next to Mr. D
Only one step is vacant ( No one standing on that step )
Denote the first step by step 1 and second step by step 2 etc.

1. If Mr. A is on the first step, Which of the following is true?
(a) Mr. B is on the second step
(b) Mr. C is on the fourth step.
(c) A person Mr. E, could be on the third step
(d) Mr. D is on higher step than Mr. C.

Ans: (d)

2. If Mr. E was on the third step & Mr. B was on a higher step than Mr. E which step must be vacant
(a) step 1
(b) step 2
(c) step 4
(d) step 5
(e) step 6

Ans: (a)

3. If Mr. B was on step 1, which step could A be on?
(a) 2&e only
(b) 3&5 only
(c) 3&4 only
(d) 4&5 only
(e) 2&4 only

Ans: (c)

4. If there were two steps between the step that A was standing and the step that B was standing on, and A was on a higher step than D , A must be on step

(a) 2
(b) 3
(c) 4
(d) 5
(e) 6

Ans: (c)

5. Which of the following is false

i. B&D can be both on odd-numbered steps in one configuration
ii. In a particular configuration A and C must either both an odd numbered steps or both an even-numbered steps
iii. A person E can be on a step next to the vacant step.

(a) i only
(b) ii only
(c) iii only
(d) both i and iii

Ans: (c)

QUE 3:

Six swimmers A, B, C, D, E, F compete in a race. The outcome is as follows.
i. B does not win.
ii. Only two swimmers separate E & D
iii. A is behind D & E
iv. B is ahead of E , with one swimmer intervening
v. F is a head of D

1. Who stood fifth in the race ?
(a) A
(b) B
(c) C
(d) D
(e) E

Ans: (e)

2. How many swimmers separate A and F ?
(a) 1
(b) 2
(c) 3
(d) 4
(e) cannot be determined

Ans: (d)

3. The swimmer between C & E is
(a) none
(b) F
(c) D
(d) B
(e) A

Ans: (a)

4. If the end of the race, swimmer D is disqualified by the Judges then swimmer B finishes in which place
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5

Ans: (b)

QUE 1:
The letters A, B, C, D, E, F and G, not necessarily in that order, stand for seven consecutive integers from 1 to 10
D is 3 less than A
B is the middle term
F is as much less than B as C is greater than D
G is greater than F
1. The fifth integer is
(a) A
(b) C
(c) D
(d) E
(e) F
Ans. (a)

2. A is as much greater than F as which integer is less than G
(a) A
(b) B
(c) C
(d) D
(e) E

Ans. (a)

3. If A = 7, the sum of E and G is
(a) 8
(b) 10
(c) 12
(d) 14
(e) 16

Ans. (a)

4. A – F = ?
(a) 1
(b) 2
(c) 3
(d) 4
(e) Cannot be determined

Ans. (a)

5. An integer T is as much greater than C as C is greater than E. T can be written as A + E. What is D?
(a) 2
(b) 3
(c) 4
(d) 5
(e) Cannot be determined

Ans. (a)

6. The greatest possible value of C is how much greater than the smallest possible value of D?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6

Ans. (a)

1. All G’s are H’s
2. All G’s are J’s or K’s
3. All J’s and K’s are G’s
4. All L’s are K’s
5. All N’s are M’s
6. No M’s are G’s

1. If no P’s are K’s, which of the following must be true?

(a) All P’s are J’s
(b) No P is a G
(c) No P is an H
(d) If any P is an H it is a G
(e) If any P is a G it is a J

Ans. (a)

2. Which of the following can be logically deduced from the conditions stated?

(a) No M’s are H’s
(b) No M’s that are not N’s are H’s
(c) No H’s are M’s
(d) Some M’s are H’s
(e) All M’s are H’s

Ans. (a)

3. Which of the following is inconsistent with one or more of the conditions?

(a) All H’s are G’s
(b) All H’s that are not G’s are M’s
(c) Some H’s are both M’s and G’s
(d) No M’s are H’s
(e) All M’s are H’s

Ans. (a)

