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QA / Exercise - 1 CEX-5301/P2B/17 /

Quantitative Aptitude – 1Comparison of Variables

Answers Key

1 e 2 e 3 a 4 e 5 b 6 b 7 c 8 b 9 d 10 a11 b 12 a 13 b 14 b 15 e 16 e 17 b 18 c 19 a 20 c21 c 22 d 23 a 24 c 25 c 26 d 27 d 28 a 29 e 30 d31 e 32 c 33 a 34 b 35 a 36 b 37 b 38 b 39 a 40 e41 b 42 b 43 d 44 b 45 a 46 b 47 e 48 a 49 b 50 a

P-2 (B)

QA / Exercise - 2 CEX-5302/P2B/17 / Page 1

Quantitative Aptitude – 2Data Interpretation – Caselet Based

Answers and Explanations

For questions 1 to 7:

1. a Cost of painting 4 walls = 3200 × 120Cost of decorating = 14 × 4800 × 36∴Required ratio = 3200 × 120 : 14 × 4800 × 36 = 10 : 63

2. b Cost of tiling the floor = 4000 × 360Cost of tiling the wall up to 0.25 m = 4000 × 6Cost of decorating = 14 × 4800 × 36∴Total cost = 168000 + 2419200 = �25,87,200

3. c Cost of painting (walls and ceiling)= 3200 × [(21 × 42) + (1134 + 2268)]= �1,37,08,800Cost of carpeting = 4800 × (21 × 42)= �42,33,600Cost of decorating = 4233600 × 14= �5,92,70,400Cost of electrification = 4233600 × 0.75= �31,75,200∴Total cost = �8,03,88,000

4. d Cost of tiling the floor after 75% increase= 51 × 59 × 4000 × 1.75 = �2,10,63,000

5. a New length = 6 × 1.2 = 7.2 m,new breadth = 6 × 1.32 = 7.92 m,new height = 5 × 1.12 = 5.6 mCost of painting 4 walls = 2 × (40.32 + 44.352) × 3200= �5,41,900.80Cost of tiling = 4000 × (7.2 × 7.92) = �2,28,096∴ Total cost = �7,69,996.80

6. b New cost of painting = Rs.6,400New cost of tiling the floor = 36 × 8000 = �2,88,000New cost of carpeting = 36 × 9600New cost of decorating = 36 × 9600 × 14New cost of electrification = 36 × 9600 × 0.75∴ Total cost = �57,31,200

7. c New cost of decorating after increase of 25%= 36 × 9600 × 14 × 1.25 = �60,48,000


9545 120170

55 65

120

Romeo & Julie t

JuliusCaesar M acbeth

8. b No. of people that have read only ‘Macbeth’ = 120

9. e No. of people that have read at least two ofShakespeare’s plays = 95 + 65 + 55 + 45 = 260

10. c No. of people that have read only one play= 170 + 120 + 120 = 410

11. c Percentage of people surveyed that have read none

of the three plays =(700 670)

100 4.29%700

− × =

12. b Approximate percentage of total people surveyed thathave read any one of the two plays ‘Julius Caesar’ or

‘Romeo and Juliet’ = 550

100 78.6%700

× =


Name Balloon Toffee

Ann 6 15

Beth 9 20

Cathy 6 25

Daisy 6 30

Esther 15 10

1 a 2 b 3 c 4 d 5 a 6 b 7 c 8 b 9 e 10 c11 c 12 b 13 e 14 b 15 c 16 b 17 e 18 d 19 c 20 d21 a 22 b 23 b 24 d 25 c 26 a 27 d 28 b 29 b 30 a31 c 32 c 33 b 34 a 35 a 36 d 37 a 38 b 39 c 40 d41 d 42 a 43 d 44 b 45 c 46 b 47 a 48 d 49 c 50 e

P-2 (B)

QA / Exercise - 2CEX-5302/P2B/17 / Page 2

13. e Difference between the toffees with Cathy and Daisy= 30 – 25 = 5

14. b Total no. of balloons with Beth and Ann together= 9 + 6 = 15

15. c Total number of balloons with all five friends together= 6 + 9 + 6 + 6 + 15 = 42

16. b Difference between the number of balloons andtoffees with Cathy = 25 – 6 = 19

17. e If Beth and Esther decide to give away their balloonsto the other three girls equally,

Then no. of balloons with Daisy = 24

6 143

+ =

For questions 18 to 22:Person Brand Marked

price in Rs.

Discounted price in Rs.

% discount

Rita LG 16000 15040 6

Tina Samsung 12000 11040 8

Nina Videocon 15000 13500 10

Sima Haier 18000 15840 12

Vina Godrej 17000 14450 15

18. d 19. c 20. d 21. a 22. b


2%3% 24%15%

5% 6%

35%

FIVE S TA R

DAIRYM ILK KIT KAT

23. b 24. d 25. c

26. a 27. d 28. b


Department Males Females Total

IT 650 850 1500

Production 1000 500 1500

Sales 450 300 750

HR 125 125 250

Finance 875 125 1000

29. b

30. a 125 : 500 = 1 : 4

31. c450

100 9%5000

× =

32. c 1000 : 875 = 8 : 7

33. b1900

100 38%5000

× =

34. a 1900 : 3100 = 19 : 31


X Y Z Total

Morning 125 75 200 400

Afternoon 100 50 150 300

Evening 225 175 400 800

Total 450 300 750 1500

35. a

36. d750

100 50%1500

× =

37. a

38. b Y had 300 viewers, which is 20% of 1500.

