PUZZLE TEST-BANK

The questions on puzzle test may be of any of the following types:

Classification Type Questions
Seating/Placing Questions
Comparison type Questions
Sequential order of things
Selection based on given conditions
Question involving family members
Jumbled up Problems


CLASSIFICATION TYPE QUESTIONS

Read the following information carefully and answer the questions:

1. There are six cities A, B, C, D, E and F.
A is not a hill station.
B and E are not historical places.
D is not industrial city.
A and D are not historical cities.
A and B are not alike.

a. Which two cities are industrial centres?
a) A and B b) E and F c) C and D d) B and F e) A and D
Ans: b
b. Which two cities are historical places?
a) A and C b) B and F c) C and F d) B and E e) A and D
Ans: c
c. Which two cities are hill stations?
a) A and B b) C and A c) B and D d) A and F E) None of these
Ans: c
d. Which city is hill station and an industrial centre but not a historical place?
a) E b) F c) A d) B e) C
Ans: a
e. Which two cities are neither historical places nor industrial centres?
a) A and B b) D and E c) F and C d) B and D e) None of these
Ans: d


2. Read the following information carefully and answer the questions:
Five friends P,Q, R, S and T travelles to five different cities of Chennai, Calcutta, Delhi, Bangalore and Hyderabad by five different of transport of Bus, Train, Aeroplane, Car and Boat from Mumbai.
The person who traveled to delhi did not travel by boat.
R went to Bangalore by car and Q went to Calcutta by aeroplane.
S traveled by boat whereas T traveled by train.
Mumbai is not connected by bus to delhi and Chennai.

a. Which of the following combinations of person and mode is not correct?
a) P-Bus b) Q-Aeroplane c) R-Car d) S- Boat e) T-Aeroplane
Ans: e
b. Which of the following combinations is true for S?
a) Delhi-Bus b) Chennai-Bus c) Chennai- Boat d) Data inadequate e) None of these
Ans: c
c. Which of the following combinations of place and mode is not correct?
a) Delhi-Bus b) Calcutta – Aeroplane c) Bangalore-Car d) Chennai- Boat e) Hyderabad- Bus.
Ans: a
d. The person traveling to Delhi went by which of the following modes?
a) Bus b) Train c) Aeroplane d) Car e) Boat
Ans: b
e. Who among the following traveled to Delhi?
a) R b) S c) T d) Data inadequate e) None of these
Ans: c

3. In a school, there were five teachers. Aand B were teaching Hindi and English. C and B were teaching English and Geography. D and A were teaching Mathematics and Hindi. E and B were teaching History and French.
a. Who among the teachers was teaching maximum number of subjects?
a) A b) B c) C d) D e) E
Ans: b
b. Which of the following pairs was teaching both Geography and hindi?
a) A and B b) B and C c) C and A d) D and B e) None of these
Ans: e
c. More than two teachers were teaching which subject?
a) History b) Hindi c) French d) Geography e) Mathematics
Ans: b
d. D, B and A were teaching which of the following subjects?
a) English only b) Hindi and English c) Hindi only d) English and Geography e) Mathematics and Hindi
Ans: c
e. Who among the teachers was teaching less than two subjects?
a) A b) B c) D d) Data inadequate e) There is no such teacher
Ans: e

4. Read the following information carefully and answer the questions:
Jayant, Kamal, Namita, Asha and Tanmay are five members of a family.
They have their birth dates from January to may, each member in one of these months.
Each one likes one particular item for his/her birthday out of Bengali Sweets, Chocolates, Pastries, Ice Cream and Dry Fruits.
The one who likes Pastries is born in the month which is exactly middle in the months given.
Asha dose not like Ice cream but brings Chocolates for Jayant in February.
Tanmay who is fond of Bengali sweets is born in the next month immediately after Namita.
Namita does not like Dry fruits or Ice cream.

a. What id the choice of Asha?
a) Pastries b) Dry fruits c) Bengali sweets d) Cannot be determined e) None of these
Ans: b
b. Which combination of month and item is true for Jayant?
a) March-Pastries b) February-Pastries c) February- Ice cream d) Cannot be determined e) None of these
Ans: e
c. What id the choice of Kamal?
a) Ice cream b) Bengali sweets c) Dry fruits d) Cannot be determined e) None of these
Ans: a
d. In which month was Kamal born?
a) January b) May c) January or May d) Data inadequate e) None of these
Ans: c

5. Read the following information carefully and answer the questions:
There are six friends A, B, C, D, E and F.
Each one is proficient in one of the games, namely Badminton, Volleyball, cricket, Hockey, Tennis and Polo.
Each owns a different colored car, namely yellow, green, black, white, blue and red.
D plays Polo and owns a yellow colored car.
C does not play either Tennis or Hockey and own neither blue nor yellow colored car.
E owns a white car and plays Badminton.
B does not play Tennis, he owns a red colored car.
A plays Cricket and owns a black car.

