Solve the following and check with the answers given at the end.

1. It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?

2. A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.

3. A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 950gm. for a kg. His gain is …%.

4.         A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?

5.         A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for ... days.

6.         A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by­­ ________ each working now for 10 hours daily, the work can be completed in time.

7.         what is a percent of b divided by b percent of a?

(a)        a          (b)        b          (c)        1          (d)        10        (d)        100

8.         A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs.­­­­_______ for the horse and Rs.________ for the cart.

9.         A tennis marker is trying to put together a team of four players for a tennis tournament out of seven available. males - a, b and c; females – m, n, o and p. All players are of equal ability and there must be at least two males in the team. For a team of four, all players must be able to play with each other under the following restrictions:

b should not play with m,

c should not play with p, and

a should not play with o.

Which of the following statements must be false?

1.      b and p cannot be selected together

2.      c and o cannot be selected together

3.      c and n cannot be selected together.

10-12.        The following figure depicts three views of a cube. Based on this, answer questions 10-12.

6                             5   Cube: 2Cube: 3Cube: 2                              4

1                   22      3                                6

10.       The number on the face opposite to the face carrying 1 is ­­­­_______ .

11.       The number on the faces adjacent to the face marked 5 are ­­_______ .

12.       Which of the following pairs does not correctly give the numbers on the opposite faces.

(1)        6,5       (2)        4,1       (3)        1,3       (4)        4,2

13.       Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of them discovered that every tree in their own orchard bore exactly the same number of apples. Further, if the third farmer gives one apple to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers?

14.       Five boys were climbing a hill. J was following H. R was just ahead of G. K was between G & H. They were climbing up in a column. Who was the second?

15-18   John is undecided which of the four novels to buy. He is considering a spy

thriller, a Murder mystery, a Gothic romance and a science fiction novel. The books are written by Rothko, Gorky, Burchfield and Hopper, not necessary in that order, and published by Heron, Piegon, Blueja and sparrow, not necessary in that order.

(3) The science fiction novel is by Burchfield and is not published by Blueja.

(4)The Gothic romance is by Hopper.

15.       Pigeon publishes ____________.

16.       The novel by Gorky ________________.

17.       John ­purchases books by the authors whose names come first and third in alphabetical order. He does not buy the books ­­______.

18.       On the basis of the first paragraph and statement (2), (3) and (4) only, it is possible to deduce that

1.      Rothko wrote the murder mystery or the spy thriller

2.      Sparrow published the murder mystery or the spy thriller

19.       If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour?

20.       If point P is on line segment AB, then which of the following is always true?

(1) AP = PB   (2) AP > PB  (3) PB > AP  (4) AB > AP  (5) AB > AP + PB

21.       All men are vertebrates. Some mammals are vertebrates. Which of the following conclusions drawn from the above statement is correct.

All men are mammals

All mammals are men

Some vertebrates are mammals.

None

22.       Which of the following statements drawn from the given statements are correct?

Given:

All watches sold in that shop are of high standard. Some of the HMT watches are sold in that shop.

a)      All watches of high standard were manufactured by HMT.

b)      Some of the HMT watches are of high standard.

c)      None of the HMT watches is of high standard.

d)      Some of the HMT watches of high standard are sold in that shop.

23-27.

1.      Ashland is north of East Liverpool and west of Coshocton.

2.      Bowling green is north of Ashland and west of Fredericktown.

3.      Dover is south and east of Ashland.

4.      East Liverpool is north of Fredericktown and east of Dover.

5.      Fredericktown is north of Dover and west of Ashland.

6.      Coshocton is south of Fredericktown and west of Dover.

23.       Which of the towns mentioned is furthest of the north – west

(a) Ashland                   (b) Bowling green                     (c) Coshocton

(d) East Liverpool         (e) Fredericktown

24.       Which of the following must be both north and east of Fredericktown?

(a) Ashland                   (b) Coshocton              (c) East Liverpool

I a only             II b only           III c only          IV a & b          V a & c

25.       Which of the following towns must be situated both south and west of at least one other town?

A.     Ashland only

B.     Ashland and Fredericktown

C.     Dover and Fredericktown

D.     Dover, Coshocton and Fredericktown

E.      Coshocton, Dover and East Liverpool.

26.       Which of the following statements, if true, would make the information in the numbered statements more specific?