39. c 400 : 300 : 800 = 4 : 3 : 8

40. d700 7

1500 15=


Name Brand Marked price (Rs.)

Discounted price (Rs.)

% discount

Amit Nike 10000 8500 15%

Bhim Reebok 12000 10800 10%

Chintu Puma 12500 11000 12%

Duggu Adidas 10800 9536 12%

Ejaz Fila 9000 8190 9%

41. d

42. a (10000 + 12000 + 12500 + 10800 + 9000) – (8500 +10800 + 11000 + 9536 + 8190) = Rs. 6,274.

43. d8500 10800 11000 9536 8190

Rs. 9605.25

+ + + + = .

44. b90

8190 Rs. 7,371100

× = .


45. c95

10800 Rs. 10,260100

× = .

46. b Income = Salary + dividend = 650000 + 75000Deductions (rebate + investment + minimum tax slab +dividend rebate) = 30000 + 25000 + 250000 + 70000Taxable income = Income – Deduction = Rs. 3,50,000

10% tax = 35000 – 15

of 35000 = Rs. 28,000.

47. a Salary – minimum tax slab – rebate= 875000 – 250000 – 30000 = Rs. 5,95,000Tax calculated = 500000 at 10% + 95000 at 20%= Rs. 69,000

Rebate of 15

of 69000 = Rs. 13,800

∴ Tax paid = 69000 – 13800 = Rs. 55,200.

48. d Let income be = x∴ x – 150000 – 250000 – 30000 = 0⇒ x = Rs. 4,30,000

49. c Rebate of 25000⇒ total tax on income = Rs. 1,25,000∴ Income = 125000 + 250000 + 150000 + 30000= Rs. 5,35,000

50. e Income = Rs. 3,45,000Investment = Rs. 75,000Taxable income = 345000 – 30000 – 75000 – 250000= –10000⇒ Since his taxable income is negative, hence the taxpaid is 0.


Quantitative Aptitude – 3Data Interpretation – Miscellaneous


For questions 1 to 5: The given data can be tabulated as:

College No. of UG students

No. of PG students

Total

C1 2100 1000 3100

C2 2400 1800 4200

C3 2850 800 3650

C4 2550 1800 4350

C5 3300 2600 5900

C6 1800 2000 3800

Total 15000 10000 25000

1. c The total number of students in C4= 2550 + 1800 = 4350.

2. b The required ratio 2400

4 : 3.1800

= =

3. a The total number of undergraduate students in C3 andC6 put together = 2850 + 1800 = 4650.

4. a The required ratio1800

3 : 4.2400

= =

5. c The average number of students25000

4167.6

= ≈

Hence, the required colleges are C2, C4 and C5.

6. b The total production of Passenger and Goods carriersput together witnessed an increase of at least 10percent only in one year and it was 2010.

7. c The total production of Passenger carriers in the firstthree years = 142 + 146 + 130 = 418The total production of Goods carriers in the last threeyears= 310 + 300 + 350 = 960Hence, the required difference = 960 – 418 = 542.

8. a The total production of Passenger carriers during thegiven period = 142 + 146 + 130 + 170 + 165= 753The total production of Goods carriers during the givenperiod = 250 + 220 + 310 + 300 + 350 = 1430Hence, the required percentage

=753

100 52.71430

× =

9. d The total production of Passenger and Goods carriersput together in 2013 = 165 × 1.4 + 350 × 1.2 = 651.Hence, the required percentage

651 515100 26.41.

515−= × =

10. a In 2009, the total production of the two types ofcarriers put together witnessed the minimumpercentage change over the previous year.

11. c The required percentage =60 50

100 20.50− × =

12. c The total sales volume of three types of batteries puttogether was the maximum in 2010 and it was equal to250000.

13. d The total sales of three types of batteries put togetherwitnessed the maximum percentage increase in 2012and it was equal to

235 160100 46.9%.

160− × ≈

14. b Required ratio = (50 + 60 + 80) : (100 + 65 + 70)= 190 : 235 = 38 : 47.

1 c 2 b 3 a 4 a 5 c 6 b 7 c 8 a 9 d 10 a11 c 12 c 13 d 14 b 15 a 16 a 17 a 18 c 19 b 20 b21 a 22 b 23 d 24 c 25 c 26 b 27 a 28 b 29 c 30 a31 a 32 e 33 d 34 c 35 e 36 d 37 b 38 b 39 a 40 b41 c 42 e 43 c 44 a 45 c 46 b 47 c 48 d 49 b 50 b

P-2 (B)


For questions 15 to 18: The given information can besurmised as shown in the table below.

State Total number of voters

Number of Male voters

Number of Female voters

Bihar 6,00,00,000 2,70,00,000 3,30,00,000

UP 3,00,00,000 1,05,00,000 1,95,00,000

MP 6,00,00,000 3,12,00,000 2,88,00,000

Gujrat 4,20,00,000 2,31,00,000 1,89,00,000

WB 4,80,00,000 2,44,80,000 2,35,20,000

15. a The required difference = 2,70,00,000 – 1,89,00,000= 81,00,000.

16. a The required number of female voters = 1,95,00,000 +2,88,00,000 + 1,89,00,000 = 6,72,00,000.