a. Who plays Volleyball?
a) B b) C c) F d) Data inadequate e) None of these
Ans: a
b. Which colored car F owns?
a) Green b) blue c) either Green or blue d) Data inadequate e) None of these
Ans: b
c. Which of the following combinations of color of car and game played is not correct?
a) Yellow-Polo b) Green-Tennis c) Black-Cricket d) Red-Hockey e) None of these
Ans: b


SEATING/PLACING ARRANGEMENTS

1. Four girls are sitting on a bench to be photographed. Shikha is to the left of Reena. Manju is to the right of Reena. Rita is between Reena and Manju. Who would be second from the left in the photograph?
a) Reena b) Shikha c) Manju d) Rita
Ans: a

2. Read the following information carefully and answer the questions:
There are five friends.
They are standing in a row facing South.
Jayesh is to the immediate right of Alok.
Pramod is between Bhagat and Subodh.
Subodh is between Jayesh and Pramod.

a. Who is at the extreme left end?
a) Alok b) Bhagat c) Subodh d) Data inadequate e) None of these
Ans: a
b. Who is in the middle?
a) Bhagat b) Jayesh c) Pramod d) Subodh e) Alok
Ans: d
c. To find answers to the above two questions, which of the given statements can be dispensed with?
a) None b) A only c) B only d) C only e) D only
Ans: b

3. Read the following information carefully and answer the questions:
Eight persons E, F, G, H, I, J, K and L are seated around a square table- two on each side.
There are three lady members and they are not seated next to each other.
J is between L and F.
G is between I and F.
H, a lady member, is second to the left of J.
F, a male member is seated opposite E, a lady member.
There is a lady member between F and I.

a. Who among the following is seated between E and H?
a) F b) I c) J d) Cannot be determined e) None of these
Ans: e
b. How many persons are seated between K and F?
a) One b) Two c) Three d) Cannot be determined e) None of these
Ans: c
c. Who among the following are the three lady members?
a) E, G and J b) E, H and G c) G, H and J d) Cannot be determined e) None of these
Ans: b
d. Who among the following is to the immediate left of F?
a) G b) I c) J d) Cannot be determined e) None of these
Ans: c
e. Which of the following is true about J?
a) J is a male member b) J is a female member c) Sex of J cannot be determined d) Position of J cannot be determined e) None of these
Ans: a

4. A, B, C, D, E and F are seated in a circle facing the centre. D is between F and B. A is second to the left of D and second to the right of E.
a. Who is facing A?
a) B b) D c) F d) either F or B e) None of these
Ans: a
b. Who among the following is facing D?
a) A b) C c) E d) cannot be determined e) None of these
Ans: b

5. In a car exhibition, seven cars of seven different companies viz. Cardilac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo were displayed in a row, facing east such that:
Cardilac car was to the immediate right of Fargo.
Fargo was fourth to the right of fiat.
Maruti car was between Ambassador and Bedford.
Fiat, which was third to the left of ambassador car, was at one of the ends.

a. Which of the following was the correct position of the Mercedes?
a) Immediate right of Cardilac b) Immediate left of Bedford c) between Bedford and Fargo d) Fourth to the right of maruti e) None of these
Ans: d
b. Which of the following is definitely true?
a) Fargo car is between Ambassador and Fiat.
b) Cardilac car is to the immediate left of Mercedes.
c) Fargo is to the immediate right of cardilac.
d) Maruti is fourth to the right of Mercedes.
e) None of these
Ans : b
c. Which cars are on the immediate either sides of the Cardilac car?
a) Ambassador and Maruti b) Maruti and Fiat c) Fiat and Mercede d) Ambassador and Fargo e) None of these
Ans: e
d. Which of the following is definitely true?
a) Maruti is to the immediate left of Ambassador.
b) Bedford is to the immediate left of Fiat.
c) Bedford is at one of the ends.
d) Fiat is second to the right of Maruti.
e) None of these
Ans: a
e. which of the following groups of cars is to the right of the Ambassador car?
a) Cardilac, Fargo and Maruti b) Maruti, Bedford and Fiat c) Mercedes, Cardilac and Fargo d) Bedford, Cardilac and Fargo
Ans : c


COMPARISON TYPE QUESTIONS

1. Read the following information carefully and answer the questions:
There is a group of five girls.
Kamini is second in height but younger than rupa.
Pooja is taller than monika but younger in age.
Rupa and monika are of the same age but rupa is tallest between them.
Neelam is taller than Pooja and elder to Rupa.

a. If they are arranged in the ascending order of height, who will be in third position?
a) monika b) rupa c) monika or rupa d) Data inadequate e) None of these
Ans: e
b. If they are arranged in the descending order of their ages, who will be in fourth position?
a) monika or rupa b) kamini c) monika d) Data inadequate e) None of these
Ans: e
c. To answer the question “who is the youngest person in the group”, which of the given statements is superfluous?
a) Only (i) b) Only (ii) c) Only (v) d) Either (i) or (ii) e) None of these
Ans: a

2. Five children were administered psychological tests to know their intellectual levels. In the report, psychologists pointed out that the child A is less intelligent than the child B. The Child C is less intelligent than the child D. The child B is less intelligent than the child C and child A is more intelligent than the child E. Which child is the most intelligent?
a) A b) B c) D d) E e) None of these
Ans: c