(a)    Coshocton is north of Dover.

(b)   East Liverpool is north of Dover

(c)    Ashland is east of Bowling green.

(d)   Coshocton is east of Fredericktown

(e)    Bowling green is north of Fredericktown

27.       Which of the numbered statements gives information that can be deduced from one or more of the other statements?

(A) 1                (B) 2                (C) 3                (D) 4                (E) 6

28.       Eight friends Harsha, Fakis, Balaji, Eswar, Dhinesh, Chandra, Geetha, and Ahmed are sitting in a circle facing the center. Balaji is sitting between Geetha and Dhinesh. Harsha is third to the left of Balaji and second to the right of Ahmed. Chandra is sitting between Ahmed and Geetha and Balaji and Eshwar are not sitting opposite to each other. Who is third to the left of Dhinesh?

29.       If every alternative letter starting from B of the English alphabet is written in small letter, rest all are written in capital letters, how the month  “ September” be written.

(1)        SeptEMbEr      (2)        SEpTeMBEr    (3)        SeptembeR

(4)        SepteMber       (5)        None of the above.

30.       The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is _______.

31.       It takes Mr. Karthik y hours to complete typing a manuscript. After 2 hours, he was called away. What fractional part of the assignment was left incomplete?

32.       Which of the following is larger than 3/5?

(1)        ½         (2)        39/50   (3)        7/25     (4)        3/10     (5)        59/100

33.       The number that does not have a reciprocal is ­­­____________.

34.   There are 3 persons Sudhir, Arvind, and Gauri. Sudhir lent cars to Arvind and Gauri as many as they had already. After some time Arvind gave as many cars to Sudhir and Gauri as many as they have. After sometime Gauri did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had.

35.       A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs.­­­­_______ for the horse and Rs.________ for the cart.

30 days.

Explanation:

Before:

One day work                          =          1 / 20

One man’s one day work          =          1 / ( 20 * 75)

Now:

No. Of workers                        =          50

One day work                          =          50 * 1 /  ( 20 * 75)

The total no. of days required to complete the work = (75 * 20) / 50  = 30

0 %

Explanation:

Since 3x / 2  = x / (2 / 3)

5.3 %

Explanation:

He sells 950 grams of pulses and gains 50 grams.

If he sells 100 grams of pulses then he will gain (50 / 950) *100  =  5.26

250 lines of codes

7 days

Explanation:

The equation portraying the given problem is:

10 *  x – 2 * (30 – x) =  216   where x is the number of working days.

Solving this we get x = 23

Number of days he was absent was 7 (30-23) days.

150 men.

Explanation:

One day’s work                       =          2 / (7 * 90)

One hour’s work                      =          2 / (7 * 90 * 8)

One man’s work                       =          2 / (7 * 90 * 8 * 75)

The remaining work (5/7) has to be completed within 60 days, because the total number of days allotted for the project is 150 days.

So we get the equation

(2 * 10 * x * 60) / (7 * 90 *  8 * 75)   =  5/7  where x is the number of men working after the 90th day.

We get x = 225

Since we have 75 men already, it is enough to add only 150 men.

(c) 1

Explanation:

a percent of b : (a/100) * b

b percent of a : (b/100) * a

a percent of b divided by b percent of a : ((a / 100 )*b) /  (b/100) * a )) = 1

Cost price of horse =  Rs. 400 & the cost price of cart = 200.

Explanation:-

Let x be the cost price of the horse and y be the cost price of the cart.

In the first sale there is no loss or profit. (i.e.) The loss obtained is equal to the gain.

Therefore         (10/100) * x     =  (20/100) * y

X         =  2 * y     -----------------(1)

In the second sale, he lost Rs. 10. (i.e.) The loss is greater than the profit by Rs. 10.