4. The statement “No L’s are J’s” is
I. Logically deducible from the conditions stated
II. Consistent with but not deducible from the conditions stated
III. Deducible from the stated conditions together with the additional statement “No J’s are K’s”

(a) I only
(b) II only
(c) III only
(d) II and III only
(e) Neither I, II nor III

Ans. (a)

QUE 2:

In country X, democratic, conservative and justice parties have fought three civil wars in twenty years. TO restore stability an agreement is reached to rotate the top offices President, Prime Minister and Army Chief among the parties so that each party controls one and only one office at all times. The three top office holders must each have two deputies, one from each of the other parties. Each deputy must choose a staff composed of equally members of his or her chiefs party and member of the third party.

1. When Justice party holds one of the top offices, which of the following cannot be true

(a) Some of the staff members within that office are justice party members
(b) Some of the staff members within that office are democratic party members
(c) Two of the deputies within the other offices are justice party members
(d) Two of the deputies within the other offices are conservative party members
(e) Some of the staff members within the other offices are justice party members.

Ans. (a)

2. When the democratic party holds presidency, the staff of the prime minister’s deputies are composed
I. One-fourth of democratic party members
II. One-half of justice party members and one-fourth of conservative party members
III. One-half of conservative party members and one-fourth of justice party members.

(a) I only
(b) I and II only
(c) II or III but not both
(d) I and II or I and III
(e) None of these

Ans. (a)

3. Which of the following is allowable under the rules as stated:

(a) More than half of the staff within a given office belonging to a single party
(b) Half of the staff within a given office belonging to a single party
(c) Any person having a member of the same party as his or her immediate superior
(d) Half the total number of staff members in all three offices belonging to a single party
(e) Half the staff members in a given office belonging to parties different from the party of the top office holder in that office.

Ans. (a)

4. The office of the Army Chief passes from Conservative to Justice party. Which of the following must be fired.

(a) The democratic deputy and all staff members belonging to Justice party
(b) Justice party deputy and all his or hers staff members
(c) Justice party deputy and half of his Conservative staff members in the chief of staff office
(d) The Conservative deputy and all of his or her staff members belonging to Conservative party
(e) No deputies and all staff members belonging to conservative parties.

Ans. (a)

1)A monkey starts climbing up a tree 20ft. tall. Each hour, it hops 3ft. and slips back 2ft. How much time would it take the monkey to reach the top?
Ans.18 hours.
2)What is the missing number in this series?
8 2 14 6 11 ? 14 6 18 12
Ans. 9

3)A certain type of mixture is prepared by mixing brand A at Rs.9 a kg. with brand B at Rs.4 a kg. If the mixture is worth Rs.7 a kg., how many kgs. of brand A are needed to make 40kgs. of the mixture?

Ans. Brand A needed is 24kgs.

4)A wizard named Nepo says “I am only three times my son’s age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old.” How old is Nepo?

Ans. 360 years old.

5)One dog tells the other that there are two dogs in front of me. The other one also shouts that he too had two behind him. How many are they?

Ans. Three.

6)A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?

Ans. Eight.

7)If it takes five minutes to boil one egg, how long will it take to boil four eggs?

Ans. Five minutes.

8)The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?

Ans. 32 8/11 minutes.

9)Solve for x and y: 1/x – 1/y = 1/3, 1/x2 + 1/y2 = 5/9.

Ans. x = 3/2 or -3 and y = 3 or -3/2.

10)Daal is now being sold at Rs. 20 a kg. During last month its rate was Rs. 16 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?

Ans. 20 %.

11)Find the least value of 3x + 4y if x2y3 = 6.

Ans. 10.

12)Can you find out what day of the week was January 12, 1979?

Ans. Friday.

13)A garrison of 3300 men has provisions for 32 days, when given at a rate of 850 grams per head. At the end of 7 days a reinforcement arrives and it was found that now the provisions will last 8 days less, when given at the rate of 825 grams per head. How, many more men can it feed?

Ans. 1700 men.

14)From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball?

Ans. 3720.

15)Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?

Ans. 167 minutes.