3. In an examination, Raj got more marks than Mukesh but not as many as Priya. Priya got more marks than Gaurav and Kavitha. Gaurav got less marks than Mukesh but his marks are not the lowest in the group. Who is second in the descending order of marks?
a) Priya b) Kavitha c) Raj d) Cannot be determined e) None of these
Ans: c

4. Ashish is heavier than Givind. Mohit is lighter than Jack. Pawan is heavier than Jack but lighter than Govind. Who among them is the heaviest?
a) Govind b) Jack c) Pawan d) Ashish e) Mohit
Ans: d

5. Read the following information carefully and answer the questions:
Gopal is shorter than Ashok but taller than Kunal.
Navin is shorter than Kunal
Jayesh is taller than Navin
Ashok is taller than Jayesh
a. Who among them is tallest?
a) Gopal b) Ashok c) Kunal d) Navin e) Jayesh
Ans: b
b. Which of the given informations is not necessary to answer the above question?
a) A b) B c) C d) D e) None of these
Ans: c
c. B is twice as old as A but twice younger than F. C is half the age of A but twice the age of D. Which two persons form the pair of oldest and youngest?
a) F and A b) F and D c) B and F d) F and C e) None of these
Ans: b

6. Sudhanshu is as much older than Kokila as he is younger than Praveen. Nitin is as old as Kokila. Which of the following statements is wrong?
a) Kokila is younger than Praveen b) Nitin is younger than Praveen c) Sudhanshu is older than Nitin d) Praveen is not the oldest e) Kokila is younger than sudhanshu
Ans:d

7. Read the following information carefully and answer the questions:
A, B, C, D, E and F are six students in a class.
B and C are shorter than F but heavier than A.
D is heavier than B and taller than C.
E is shorter than D but taller than F.
F is heavier than D.
A is shorter than E but taller than F.

a. Who among them is the tallest?
a) A b) B c) D d) E e) None of these
Ans: c
b. Who is third from the top when they are arranged in descending order of height?
a) A b) B c) C d) E e) None of these
Ans: a
c. Which of the following groups of friends is shorter than A?
a) B, C only b) D, B, C only c) E, B, C only d) F, B, C only e) None of these
Ans: d
d. Who among them is the lightest?
a) A b) B c) C d) B or C e) None of these
Ans: e
e. Which of the following statements is true for F as regards height and weight?
a) He is lighter than E and taller than E.
b) He is Heavier than B and taller than E.
c) He is heavier than B and C but shorter than D.
d) He is lighter than E and also shorter than E.
e) He is lighter than B and C but taller than D.
Ans: c

8. Read the following information carefully and answer the questions:
Six friends P, Q, R, S, T and U are members of a club and play a different game of Football, Cricket, Tennis, Basketball, Badminton and Volleyball.
T who is taller than P and S plays Tennis
The tallest among them plays Basketball.
The shortest among them plays Volleyball.
Q and S neither play Volleyball nor Basketball.
R plays Volleyball.
T is between Q who plays Football and P in order of height.

a. Who among them is taller than R but shorter than P/
a) Q b) T c) U d) Data inadequate e) None of these
Ans: e
b. Who will be at the third place if they are arranged in the descending order of their height?
a) Q b) P c) S d) T e) None of these
Ans: d
c. Which of the following statements is not true?
a) P is shorter than R b) Q is taller than S c) S is taller than R d) T is taller than R e) U is taller than Q
Ans: a
d. Who among them plays Basketball?
a) Q b) R c) S d) U e) None of these
Ans : d
e. What does S play?
a) Cricket b) Badminton c) Football d) Either cricket or Badminton e) None of these
Ans: d

9. At the end of the cricket series, when five players were arranged in the ascending order of runs scored by them, O was fourth while N was first. When they were arranged in descending order for wickets taken by them, K replaces O while replaces L. M, s position remains unchanged. K has scored more runs than M. L is having first rank in one ranking and fifth in another.
a. Who has scored the highest runs in the series?
a) K b) L c) M d) Cannot be determined e) None of these
Ans: b
b. Who has taken the lowest number of wickets?
a) L b) M c) P d) Cannot be determined e) None of these
Ans: e


SEQUENTIAL ORDER OF THINGS

1. Seven executives P, Q, R, S, T, U and W reach office in a particular sequence. U reaches immediately before P but dose not immediately follow S. R is the last one to reach office. T follows immediately after P and is subsequently followed by W.
a. Among the executives, who reaches the office first?
a) Q b) S c) U d) cannot be determined e) None of these
Ans: b
b. Who ranks foruth in the sequence of reaching office?
a) W b) U c) T d) cannot be determined e) None of these
Ans: d