Therefore         (5 / 100) * x     =  (5 / 100) * y + 10 -------(2)

Substituting (1) in (2) we get

(10 / 100) * y   =  (5 / 100) * y + 10

(5 / 100) * y     =  10

y = 200

From (1) 2 * 200 = x = 400

3.

Explanation:

Since inclusion of any male player will reject a female from the team. Since there should be four member in the team and only three males are available, the girl, n should included in the team always irrespective of others selection.

5

1,2,3 & 4

B

11 & 9 apples per tree.

Explanation:

Let a, b, c, d & e be the total number of apples bored per year in A, B, C, D & E ‘s orchard. Given that             a + 1 = b + 3 = c – 1 = d + 3 = e – 6

But the question is to find the number of apples bored per tree in C and D ‘s orchard. If is enough to consider c – 1 = d + 3.

Since the number of trees in C’s orchard is 11 and that of D’s orchard is 13. Let x and y be the number of apples bored per tree in C & d ‘s orchard respectively.

Therefore 11 x – 1 = 13 y + 3

By trial and error method, we get the value for x and y as 11 and 9

G.

Explanation:

The order in which they are climbing is R – G – K – H – J

15 – 18

Novel Name                 Author              Publisher

Spy thriller                    Rathko             Heron

Murder mystery            Gorky              Piegon

Gothic romance            Burchfield         Blueja

Science fiction              Hopper                        Sparrow

Explanation:

Given

Novel Name                 Author              Publisher

Spy thriller                    Rathko             Heron

Murder mystery            Gorky              Piegon

Gothic romance            Burchfield         Blueja

Science fiction              Hopper                        Sparrow

Since Blueja doesn’t publish the novel by Burchfield and Heron publishes the novel spy thriller, Piegon publishes the novel by Burchfield.

Since Hopper writes Gothic romance and Heron publishes the novel spy thriller, Blueja publishes the novel by Hopper.

Since Heron publishes the novel spy thriller and Heron publishes the novel by Gorky, Gorky writes Spy thriller and Rathko writes Murder mystery.

451 times.

Explanation:

There are 60 minutes in an hour.

In ¾ of an hour there are (60 * ¾) minutes  = 45 minutes.

In ¾ of an hour there are (60 * 45) seconds = 2700 seconds.

Light flashed for every 6 seconds.

In 2700 seconds 2700/6 = 450 times.

The count start after the first flash, the light will flashes 451 times in ¾ of an hour.

(4)

Explanation:

P

A                                                         B

Since p is a point on the line segment AB, AB > AP

Ahmed

Fakis                                        Chandra

Explanation:              Harsha                                                            Geetha

Eswar                                       Balaji

Dhinesh

(5).

Explanation:

Since every alternative letter starting from B of the English alphabet is written in small letter, the letters written in small letter are b, d, f...

In the first two answers the letter E is written in both small & capital letters, so they are not the correct answers. But in third and fourth answers the letter is written in small letter instead capital letter, so they are not the answers.

x = 4

Explanation:

Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8

Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2x = 6x

Also, the perimeters of both are equal.

(i.e.)     4x + 8 = 6x

(i.e.)     2x = 8 è x = 4.

(y – 2) / y.

Explanation:

To type a manuscript karthik took y hours.

Therefore his speed in typing  = 1/y.

He was called away after 2 hours of typing.

Therefore the work completed = 1/y * 2.

Therefore the remaining work to be completed = 1 – 2/y.

(i.e.) work to be completed  = (y-2)/y

(2)

1

Explanation:

One is the only number exists without reciprocal because the reciprocal of one is one itself.

Explanation:

Sudhir                      Arvind                          Gauri

Finally                                      24                                24                                24

Before Gauri’s transaction     12                                    12                                48

Before Arvind’s transaction       6                                 42                                24

Before Sudhir’ s transaction      39                                21                                12

Cost price of horse:      Rs. 400 &

Cost price of cart:         Rs. 200

Explanation:

Let x be the cost of horse & y be the cost of the cart.

10 % of loss in selling horse = 20 % of gain in selling the cart

Therefore         (10 / 100) * x = (20 * 100) * y

è                x = 2y -----------(1)

5 % of loss in selling the horse is 10 more than the 5 % gain in selling the cart.