17. a Total number of male voters = 11,62,80,000Total number of female voters = 12,37,20,000Hence, the required percentage

=11,62,80,000

100 93.98 94.12,37,20,000

× = ≈

18. c Number of male voters in UP, Bihar and WB= 2,70,00,000 + 1,05,00,000 + 2,44,80,000= 6,19,80,000Number of female voters in Gujarat and MP= 1,89,00,000 + 2,88,00,000 = 4,77,00,000

Required percentage =47700

10061980

× = 77%.

19. b The mean of maximum the temperatures

44 40.8 45.2 41.8 38.8 46.2 44.87

+ + + + + +=

301.643.08 C

7= = °

The mean of minimum the temperatures

26.6 28.6 31.8 29.2 24.8 28 24.87

+ + + + + +=

193.827.68 C

7= = °

Hence, the required difference (in º C) = 43.08 – 27.68= 15.4.

20. b The percentage increase in the minimum temperatureon 3rd, May over the previous day

31.8 28.6 3.2100 11.18%

28.6 28.6−= × = =

The percentage increase in the maximum temperatureon 3rd, May over the previous day

45.2 40.8 4.4100 100 10.78%

40.8 40.8−= × = × =

Hence, the required difference = 11.18 – 10.78 = 0.4(more).

21. a The maximum difference between the maximum andminimum temperature was witnessed on 7th May andit was 44.8 – 24.8 = 20º C.The minimum difference between the maximum andminimum temperature witnessed on 2nd May and itwas 40.8 – 28.6 = 12.2º C.

22. b Average temperature on 2nd May =28.6 40.8

2+

= 34.7°C

Average temperature on 6th May =28 46.2

2+

= 37.1°C

Difference = 2.4°C.

23. d The absolute difference between the exports andimports was third smallest in June and was equal to480 – 325 = 155 million units.

24. c The Exports of Likor was the maximum in March and

was equal to 5

4080 170012

× = million units.

25. c The value of the average Imports (in million units) of

Otium in; April4

2600 80013

= × =

May1

800 2004

= × =

June5

480 20012

= × =

Hence, the required average800 200 200

3+ +=

= 400 million units.

26. b It is clear from the data that the required ratio wasmaximum in February and was approximately 2 : 1.

27. a Required percentage =725 500

100500

− × = 45%.

28. b Average cost of production (in thousand Rs.)

=625 500 450 400 500 525

6+ + + + +

= 500

The cost of production is more than the average costin 2 years.

29. c Average sales revenue (in thousand Rs.)

=750 725 550 600 800 800

6+ + + + +

= 704

The sales revenue is less than the average in twoyears.


30. a New cost of production in 2009 (in thousand Rs.)= 1.25 × 625 = 781.25New cost of production in 2012 (in thousand Rs.)= 1.3 × 400 = 520Total cost of production in both the years (in thousandRs.) = 781.25 + 520 = 1301.25

∴ Required percentage =1301.25 800

100800

− ×

= 62.7%.

31. a Profit % in year 2009 =750 625

100625

− × = 20%

Profit % in year 2010 =725 500

100500

− × = 45%


100450

− × = 22.2%


100400

− × = 50%


100500

− × = 60%


100525

− × = 52.3%

32. e New sales revenue in 2010 (in thousand Rs.)= 1.2 × 725 = 870New sales revenue in 2011 (in thousand Rs.)= 1.25 × 550 = 687.5New sales revenue in 2012 (in thousand Rs.)= 1.3 × 600 = 780New cost of production in 2012 (in thousand Rs.)= 1.2 × 400 = 480New cost of production in 2013 (in thousand Rs.)= 1.25 × 500 = 625New cost of production in 2014 (in thousand Rs.)= 1.35 × 525 = 708.75New average sales revenue (in thousand Rs.)

=870 687.5 780 750 800 800

6+ + + + +

= 781.25

New average cost of production (in thousand Rs.)

=625 500 450 480 625 708.75

6+ + + + +

= 565

∴ Difference (in thousand Rs.) = 781 – 565 = 216.

33. d Required ratio = 15 : 10 = 3 : 2.

34. c Required ratio

= 10 12 10

56000 : 86000 56000100 100 100

× × − ×

= 5600: 4720 = 70 : 59.

35. e Average number of male employees in I , II and III

=

(15 12 10)56000

1003

+ + ×= 5040.

36. d Number of female employees in IV

=14 18

86000 56000100 100

× − × = 1960

Number of female employees in VII

=7 9

86000 56000100 100

× − × = 980

Required average =1960 980

2+

= 1470

37. b Number of female employees in II, III & IV

=(12 8 14) (10 12 18)

86000 56000100 100+ + + +× − × = 6840

Average number of females in II, III & IV

=6840

3= 2280

New average = 1.4 × 2280 = 3192.

38. b Total number of employees in V, VI and VII

=17 16 7

86000100+ + × = 34400

Total number of male employees in II, III and IV

=10 12 18

56000100

+ + × = 22400

Required percentage =34400 22400

10022400

− × = 53.6%.