2. The Director of the Institute has announced that six guest lectures on different areas like leadership, Decision making, Quality circles, Motivation, Assessment centre and group discussion are to be organized only one on each day from Monday to Sunday.
Motivation should be organized immediately after Assessment centre
Quality circle should be organized on Wednesday and should not be followed by group discussion.
Decision making should be organized on Friday and there should be a gap of two days between leadership and group discussion
One day there will be no lecture (Saturday is not that day), just before that day group discussion will be organized.
a. Which of the pairs of lectures were organized on first and last day?
a) Quality circle and Motivation b) Group discussion and quality circle c) Group discussion and decision making d) leadership and assessment centre e) None of these
Ans: e
b. How many lectures are organized between motivation and quality circle?
a) one b) two c) three d) four e) None of these
Ans: c
c. which day will the lecture on leadership be organized?
a) Tuesday b) Wednesday c) Friday d) Saturday e) None of these
Ans: e
d. On which day there is no lecture?
a) Sunday b) Monday c) Tuesday d) Wednesday e) None of these
Ans: c
e. Which of the following informations is not required for the above lecture arrangements?
a) Only (i) b) Only (ii) c) only (iii) d) Only(iv) e) All are required
Ans: e

3. Five plays A, B, C, D and E are to be staged from Monday to Friday of a week. On each day, only one play will be staged. D or E should not be either the first or last to be staged. E should be immediately followed by C. B should be staged immediately after D. One play is staged between A and B.
a. Which is the first play to be staged?
a) A b) B c) C d) cannot be determined e) None of these
Ans: a
b. Which of the following is the correct sequence of staging all the plays?
a) A D B C E b) A E C D B c) B D A E C d) D B E C A e) None of these
Ans: e
c. Which play was staged on Wednesday?
a) A b) B c) Either B or C d) Cannot be determined e) None of these
Ans: b


SELECTION BASED ON GIVEN CONDITIONS

1. Eight students A, B, C, D, E, F, G and H are planning to enjoy car racing. There are only two cars and following are conditions;
One car can accommodate maximum five and minimum four students
A will sit in the same car in which D is sitting but H is not in the dame car.
B and C can’t sit in the same car in which D is sitting.
F will sit in the car of four people only along with A and E but certainly not with G.
a. If H and G are sitting in the same car, who are other two students sitting in the same car?
a) B and C b) C and D c) B and D d) E and B e) None of these
Ans: a
b. If E and A are sitting in the dame car, which of the following statements is true?
a) Five students are sitting in the same car.
b) B is sitting in the same car.
c) F is not sitting in the same car.
d) G is not sitting in the same car.
e) None of these
Ans: d
c. Which of the following statements is superfluous for the above sitting arrangements?
a) Only (i) b) Only (ii) c) Only (iii) d) Only iv) e) None of these
Ans: a

FAMILY BASED PROBLEMS

1. Read the following information carefully and answer the questions:
P, Q, R, S, T and U are six members in a family in which there are two married couples.
T, a teacher is married to the doctor who is mother of R and U.
Q, the lawyer is married to P,
P has one son and one grandson.
Of the two married ladies one is a housewife.
There is also one student and one male engineer in the family
a. How is P related to R?
a) Grandfather b) Mother c) sister d) Grandmother e) None of these
Ans: d
b. Who among the following is the housewife?
a) P b) Q c) S d) T e) None of these
Ans: e
c. How is related to U?
a) Brother b) Sister c) Brother or sister d) Data inadequate e) None of these
Ans: c
d. Which of the following represents the group of females in the family?
a) PSR b) PSU c) QTR d) Data inadequate e) None of these
Ans: d
e. Which of the following is true about the grand-daughter in the family?
a) She is a lawyer b) She is a student c) She is an engineer d) Data inadequate e) None of these
Ans: b

2. Read the following information carefully and answer the questions:
There is a family of six members A, B, C, D, E and F.
There are two married couples in the family and the family members represent three generations.
Each member has a distinct choice of a color amongst green, yellow, black, red, white and pink.
No lady member likes either green or white.
C, who likes black color, is the daughter-in-law of E.
B is brother of F and son of D and likes pink.
A is grandmother of F and F does not like red.
The husband has a choice of green color, his wife like yellow.

a. Which of the following is the color preference of A?
a) Red b) Yellow c) Either Red or Yellow d) cannot be determined e) None of these
Ans: b
b. How many male members are there in the family?
a) two b) three c)four d) cannot be determined e) None of these
Ans: c
c. Which of the following is true about F?
a) Brother of B b) Sister of B c) Daughter of C d) Either sister or brother of B e) None of these
Ans: a
d. Which of the following is the color combination of one of the couples?
a) Red-Yellow b) Yellow-red c) Green-Black d) Yellow-Green e) None of these
Ans: d
e. Which of the following is one of the married couples?
a) AC b) CD c) DA d) cannot be determined e) None of these
Ans:b