16)For a motorist there are three ways going from City A to City C. By way of bridge the distance is 20 miles and toll is $0.75. A tunnel between the two cities is a distance of 10 miles and toll is $1.00 for the vehicle and driver and $0.10 for each passenger. A two-lane highway without toll goes east for 30 miles to city B and then 20 miles in a northwest direction to City C.

16.1) Which is the shortest route from B to C

(a) Directly on toll free highway to City C
(b) The bridge
(c) The Tunnel
(d) The bridge or the tunnel
(e) The bridge only if traffic is heavy on the toll free highway

Ans. (a)

16.2) The most economical way of going from City A to City B, in terms of toll and distance is to use the

(a) tunnel
(b) bridge
(c) bridge or tunnel
(d) toll free highway
(e) bridge and highway

Ans. (a)

16.3) Jim usually drives alone from City C to City A every working day. His firm deducts a percentage of employee pay for lateness. Which factor would most influence his choice of the bridge or the tunnel ?

(a) Whether his wife goes with him
(b) scenic beauty on the route
(c) Traffic conditions on the road, bridge and tunnel
(d) saving $0.25 in tolls
(e) price of gasoline consumed in covering additional 10 miles on the bridge

Ans. (a)

16.4) In choosing between the use of the bridge and the tunnel the chief factor(s) would be:
I. Traffic and road conditions
II. Number of passengers in the car
III. Location of one’s homes in the center or outskirts of one of the cities
IV. Desire to save $0.25

(a) I only
(b) II only
(c) II and III only
(d) III and IV only
(e) I and II only

Ans. (a)

1)If 2x-y=4 then 6x-3y=?
(a)15
(b)12
(c)18
(d)10
Ans. (b)

2)If x=y=2z and xyz=256 then what is the value of x?

(a)12
(b)8
(c)16
(d)6

Ans. (b)

3)Pipe A can fill in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins. If all of them work together, find the time taken to fill the tank

(a) 17 1/7 mins
(b) 20 mins
(c) 8 mins
(d) none of these

Ans. (a)

4)Thirty men take 20 days to complete a job working 9 hours a day. How many hour a day should 40 men work to complete the job?

(a) 8 hrs
(b) 7 1/2 hrs
(c) 7 hrs
(d) 9 hrs

Ans. (b)

5)Find the smallest number in a GP whose sum is 38 and product 1728

(a) 12
(b) 20
(c) 8
(d) none of these

Ans. (c)

6)A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs. Find the speed of the boat in still water and the speed of the water current?

(a) 1/2 kmph
(b) 7/12 kmph
(c) 5 kmph
(d) none of these

Ans. (b)

7)A goat is tied to one corner of a square plot of side 12m by a rope 7m long. Find the area it can graze?

(a) 38.5 sq.m
(b) 155 sq.m
(c) 144 sq.m
(d) 19.25 sq.m

Ans. (a)

8)Mr. Shah decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?

Ans.46 steps.

9)The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?

Ans.40 years.

10)ABCE is an isosceles trapezoid and ACDE is a rectangle. AB = 10 and EC = 20. What is the length of AE?

Ans. AE = 10.

11)In the given figure, PA and PB are tangents to the circle at A and B respectively and the chord BC is parallel to tangent PA. If AC = 6 cm, and length of the tangent AP is 9 cm, then what is the length of the chord BC?

Ans. BC = 4 cm.

12)Three cards are drawn at random from an ordinary pack of cards. Find the probability that they will consist of a king, a queen and an ace.

Ans. 64/2210.

13)A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were ?

Ans. 991.

14)If Log2 x – 5 Log x + 6 = 0, then what would the value / values of x be?

Ans. x = e2 or e3.

15)The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. The ten’s place of the original number is equal to twice the difference between its digits. What is the number?

Ans. 46

16)Can you tender a one rupee note in such a manner that there shall be total 50 coins but none of them would be 2 paise coins.?

Ans. 45 one paisa coins, 2 five paise coins, 2 ten paise coins, and 1 twenty-five paise coins.