39. a New production of wheat in 2003 (in quintals)= 1.3 × 2900 = 3770New production of wheat in 2004 (in quintals)= 1.4 × 2900 = 4060New production of wheat in 2005 (in quintals)= 1.45 × 3000 = 4350New production of wheat in 2007 (in quintals)= 1.4 × 2900 = 4060Total production of wheat in Madhya Pradesh(in quintals) = 2400 + 3300 + 2900 + 2900 + 3000 +2400 + 2900 = 19800New production of wheat (in quintals) = 2400 + 3300+ 3770 + 4060 + 4350 + 4060 + 2400 = 24340

∴ Required percentage =24340 19800

10019800

− × = 22%

40. b Average production of wheat (in quintals)

=3500 3000 2100

3+ +

= 2866.66

41. c Average production of wheat in Bihar (in quintals)

=2800 2700 2800 3800 2100 3800 3600

7+ + + + + +

= 3086


42. e Production of wheat in 2001 (in quintals)= 1.2 × 2800 = 3360Production of wheat in 2002 (in quintals)= 1.25 × 2700 = 3375Production of wheat in 2003 (in quintals)= 1.28 × 2800 = 3584Production of wheat in 2004 (in quintals)= 1.35 × 3800 = 5130Average production of wheat in Bihar (in quintals)

=2800 2700 2800 3800

4+ + +

= 3025

New average production of wheat in Bihar (in quintals)

=3360 3375 3584 3800

4+ + +

= 3529.75

∴ Required percentage =3529.75 3025

1003025

− ×

= 16.68%

43. c Required percentage =28100 27600

10027600

− × = 1.9%

44. a Total production of wheat in 2007(in quintals)= 2900 + 3400 + 3600 = 9900 quintals

45. c Required difference =7 8

28200 3120010 13

× − ×

= 19740 – 19200 = 540

46. b Number of books distributed =

7933800

10025

×= 1068

47. c Average required =

6 1335700 37800

17 182

× + ×= 19950

48. d Total number of books = 92 79

29700 33800100 100

× + ×

= 27324 + 26702 = 54026

49. b New number of books published by P, Q and R= 1.3 × (31200 + 33800 + 35700) = 130910New number of books published by M, N, O and S= 0.8 × (28200 + 32200 + 29700 + 37800) = 102320

∴ New average = 130910 102320

7+

= 33318.

50. b Required ratio = 31200 : 33800 = 156 : 169.


Quantitative Aptitude – 4Data Sufficiency – Quant Based


1. c Statement I is not sufficient as we don’t know theweightage of each subject.Statement II alone is not sufficient as percentage marksare not given.Using both the statements I and II, we can find the

average marks = 50 65 70

3+ +

= 185

61.66%3

=

2. c None of the statements alone is sufficient.Using both the statements I and II,Area for razing = π r2

= 22

47

× 288m

7=

Cost of razing 88

10 Rs.125.717

= × =

Circumference of ground 2 r= π = 2 × 22 88

2 m7 7

× =

Cost of putting up fence = 887

× 7 = Rs. 88

Total cost = Rs. (125.71 + 88) = Rs. 213.71

3. a From statement I, a 6b 21

=

⇒ 21 a = 6 b ⇒ 7a – 2a = 0∴ Statement I alone is sufficient.Statement II is insufficient.

4. b Statement I alone is insufficient.Statement II alone is sufficient.

As probability = 1.x

x 2x 3x+ + =

x6x

= 16

5. e As even by using both the statements we don’t knowthe speed of the train, hence answer cannot bedetermined.

6. d From statement I:Let milk and water be 5x and 2x respectively.

∴ 5x 2

2x 3 1=

+ ⇒ x = 6

∴ Volume of milk and water is 30 litre and 12 litre.Let water to be added be y litres.

∴30 5

12 y 3=

+ 90 60 5y⇒ = +

y 6 litres.⇒ =∴ Statement I alone is sufficient.From statement II:In 70 litres of mixture:milk = 50 litres and water = 20 litresLet x litres of water be added.

∴50 5

20 x 3=

+ ⇒ x = 10 litres.Hence, both statements are sufficient.

7. a Statement I: (2, 15) is the only pair that satisfies thegiven condition.Statement II: (1, 30), (3, 10) and (5, 6) satisfy the givencondition. There is no unique answer.Hence, only statement I alone is sufficient.

8. e Let r be the radius of the circle.

From statement I, 2r

72 rπ >π or r > 14.

From statement II, 2r < 32 or r < 16As even; by using both the statements we cannot findthe unique solution.Hence, both statements are insufficient.

9. a Statement I:

A B C 180∠ + ∠ + ∠ = °�

B A C 90∴∠ = ∠ + ∠ = °Statement I alone is sufficient.

Statement II:We can’t say which is the bigger side. As for a rightangled triangle AC2 = AB2 + BC2.

1 c 2 c 3 a 4 b 5 e 6 d 7 a 8 e 9 a 10 a11 c 12 b 13 c 14 c 15 c 16 d 17 c 18 e 19 b 20 e21 c 22 d 23 d 24 b 25 e 26 b 27 d 28 a 29 e 30 b31 e 32 b 33 e 34 a 35 b 36 c 37 d 38 a 39 d 40 e41 c 42 b 43 e 44 d 45 a 46 e 47 e 48 b 49 a 50 e

P-2 (B)


10. a Statement I:Rakhi can build half the wall in 30 days.∴ She can complete the wall in 60 days.Let there be 60 units of work in completing the wall.∴ Rakhi does 1 unit per day.Ramesh and Rakhi complete the wall in 10 days∴ Ramesh does 50 units in 10 days (as Rakhi does1 unit / day)

∴ Ramesh does 50

510

= unit per day.

Hence, Ramesh completes work in 60

125

= days

Statement II:We don’t get any relevant information. The informationgiven is similar to given in the question.