3. Read the following information carefully and answer the questions:
A, B, C, D, E and F are six members in a family in which there are two married couples.
D is brother of F. Both D and F are lighter than B.
B is mother of D and lighter than E.
C, a lady, is neither heaviest nor the lightest in the family.
E is lighter than C.
The grandfather in the family is the heaviest.
a. How is E related to F?
a) Grandmother b) Brother c) Father d) Data inadequate e) None of these
Ans: c
b. Which of the following is a pair of married couples?
a) AB b) BC c) AD d) BE e) None of these
Ans: d
c. How many male members are there in the family?
a) Two b) Three c) Four d) Data inadequate e) None of these
Ans: d
d. Who among the following will be in the second place if all the members in the family are arranged in the descending order of their weights?
a) A b) C c) D d) Data inadequate e) None of these
Ans: b
e. How is C related to D?
a) Grandmother b) Cousin c) Sister d) Mother e) None of these
Ans: a

APTITUDE I

Numbers

Example
1605 × 1605 = (1605)2
= (1600 + 5)2
= (1600)2 + 52 + 2 × 1600 × 5
= 2560000 + 25 16000
= 2576025

Exercise
1. The unit’s digit in the product (3127)173 is
a) 1 b) 3 c) 7 d) 9
Ans: c) 7
2. The difference between the place values of 7 in the numeral 574873 is
a) 69930 b) 59930 c) 96390 d) 69305
Ans: a) 69930
3. The unit’s digit in the product (274×318×577×313) is
a) 2 b) 3 c) 4 d) 5
Ans: a) 2
4. The digit in this unit place of the number represented by (795 – 358) is
a) 7 b) 0 c) 6 d) 4
Ans: d) 4
5. Given that (12 + 22 + 32 + … + 102) = 385, then the value of (22 + 42 + 62 + … + 202) is equal to
a) 770 b) 1540 c) 1155 d) (385)2
Ans: b) 1540
6. If x * y = (x + 2) 2. (y – 2), then the value of (7*5) is
a) 175 b) 205 c) 213 d) 243
Ans: d) 243
7. If 2x – 1 + 2x+1 = 320, then the value of x is
a) 4 b) 5 c) 6 d) 7
Ans: d) 78. If the number 42573 * is completely divisible by 72, then which of the following number should replace the asterisk ?
a) 4 b) 5 c) 6 d) 7
Ans: c) 6
9. There is one number which is formed by writing one digit 6 times (e.g. 111111, 444444 etc.). Such number is always divisible by
a) 7 b) 11 c) 13 d) All of these
Ans: d) All of these
10. The number nearest to 99547 which is exactly divisible by 687 is
a) 100166 b) 98928 c) 99479 d) 99615
Ans: d) 99615


H.C.F. & L.C.M. of Numbers

Example

A) H.C.F of 23 × 32 × 5 × 74, 22 × 35 × 52 × 73, 23 × 53 × 72 ?
Sol: The prime numbers common to given numbers are 2, 5 & 7.
H.C.F. = 22 × 5 × 72 = 980.
B) L.C.F of 22 × 33 × 5 × 72, 23 × 32 × 52 × 74, 2 × 3 × 53 × 7 × 11 ?
Sol: L.C.M. = product of highest powers of 2,3,5,7 and 11.
= 23 × 33 × 53 × 74 × 11.

Exercise

1. Two numbers are in the ratio of 15: 11. If their H.C.F. is 13, then the numbers are
a) 75, 55 b) 105, 77 c) 15, 11 d) 195, 143
Ans: d) 195,143.
2. The sum of two numbers is 528 and their H.C.F. is 33. The number of pair of such numbers satisfying and above condition is
a) 6 b) 12 c) 8 d) 4
Ans: d) 43. The L.C.M. of three different numbers is 120. Which of the following can not be their H.C.F.?
a) 8 b) 12 c) 24 d) 35
Ans: d) 35
4. The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is
a) 30 b) 36 c) 46 d) 56
Ans: c) 46
5. The least number of five digits which is exactly divisible by 12, 15 and 18 is
a) 10010 b) 10015 c) 10020 d) 10080
Ans: d) 10080
6. The largest number which divides 25, 73 and 97 to leave the same remainder in each case is
a) 24 b) 23 c) 21 d) 6
Ans: a) 24
7. What is the least number which when divided by 8,9,12 and 15 leaves the same remainder 1 in each case is
a) 179 b) 181 c) 359 d) 361
Ans: d) 361
8. What is the greatest number of three digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case is
a) 975 b) 996 c) 939 d) 903
Ans: a) 975
9. The H.C.F. and L.C.M. of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is
a) 50 b) 100 c) 125 d) 250
Ans: c) 125
10. Six bells commence tolling together and toll at intervals of 2, 4, 6,8,10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
a) 4 b) 10 c) 15 d) 16
Ans: d) 16

Decimal Fractions

Example

67.32+? = 431.146
Sol: Let 67.32 + X = 431.146.
Then, X = (431.146 – 67.32) = 363.826.