Therefore         (5 / 100) * x - 10 = (5 / 100) * y

è        5x - 1000         =          5y

Substituting (1)

10y - 1000 = 5y

5y = 1000

y = 200

x = 400            from (1)

Exercise 2.1

For the following, find the next term in the series

1.  6, 24, 60,120, 210

a) 336           b) 366              c) 330              d) 660

Explanation : The series is 1.2.3, 2.3.4, 3.4.5, 4.5.6, 5.6.7, .....          ( '.' means product)

2.  1, 5, 13, 25

Explanation : The series is of the form   0^2+1^2, 1^2+2^2,...

3. 0, 5, 8, 17

Explanation : 1^2-1, 2^2+1, 3^2-1, 4^2+1, 5^2-1

4. 1, 8, 9, 64, 25    (Hint : Every successive terms are related)

Explanation : 1^2, 2^3, 3^2, 4^3, 5^2, 6^3

5. 8,24,12,36,18,54

6. 71,76,69,74,67,72

7. 5,9,16,29,54

Explanation : 5*2-1=9; 9*2-2=16; 16*2-3=29; 29*2-4=54; 54*2-5=103

8. 1,2,4,10,16,40,64 (Successive terms are related)

Explanation : The series is powers of 2 (2^0,2^1,..).

All digits are less than 8.  Every second number is in octal number system.

128 should follow 64. 128 base 10 = 200 base 8.

Exercise 2.2

Find the odd man out.

1. 3,5,7,12,13,17,19

Explanation : All but 12 are odd numbers

2. 2,5,10,17,26,37,50,64

Explanation : 2+3=5; 5+5=10; 10+7=17; 17+9=26; 26+11=37; 37+13=50; 50+15=65;

3. 105,85,60,30,0,-45,-90

Explanation : 105-20=85; 85-25=60; 60-30=30; 30-35=-5; -5-40=-45; -45-45=-90;

Exercise 3

Solve the following.

1. What is the number of zeros at the end of the product of the numbers from 1 to 100?

2. A fast typist can type some matter in 2 hours and a slow typist can type the same in 3 hours. If both type combinely, in how much time will they finish?

Answer : 1 hr 12 min

Explanation :    The fast typist's work done in 1 hr = 1/2

The slow typist's work done in 1 hr = 1/3

If they work combinely, work done in 1 hr = 1/2+1/3 = 5/6

So, the work will be completed in 6/5 hours. i.e., 1+1/5 hours = 1hr 12 min

3. Gavaskar's average in his first 50 innings was 50. After the 51st innings, his average was 51. How many runs did he score in his 51st innings. (supposing that he lost his wicket in his 51st innings)

Explanation : Total score after 50 innings = 50*50 = 2500

Total score after 51 innings = 51*51 = 2601

So, runs made in the 51st innings = 2601-2500 = 101

If he had not lost his wicket in his 51st innings, he would have scored an unbeaten 50 in his 51st innings.

4. Out of 80 coins, one is counterfeit. What is the minimum number of weighings needed to find out the counterfeit coin?

5. What can you conclude from the statement : All green are blue, all blue are red. ?

(i)                  some blue are green

(ii)                some red are green

(iii)               some green are not red

(iv)              all red are blue

(a)     i or ii but not both

(b)    i & ii only

(c)     iii or iv but not both

(d)    iii & iv

6. A rectangular plate with length 8 inches, breadth 11 inches and thickness 2 inches is available. What is the length of the circular rod with diameter 8 inches and equal to the volume of the rectangular plate?

Explanation : Volume of the circular rod (cylinder) = Volume of the rectangular plate

(22/7)*4*4*h = 8*11*2

h = 7/2 = 3.5

7. What is the sum of all numbers between 100 and 1000 which are divisible by 14 ?

Explanation : The number closest to 100 which is greater than 100 and divisible by 14  is 112, which is the first term of the series which has to be summed.

The number closest to 1000 which is less than 1000 and divisible by 14 is 994, which is the last term of the series.