11. c Answer can not be found using each statement alone.Let Shekhar eat x rasgullas.From statement I, x + 7 > 20 or x > 13From statement II, x – 5 < 10 or x < 15Using both statements, x = 14Hence, using both the statements together we cananswer the question.

12. b Statement I: Number of 1 rupee and 50 paisa coins can

be 3 and 2 or 4 and 0. 3 24 0As >

> .

Hence, no unique answer.Statement II:The only possibility of five coins making Rs. 4 is whenthere are three coins of Re. 1 coins and two coins of50 paisa coins. Hence, statement II alone is sufficientto answer the question.

13. c From statement I, we can calculate that the height andradius of the given cone. It would be either 5 cm or12 cm. Combining it with statement II, we get radius= 5 cm.Using both the statements together we can answerthe question.

14. c From statement I, we getx3 + 5x2 + 6x = 0⇒ x (x + 2) (x + 3) = 0⇒ x = 0, –2, –3From statement II, we getx2 + x – 6 = 0⇒ (x + 3) (x – 2) = 0⇒ x = 2, –3Using both the statements together we can answerthe question, i.e. x = –3.

15. c Statement I and II alone is not sufficient to answer thequestion. Using both statementsInitial weight ratio 3 : 4 : 5 …(i)Final weight ratio 5 : 4 : 3 …(ii)(Weight of 3rd heap is not being changed(3 : 4 : 5) × 3 = 9 : 12 : 15

(5 : 4 : 3) × 5 = 25 : 20 : 15Percentage change in weight of Heap 1st

− × = × = 25 9 16

100 100 177%9 9

Percentage change in weight of Heap 2nd

− × = × = 20 12 8

100 100 66.67%12 12

16. d From statements I, II and III,

Total dis tanceAverage speed

Total time=

x 3x x5 5 5

x 3x x5 5 540 50 60

+ +=

+ +

Hence, all the three statements required to answerthe question.

17. c From statement I: A : B = 2 : 3From statement II: B - A = 16From statement III: B + 10 = A + 10 + 16Statements II and III are same.Hence, either statements I & II or statements I & III arerequired to answer the question.

18. e Let x be the digit in the unit’s place and y be the digit inten’s place.From statement I: y = 3xFrom statement II: x + y = 8From statement III: (10y + x) – (10x + y) = 36Solving any two equations, we get x = 2 and y = 6.Hence, using any set of two statements we cananswer the question.

19. b From statement I: X - Y = 3000From statement III: X + Y = 37,000Solving I and III, we get X = Rs. 20,000 andY = Rs.17,000.Statement II is not useful.Hence, using statements I and III together we cananswer the question.

20. e From I, II and III,

( )( )2 2x y 4

x y x y 4

x y 2

− =⇒ + − =

⇒ − =

( )( )( )

2 22 2

3 3

x y x xy yx xy y

x y

x y 84

x y 2

− + +∴ + + =

−

−= = =−

Therefore, I, II and III will answer the question.


21. c From statements I and III,Let Geeta purchase x items, then Seeta purchased 3xitems (statement I) and Seeta purchased (x + 50) items(statement III).∴ x + 50 = 3x⇒ 2x = 50⇒ x = 25Geeta purchased 25 items and Seeta purchased 75items.Statement II is not useful.

22. d From statement I,

As mn

is odd then pair (m, n) can be (6, 2), (5, 1),

(3, 1), (7, 1), (9, 1), ... so on.From statement II, mn = 12 where m, n < 10Using statement III, pairs can be (3, 4), (4, 3), (6, 2)Combining these two statements with statement III,we get (6, 2) as the answer.

23. d From statement I, two pairs are possible (4, 4) or(1, 6).Combining it with statement III, we get (1, 6) is theanswer.From statement III, the number of boys and girls areequal i.e. (4, 4).Answer can be found out either using only statementII or by using statements I & III together.

24. b From statements I and II,Average weight of 3 new members

= 64 75 66 3 20

3+ + + ×

= 2653

= 88.3 kg.

Statement III is not useful.

25. e As even by all three statements we can’t find thedimensions of the tile. Hence, the answer cannot bedetermined.

26. b Let R = Number of days needed by Ramu alone to doworkS = Number of days needed by Shamu alone to doworkK = Number of days needed by Kallu alone to do workFrom statement I

1 1 1R K 6

⇒ + = ...(i)

From statement II

1 1 1R S 5

+ = ...(ii)

From statement III

1 1 1 1R S K 3.75

+ + = ...(iii)

From (i) and (ii),

1 1 1K 3.75 5

= −

K = 15 days⇒

27. d All three statements are necessary to arrive at theanswer.Let the total number of cartons be x.Then, the number of defective and non-defectivecarton would be 0.4x and 0.6x respectively.⇒ 70(0.6x – 0.4x) = 980Solving above equation, we can get the total numberof defective cartons.

28. a Discount is calculated on list price, 5% = Rs. 20Hence, list price (100%) = Rs. 20 × 20 = Rs. 400.Only statement I is needed to answer the question.

29. e All three statements are insufficient to answer thequestion.

30. b Statement I is unnecessary to answer the question.Shape of track and direction of running is not requiredto determine the answer.

31. e None of the statements gives us the information thatwhether the sides of the given figure are equal or not.Hence, the question cannot be answered with all threestatements.

32. b From statements I and III,12 × Breadth = 102⇒ Breadth = 8.5m∴ Perimeter = 2(12 + 8.5) mWe cannot infer the exact value for breadth ofrectangle by using statement II.Using statements I and III, we can answer the questionand hence statement II can be dispensed with.