Exercise

1. If 1.125 × 10k = o.oo1125, then the value of k is
a) -4 b) -3 c) -2 d) -1
Ans: b) -3
2.4.8438 /.069 =?
a) 60.2 b) 70.2 c) 69.2 d) 71.2
Ans: b) 70.2
3. The value of (3.75×3.75 –2×3.75×2.75+2.75+2.75×2.75) is
a) 1 b) 1.75 c) 4.75 d) 6.50
Ans: a) 1
4. The expression (11.98 × 11.98 + 11.98×X+.02×.02) will be a perfect square for x equal to
a) .02 b).2 c).04 d) 0.4
Ans: c) .04
5. The value of (25.732)2 – (15.732)2 is
a) 414.64 b) 41.464 c) 4146.4 d) 401464
Ans: a) 414.64
6. 0.7683 + 0.369 + 0.05 + 0.8 =?
a) 0.8065 b) 1.9873 c) 0.8110 d) None
Ans : b) 1.9873
7. 5463 +546.3 – 54.63 / ? = 5999.3
a) .05463 b) .5463 c) 5.463 d) None
Ans: c) 5.463
8. 852.2109 + 106.78 – 59.157 = ?
a) 899.8339 b) 889.8339 c) 899.9833 d) 804.5879
Ans: a) 899.8339
9. (.08 × .007) is equal to
a) .056 b) .0056 c).00056 d) .56
Ans: c).00056
10. 1 litre of water weighs 1 k.g. How many cubic milliletres of water with weighs 0.1 gm?
a) 0.1 b) 1 c) 10 d) 100
Ans: d) 100

Average

Example

There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Er 1. What was the original expenditure of the mess?
Sol. Let the original average expenditure be Rs X. Then,
42 (X – 1) – 35X = 42.
→ 7X = 84 → X = 12.
Original expenditure = Rs (35 × 12) = Rs 420.

Exercise

1. The average of first five prime numbers is
a) 4.5 b) 5 c) 5.6 d) 7.5
Ans: c) 5.6
2. The average of first five multiple of 3 is
a) 3 b) 9 c) 12 d) 15
Ans: b) 9
3. The average of four consecutive even numbers is 27. The largest of these numbers is
a) 36 b) 32 c) 30 d) 28
Ans: c) 30
4. The average of two numbers is M. if one number is N, then the other number is
a) 2 N b) 2 M c) M – N d) 2 M – N
Ans: d) 2 M – N
5. Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44, the largest number is
a) 24 b) 36 c) 72 d) 108
Ans: c) 72
6. The average of ten numbers is 7. If each number is multiplied by 12, then the average of new set of numbers is
a) 7 b) 19 c) 82 d) 84
Ans: d) 84
7. The average of 11 observation is 60. If the average of first five observations is 58 and that of the last five is 56, then the sixth observation is
a) 90 b) 110 c) 85 d) 100
Ans: d) 100
8. In seven given numbers, the average of first four numbers is 4 and that of the last four numbers is also 4. If the average of these seven numbers is 3, the fourth number is
a) 3 b) 4 c) 7 d) 11
Ans: b) 4
9. The average age of 30 students is 9 years. If the age of their teacher is included, it becomes 10 years. The age of the teacher (in years) is
a) 27 b) 31 c) 35 d) 40
Ans: d) 40
10. The average weight of 9 mangoes increases by 20 g if one of them weighing 120 g is replaced by another. The weight of the new mango is
a) 180 g b) 200 g c)260 g d) 300 g
Ans: d) 300 g

APTITUDE II

Problems on Numbers

Example

The average of four consecutive even numbers is 27. Find the largest of these numbers.
Sol. Let the four consecutive even numbers be X, X + 2, X +4 & X + 6
Their total sum = (27 × 4) = 108.
X + X +2 +X + 4 + X + 6 = 108 or 4X = 96 or X = 24.
Largest number = (X +6) = 30.

Exercise

1. A number exceeds 20% of itself by 40. The number is
a) 50 b) 60 c) 80 d) 320
Ans: a) 50
2. If 16% of 40% of a number is 8, the number is
a) 320 b) 225 c) 200 d) 125
Ans: d) 125
3. The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is
a) 16 b) 15 c) 18 d) 20
Ans: b) 15
4. I one-seventh of a number exceeds its eleventh part by 100, then the number is
a) 770 b) 1100 c) 1825 d) 1925
Ans: d) 1925
5. The sum of the square of two numbers is 3341 and the difference of their square is 891. The numbers are
a) 25, 46 b) 35, 46 c) 25, 36 d) none of these
Ans: b) 35, 46
6. The numbers which when added to 10 times itself gives 264, is
a) 20 b) 22 c) 24 d) 26
Ans: c) 24
7. A number when divided by 4 is reduced by 21. The number is
a) 18 b) 20 c) 28 d) 38
Ans; c) 28
8. A number exceeds its four-seventh by 18. What is the number ?
a) 36 b) 49 c) 63 d) None
Ans: None
9. The sum of three consecutive odd numbers is 57. The middle one is
a) 17 b) 19 c) 21 d) 23
Ans: b) 19
10. The sum of the digits of a two-digit number is 9 less than the number. Which of the following digits is at unit place of the number?
a) 1 b) 2 c) 4 d) Data inadequate
Ans: d) Data inadequate

Percentage

Example

Which is greatest in 16 2/3%, 2/15 and 0.17 ?
Sol. 16 2/3% = (50/3 × 1/100) = 1/6 = 0.1666,
2/15 = 0.133 & the third number is 0.17.
Clearly, 0.17 is the greatest.