112 + 126 + .... + 994 = 14(8+9+ ... + 71) = 35392

8. If s(a) denotes square root of a, find the value of s(12+s(12+s(12+ ......         upto infinity.

Explanation : Let x = s(12+s(12+s(12+.....

We can write  x = s(12+x). i.e., x^2 = 12 + x. Solving this quadratic equation, we get x = -3 or x=4. Sum cannot be -ve and hence sum = 4.

9. A cylindrical container has a radius of eight inches with a height of three inches. Compute how many inches should be added to either the radius or height to give the same increase in volume?

Explanation : Let x be the amount of increase. The volume will increase by the same amount if the radius increased or the height is increased.

So, the effect on increasing height is equal to the effect on increasing the radius.

i.e., (22/7)*8*8*(3+x) = (22/7)*(8+x)*(8+x)*3

Solving the quadratic equation we get the x = 0 or 16/3. The possible increase would be by 16/3 inches.

10. With just six weights and a balance scale, you can weigh any unit number of kgs from 1 to 364. What could be the six weights?

Answer : 1, 3, 9, 27, 81, 243 (All powers of 3)

11. Diophantus passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor; five years after his marriage a son was born who died four years before his father at half his final age. How old is Diophantus?

Explanation : x/6 + x/12 + x/7 + 5 + x/2 + 4 = x

12 . If time at this moment is 9 P.M., what will be the time 23999999992 hours later?

Explanation : 24 billion hours later, it would be 9 P.M. and 8 hours before that it would be 1 P.M.

13. How big will an angle of one and a half degree look through a glass that magnifies things three times?

Explanation : The magnifying glass cannot increase the magnitude of an angle.

14. Divide 45 into four parts such that when 2 is added to the first part, 2 is subtracted from the second part, 2 is multiplied by the third part and the fourth part is divided by two, all result in the same number.

Explanation: a + b + c + d =45;         a+2 = b-2 = 2c = d/2; a=b-4; c = (b-2)/2; d = 2(b-2);            b-4 + b + (b-2)/2 + 2(b-2) = 45;

15. I drove 60 km at 30 kmph and then an additional 60 km at 50 kmph. Compute my average speed over my 120 km.

Explanation : Time reqd for the first 60 km = 120 min.; Time reqd for the second 60 km = 72 min.; Total time reqd = 192 min

Avg speed = (60*120)/192 = 37 1/2

Questions 16 and 17 are based on the following :

Five executives of European Corporation hold a Conference in Rome

Mr. A converses in Spanish & Italian

Mr. B, a spaniard, knows English also

Mr. C knows English and belongs to Italy

Mr. D converses in French and Spanish

Mr. E , a native of Italy knows French

16.   Which of the following can act as interpreter if Mr. C & Mr. D wish to converse

a) only Mr. A   b) Only Mr. B  c) Mr. A & Mr. B        d) Any of the other three

Answer : d) Any of the other three.

Explanation :  From the data given, we can infer the following.

A knows Spanish, Italian

B  knows Spanish, English

C  knows Italian, English

D  knows Spanish, French

E   knows Italian, French

To act as an interpreter between C and D, a person has to know one of the combinations Italian&Spanish, Italian&French, English&Spanish,         English&French

A, B, and E know atleast one of the combinations.

17. If a 6th executive is brought in, to be understood by maximum number of original five he should be fluent in

a) English & French      b) Italian & Spanish      c) English & French      d) French & Italian

Answer :  b) Italian & Spanish

Explanation : No of executives who know

i) English is 2

ii) Spanish is 3

iii) Italian is 3

iv) French is  2

Italian & Spanish are spoken by the maximum no of executives. So, if the 6th executive is fluent in Italian & Spanish, he can communicate with all the original five because everybody knows either Spanish or Italian.

What is the sum of the first 25 natural odd numbers?

Explanation : The sum of the first n natural odd nos is square(n).

1+3 = 4 = square(2) 1+3+5 = 9 = square(3)

The sum of any seven consecutive numbers is divisible by

a)      2  b) 7  c) 3  d) 11