33. e From statements I, II and III,In a class of 300 students,

Girls = 1

boys2

∴ Boys = 200 and Girls = 10050% of boys that appeared for test = 10048% of girls that appeared for test = 48∴ Total students appeared = 148Hence, none of the three statements can be dispensedwith.

34. a From statements II and III,Rita’s income = Rs.6,000

Amir’s income 6000

80 Rs.4,800100

= × =

Hence, statement I is redundant.

35. b Statement II, an even number multiplied by any numbergives another even number. Since ps is even.Therefore, pqrs is even.Hence, using statement II alone we can answer thequestion.


36. c From statement I, P alone can empty the tank in 5hours, but we do not have data for pipe Q. So, wecannot answer the question using statement I alone.From statement II, pipe Q is one-fourth as efficient aspipe P but rate of pipe P is not given. So, we cannotanswer the question using statement II alone.Combining both staements, we get P alone can emptythe tank in 5 hours. Q alone takes 20 hours to emptythe tank.If pipe P start first, then at the end of two hours

1 1 15 20 4

+ = th part of tank will be emptied i.e. tank will

be emptied in 8 hours.If pipe Q start first, then at the end of two hours

1 1 120 5 4

+ = th part of tank will be emptied i.e. tank will

be emptied in 8 hours.Hence, using both statements together we can answerthe question.

37. d From statement I, let 5 years before the age of sonand his father was 7x and 2x respectively. Then, theirpresent age are 7x + 5 and 2x + 5.Therefore, 7x + 5 = 3(2x + 5)⇒ x = 10Therefore, present age of son= 2x + 5 = 20 + 5 = 25 yearsFrom statement II, let after five years, the age of sonand his father will be 8x and 3x respectively. Thentheir present age are 8x – 5 and 3x – 5 respectively.Therefore, 8x – 5 = 3(3x – 5)⇒ x = 10Therefore, present age of son= 3x – 5 = 30 – 5 = 25 yearsHence, using either statement I or II alone we cananswer the question.

38. a Using statements II and III,Total tax = Rs. 250 × 0.05∴ Sales tax = Rs. 250 × 0.05 – Rs. 1.50.Now, we can find the sale tax per copy.Statement I is not useful and hence, can bedispensed with.

39. d All statements are insufficient. Even by using all ofthem we can’t answer the question because we don’tknow the height of the trapezium or the distancebetween its parallel sides.

40. e Using statement III,Plastic black : Plastic blue = 7 : 5Using statement II:Number of plastic-blue balls = 50

5 Plastic balls 50

12=

∴ Total plastic balls = 120

∴7

Plastic balls =7012

Combining all three statements:

Black Blue

Plastic 70 50

Steel 30 30

Only by using all statements together we can answerthe question.

41. c Statement I and II are insufficient to answer thequestion if we consider each of them separately. Butusing both of them together we can answer thequestion.Ratio = 7 : 5 = 7x : 5xDifference = 14� 2x = 14 ⇒ x = 7Ramesh’s runs = 7 × 7 = 49Suresh’s runs = 5 × 7 = 35Hence, statement III can be dispensed with.

42. b Statements I, II and III alone are insufficient.From statement I:Total weight of 16 persons = 16 × 25 kgFrom statement II:Total weight of 16 persons = 16 × 22 kgUsing statements I and II together we can answer thequestion. The excluded person weighs twice theAbhishek.As 16 × 22 = 16 × 25 – x� x = 16 × 3 = 48 kg� Abhishek’s weight = 24 kg.Hence, statement III can be dispensed with.

43. e Statement III, number of students passed in 2000 is350Statement II, number of students passed in 1999

= 3501.1

Using statements I, II and III, we get

Number of students appeared in 1999 = 350

1.1 0.6×Hence, none of the statement can be dispensed with.

44. d Let x be the length and s be the speed of the train.

Statement I gives, x 240

s28

+ =

Statement II gives, x = 180 m

Statement III gives, x 195

s25+ =

Therefore, using any set of two equations we canfind the speed of the train. Hence, any of the threestatements can be dispensed with.


45. a From statement I,

Listed price = 13500

Rs.15,000.0.9

=

From statement II and III,Listed price = Selling price= Rs. 12,000 × 1.25Hence, either statement I or statements II & II can bedispensed with.

46. e Let x be unit’s digit and y be ten’s digit. Then,Statement I: 2(10y + x ) = 10x + y + 6 � 19y – 8x = 6

Statement II: x = 2yStatement III: x + y = 6Using any set of two statements we can answer thequestion.The two digit number is 24.Hence, any one statement can be dispensed with.

47. e From statement II,n(TV or Ra) = n(TV) + n(Ra) – n(TV and Ra)

⇒ 2500 = 1750 + 750 – n(TV and Ra)

⇒ n(TV and Ra) = 1750 + 750 – 2500 = 0

Statements I and III are not useful. Hence, both thestatements I and III can be dispensed with.

48. b Let the number of burgers be x, thenStatement I: x + 4 > 28 or x > 24Statement III: (x – 5) < 21 or x < 26There is no unique answer.But using both I and III, x > 24, x < 26∴ 24 < x < 26So, using both statements I and III, we get the answeras he eats 25 full burgers.Statement II is not useful. Hence, statement II can bedispensed with.