Exercise

1. If 30% of a number is 12.6, then the number is
a) 41 b) 51 c) 52 d) 42
Ans: d) 42
2. If 15% of 40 I greater than 25% of a number by 2, the number is
a) 16 b) 20 c) 24 d) 32
Ans: a) 16
3. What will be 160% of a number whose 200% is 140?
a) 200 b) 160 c) 140 d) 112
Ans: d) 112
4. If 75% of a number is added to 75, the result is the number itself. Then, the number is
a) 400 b) 300 c) 600 d) 50
Ans: b) 300
5. The population of a town has increased from 133575 to 138918. The percent increase in population is
a) 2.5 b) 3 c) 3.5 d) 4
Ans: d) 4
6. Subtracting 6% of x from x is equivalent to multiplying x by how much?
a) .94 b) 9.4 c) .094 d) 94
Ans: .94
7. It is known that 20% of the mangoes are rotten. If the number of rotten mangoes is 35, then the total number of mangoes is
a) 150 b) 175 c) 180 d) 185
Ans: b) 175
8. A student has to secure 40% marks to pass. He gets 178 marks and fails by 22 marks. The maximum marks are
a) 200 b) 500 c) 800 d) 1000
Ans: b) 500
9. A reduction of 12.5% in the price of a dining table brought down its price to Rs. 4375. The original price (in Rs.) of the table was
a) 6000 b) 5400 c) 5200 d) 5000
Ans: d) 5000
10. In an examination, 1100 boys and 900 girls appeared. 50% of the boys and 40% of the girls passed the examination. The percentage of candidates failed is
a) 45 b) 45.5 c) 54.5 d) 59.2
Ans: c) 54.5
11. 300 grams of sugar solution has 40% sugar in it. How much sugar should be added to make it 50 % in the solution?
a) 10 gms b) 40gms c) 60 gms d) 80 gms
Ans: c) 60 gms
12. The price of an article is cut by 20%. To restore it to the former value, the new price must be increased by
a) 20% b) 25% c) 16 d) 24%
Ans: b) 25%
13. A’s income is 25% more than B’s income in terms of A’s income is
A) 75% b) 80% c) 90% d) 96%
Ans: b) 80%
14. The price of sugar is increased by 20%. As a result, a family decreases its consumption by 25%. The expenditure of the family on sugar will be decreased by
a) 10% b) 5% c) 14% d) 15%
Ans: a) 10%
15. The length and breath of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by
a) 42% b) 62% c) 82% d) None
Ans: c) 82%

Problems on Ages

Example

Ramu was 4 times as old as his son 8 years ago. After 8 years, Ramu will be twice as old as his son. What are their present ages?
Sol. Let son’s age 8 years ago be X years.
Then, Ramu’s age at that time = 4X years.
Son’s age after 8 years = (X + 8) + 8 = (X + 16) years.
Ramu’s age after 8 years = (4X + 8) + 8 = (X + 16) years.
2(X + 16) = 4X + 16 or x = 8.
Son’s present age = (X + 8) = 16 years.
Ramu’s present age = 4X + 8) = 40 years.

Exercise

1. The ratio of the ages of Meena and Meera is 4: 3. The sum of their ages is 28 years. The ratio ages after 8 years will be
a) 4: 3 b) 12: 11 c) 7: 4 d) 6: 5
Ans: d) 6: 5
2. The ages of Ram and Mukta are in the ration of 3: 5. After 9 years the ratio of their ages will becomes 3: 4. The present age of Mukta (in years) is
a) 9 b) 15 c) 18 d) 24
Ans: b) 15
3. In 10 years, a will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is
a) 19 years b) 29 years c) 39 years d) 49 years
Ans: c) 39 years
4. Two years ago a man was 6 times as old as his son. After 18 years he will be twice as old as his son. Their present ages (in years) are
a) 32, 7 b) 34, 9 c) 36, 11 d) None of these
Ans: d) None of these
5. The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
a) 30, 10 b) 25, 5 c) 29, 9 d) 50, 30
Ans: b) 25, 5
6. Pushpa is twice as old as Rita was 2 years ago. If the difference of their ages be 2 years, how old is Pushpa today?
a) 6 years b) 8 years c) 10 years d) 12 years
Ans: b) 8 years
7. Ratio of Ashok’s age to Sandeep’s age is 4:3. Ashok will be 26 years old after 6 years. How old is Sandeep now?
a) 12 years b) 15 years c) 19 years d) 21 years
Ans: b) 15 years
8. The ratio of Vimal’s age and Aruna’s age is 3: 5 and the sum of their ages is 80 years. The ratio of their ages after 10 years will be
a) 2: 3 b) 1: 2 c) 3: 2 d) 3: 5
9. The average age of 12 students is 20 years. If the age of one more student is included, the average decreases by 1. What is the age of the new student?
a) 5 years b) 7 years c) 9 years d) 11 years
Ans: b) 7 years
10. The average age of an adult class is 40 years. Twelve new students with an average age of 32 years join the class, thereby decreasing the average of the class by 4 years. The original strength of the class was
a) 10 b) 11 c) 12 d) 15
Ans: c) 12

Profit &Loss

Example

Hari purchased 25 kg of wheat at Rs. 4 per kg and 35 kg of wheat at Rs. 4.50 per kg. he sold the mixture at Rs. 4.25 per kg. Finds his gain or loss.
Sol. Total C.p = Rs. (25 × 4 + 35 × 4.50) = Rs. 257.50.
Total S.P. = Rs. (60 × 4.25) = Rs. 255.
Loss = Rs. (257.50 – 255) = =Rs. 2.50.

Exercise

1.Cost of 3 cricket balls = cost of 2 pairs of leg pads.
Cost of 3 pairs of leg pads = cost of 2 pairs of gloves.
Cost of 3 pairs of gloves = cost of 2 cricket bats.
If a cricket bat costs Rs.54, what is the cost of a cricket ball?
a) Rs.12 b) Rs.14 c) Rs.16 d) Rs.18
Ans: c) Rs.16
2.There would be 10% loss if a toy is sold at Rs. 10.80 per price. At what price should it be sold to earn a profit of 20%?
a) Rs.12 b) Rs.12.96 c) Rs.14.40 d) None
Ans: c) Rs.14.40
3. A fruit seller purchases oranges at the rate of 3 for Rs 5 and sells them at 2 for Rs 4. His profit in the transaction is
a) 10% b) 15% c) 20% d) 25%
Ans: c) 20%
4. A man bought a number of oranges at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20%?
a) Rs 4 b) Rs 5 c) Rs 6 d) Rs 7
Ans: c) Rs 6
5. A man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many oranges does he buy ?
a) 30 dozens b) 40 dozens c) 50 dozens d) 60 dozens
Ans: c) 50 dozens
6. By selling 45 lemons for Rs. 40, a man loses 20%. How many should he sell for Rs 24 to gain 20% in the transaction ?
a) 16 b) 18 c) 20 d) 22
Ans: b) 18
7.A person bought 20 litres of milk at the rate of Rs 8 per litre. He got it churned after spending Rs 10 and got 5 kg of gream and 20 litres of toned milk. If he sold the cream at Rs. 30 per kg and toned milk at Rs 4 per litre, his profit in the transaction is
a) 25% b) 35.3% c) 37.5% d) 42.5%
Ans: b) 35.3%
8. A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 25%. If C pays Rs 1500, what did A pay for it ?
a) Rs 825 b) Rs 1000 c) Rs 1100 d) 1125
Ans: b) Rs 1000
9. If the S.P of Rs 24 results in a 20% discount on list price, what S.P would result in a 30% discount on list price ?
a) Rs 27 b) Rs 21 c) Rs 20 d) Rs 9
Ans: b) Rs 21
10. A shopkeeper professes to sell all things at a discount of 10%, but increases the S.P. of each article by 20%. His gain on each article is
a) 6% b) 8% c) 10% d) 12%
Ans: b) 8%

PROBLEMS ON AGES

1. The ratio of the ages of Meena and Meera is 4: 3. The sum of their ages is 28 years. The ratio ages after 8 years will be
a) 4: 3 b) 12: 11 c) 7: 4 d) 6: 5
Ans: d) 6: 5
2. The ages of Ram and Mukta are in the ration of 3: 5. After 9 years the ratio of their ages will becomes 3: 4. The present age of Mukta (in years) is
a) 9 b) 15 c) 18 d) 24
Ans: b) 15
3. In 10 years, a will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is
a) 19 years b) 29 years c) 39 years d) 49 years
Ans: c) 39 years
4. Two years ago a man was 6 times as old as his son. After 18 years he will be twice as old as his son. Their present ages (in years) are
a) 32, 7 b) 34, 9 c) 36, 11 d) None of these
Ans: d) None of these
5. The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
a) 30, 10 b) 25, 5 c) 29, 9 d) 50, 30
Ans: b) 25, 5
6. Pushpa is twice as old as Rita was 2 years ago. If the difference of their ages be 2 years, how old is Pushpa today?
a) 6 years b) 8 years c) 10 years d) 12 years
Ans: b) 8 years
7. Ratio of Ashok’s age to Sandeep’s age is 4:3. Ashok will be 26 years old after 6 years. How old is Sandeep now?
a) 12 years b) 15 years c) 19 years d) 21 years
Ans: b) 15 years
8. The ratio of Vimal’s age and Aruna’s age is 3: 5 and the sum of their ages is 80 years. The ratio of their ages after 10 years will be
a) 2: 3 b) 1: 2 c) 3: 2 d) 3: 5
9. The average age of 12 students is 20 years. If the age of one more student is included, the average decreases by 1. What is the age of the new student?
a) 5 years b) 7 years c) 9 years d) 11 years
Ans: b) 7 years
10. The average age of an adult class is 40 years. Twelve new students with an average age of 32 years join the class, thereby decreasing the average of the class by 4 years. The original strength of the class was
a) 10 b) 11 c) 12 d) 15
Ans: c) 12