49. a Statement I: N = 9k + 1From this we can’t draw any conclusion.Statement II: Prime numbers less than 37.2, 3, 5, 7, 11, 13, 17, 19, 23, ..., 31 (sq. will be of 3 digit)Statement III: Increment is in 3- digit. Thus, LetN = ABC

C B A

–A B C

6 9 3

9 8 2

–2 8 9

6 9 3

� ( C > A)Using statements II and III we can get the answer.Hence, statement I can be dispensed with.

50. e Statements IV and III provides-� 80% males were Americans∴ 20% males were Indian∴ 20% = 6 male Indian100% = 30Number of male Americans = 30 – 6 = 24Using statement II,Number of females = 25Total = 30 + 25 = 55Using statement I,Number of Americans = 45Number of Indians = 10Therefore, number of Indian females = 10 – 6 = 4Hence, non of the statements can be dispensed with.


Quantitative Aptitude – 5Data Sufficiency – Reasoning Based


1. c Using both statements we know that H has only twochildren and only one of them is a boy.∴ H has 1 daughter.

2. e From both the statements, we don’t know how manypeople are sitting around the table.

3. e Even by using both statements we can’t find therelation between D and Q.

4. d Using either of the statements we can find that Raviwas born in year 1955.

5. c Using both statements we find that the code of drinkis ‘na’

6. b Using statement II we can say

M r.M urthy

M r. Thom as boards

M r. Thom as ge ts down

M r. Rahman boards

A BC E D

Statement I is not useful. Hence, statement II alone wecan answer the question.

7. e Using the data given in the statement the order ofages can beV XX or VY YWith statement II we can’t find W lies between X and Vor above X and V.With statement I we can’t find the relation between theages of Z and X.

8. e Even by using both statements we can’t conclude thatif Sampada goes for shopping then Rashmi also goesfor shopping.

9. d Using either statements we can conclude that Rekhais sister of Reema.

10. c Using both statements we can conclude that C is notlying.∴ A is also not lyingHence, B is lying.

11. b Statement I is not sufficient as we don’t know whetherthe year is a leap year or not.Statement II: We can find out the answer. It will beMonday on 15th August this year.

12. e From statement I, Ajay > Vijay, Sunil. Combining it withstatement II, we get Ajay > Vijay, Sunil > SantoshWe cannot find about Govind.Even after using both statements, we cannot answerthe question.

13. c From statement I, R and T stay on 2nd and 4th floors.From statement II, S stays on 2nd or 3rd or 4th floor.Using both the statements together, we getFloor from bottom:1st 2nd 3rd 4th 5th P R S T QTherefore, T stays on 4th floor from the bottom.Hence, using both the statements together, we cananswer the question.

14. c From statement I alone as well as statement II alonewe cannot answer the question.Using both the statements together, we get16th(Eka) + 2Boys + 3 Girls + 12th(Vishal)Total students in the class = 16 + 2 + 3 + 12 = 33Hence, using both the statements together we cananswer the question.

15. d From statement I, since no girl is facing in east.Therefore, one of the two boys is sitting at west.So, from statement I alone we can answer thequestion. From statement II, since no boy is facingnorth. Therefore, one of the two boys is sitting atnorth. So, from statement II alone we can answer thequestion. Hence, the question can be answered byusing either statement alone.

1 c 2 e 3 e 4 d 5 c 6 b 7 e 8 e 9 d 10 c11 b 12 e 13 c 14 c 15 d 16 c 17 e 18 c 19 d 20 e21 b 22 a 23 a 24 e 25 e 26 e 27 a 28 d 29 b 30 e31 d 32 c 33 e 34 b 35 e 36 c 37 b 38 c 39 c 40 d41 c 42 c 43 e 44 a 45 c 46 e 47 d 48 a 49 c 50 b

P-2 (B)


16. c Using both statements together we can conclude thatBhawana is the daughter of Sukhram.Hence, using both statements together we can answerthe question.

17. e From statement I, Daya > Anand, ChapalFrom statement II, Esh > Bansi > DayaUsing both statements together we can conclude thatEsh > Bansi > Daya > Anand, ChapalBut we cannot conclude who is youngest betweenAnand and Chapal.Hence, using both statements together, we cannotanswer the question.

18. c From statement I, D > C > AFrom statement II, C > BFrom both the statements, we getD > C > B, ATherefore, D is tallest.Hence, using both the statements together we cananswer the question.

19. d From statement I,

A

D

B A

C

D C is sitting immediate left of B.From statement II,

B A

C

D C is sitting immediate left of B.Hence, the question can be answered by using eitherstatement alone.

20. e From statement I as well as statement II we cannotanswer the question. Using both the statements, therecan be two possibilities. Either Lalu is in front ofMulayam or behind him which will result in two differentnumber of peoples in the queue.Hence, using both statements together, we cannotanswer the question.

21. b From statement I, V _ _ _ XFrom statement I alone we cannot answer thequestion.From statement II, _ _ U _ _U is standing at the middle position.Hence, from statement II alone we can answer thequestion.

22. a From the given information we can conclude that:-History--HistoryHistory-From statement I,EnglishHistoryEnglish-HistoryHistory-Therefore, fifth book from bottom is English.From statement I alone we can answer the question.

From statement II,-History-HindiHistoryHistoryHindiFrom statement II alone we cannot answer the question.

23. a The code of ‘are’ is 6.From statement I, ‘good’ is coded as ‘5’ and ‘bad’ iscoded as ‘3’. Therefore, ‘and’ is coded as ‘8’.From statement I alone we can answer the question.From statement II, ‘you’ is coded as ‘2’ and ‘and I’ iscoded as ‘41’.The code of ‘and’ is ‘4’ or ‘1’.From statement II alone we cannot answer the question.

24. e From statement I, B’s mother is the only daughter ofmy mother-in-law means B’s mother is A’s wife.B will be A’s son or daughter. Since, gender of B is notclear. Therefore, from statement I alone we cannotanswer the question.Statement II is of no use.Using both the statements together, we cannot answerthe question. Since, gender of B is not clear.

25. e From statement I, Thakur > Beeru > Jay or Thakur= Beeru > JaySo, from statement I alone we cannot answer thequestion.From statement II, Thakur > JaySo, from statement II alone we cannot answer thequestion. Using both the statements together wecannot answer the question.

26. e Statement I gives Y is the father of X. Statement IIgives Y is the uncle of X. Statement III gives X is amale. Hence, using either statements I & III together orstatements II & III together we can answer the question.


27. a From statement I, _ _ _ Asha _ _ Reena _ _ __ _ _ _ _So, total number of children in the row = 15. StatementsII and III are not useful. Hence, using statement I alonewe can answer the question.

28. d From statements I and II, since E is to the east of D,therefore B is to the north-west from E. From statementIII, since A is to the south of E and B is to the west of A.Therefore, B is to the south-west from E. Hence, usingeither statements I & II together or statement III alonewe can answer the question.

29. b Statement I gives Pankaj > Amir > Sunil and Sanjay >Amir, Vinod. From statement I alone we cannot findthe eldest friend. Statement II gives Pankaj > Amir >Sunil and Sanjay > Amir, Vinod. Since Pankaj is not theeldest, therefore Sanjay is the eldest friend. Hence,from statement II alone we can answer the question.Statement III gives the same information as given instatements I and II.

30. e Combining all the three statements I, II and III, we getJ M K L N or K M J L N or N M J L KHence, using all the three statements we cannotanswer the question.

31. d From statement I: N < O < P(Order of heights)From statement II: M < LBoth I and II are not sufficient to answer the question.

32. c From statement I it is clear that Leena does not facethe centre.From statement II it is clear that Ali doesn’t face thecentre.∴ From either I or II, it is clear that all are not facingthe centre.

33. e From statement I it is clear that T is the grandparentof Q.From statement II it is clear that L and T are father andmother of N.⇒ T is the grandmother of Q.

34. b Statement I does not give the direction of B from Aclearly.Statement II implies that A is to the west of B at adistance of (4 + 2) = 6 km.

35. e Statement I does not specify the no. of brothers andsisters of Bharat.Statement II says that Meena has only one granddaughter.Combining I and II ⇒ Bharat has one brother

36. c From statement I:(order of weight) Q > R, S, T, > PFrom statement II:(order of weights) Q > R > S, T, PEither I or II is sufficient to say that Q is the heaviest.

37. b From statement I it is not clear as to who not facingthe centre.From statement II we get the following arrangement.

E

B

C A

D

It is clear that A is not facing the centre.∴ From II, it is clear that all are not facing the centre.

38. c From statement I: Chemistry is on Thursday.

Botany Math Physics Chemistry Zoology

Monday Tuesday Wednesday Thursday Friday

From statement II: several options are possible, butchemistry never falls on Wednesday.

39. c Statement I implies that it is not 9 o’clock, because at9:30 the angle between the two hands is > 90°.Statement II implies that it is not 9 o’clock because at8:45 the two hands do not coincide.

40. d From statement I it is clear that T is the grand child ofB but whether T is M/F is not clear.Statement II does not give any information in thisregard.So, both I and II are not sufficient to answer thequestion.

41. c Statement I:B R I C K P I N(reversed)

K

L

C

D

I

J

R

S

B

C

N

O

I

J

P

Q∴ GATES will be coded as ‘TFUBH’.Statement II:W A T E R D I S H(reversed)

R

S

E

F

T

U

A

B

W

X

H

I

S

T

I

J

D

E∴ GATES will be coded as ‘TFUBH’.

42. c From statement I the codes for ‘3, 5’ are ‘B, D’ socode for ‘7’ is ‘*’.From statement II the codes for ‘4, 2’ are ‘J A’ so codefor ‘7’ is ‘*’.

43. e Statement I or II alone is not sufficient to decide thecode for ‘party’. Combining I and II we get the codefor party as ‘tu’


44. a From statement I: P > Q and R < SFrom statement II: R < Q < PFrom statement III: P < S∴ Statements II and III will answer the question.So, statement I can be dispensed with.

45. c From statement I,

D heeraj

Bhola

Dheeraj

Bhola

Chalton

Chalton is sitting opposite to Dheeraj.

Combining statements II and III, we get

D he eraj

B hola

A li

E ka

Fatay

Ali is sitting opposite to Dheeraj.Hence, either statement I or statements II & III can bedispensed with.

46. e Statement I gives Jaya is the mother of Abhishek.Combining it with statements II and III, we get Abhishekis the daughter of Jaya. Hence, none of the statementscan be dispensed with.

47. d Statement I gives ‘de pa’ means ‘very good’. StatementII gives ‘de’ means ‘very’. Using both the statements Iand II, we get the code of ‘good’ as ‘pa’. Statement IIIgives the code of ‘good’ as ‘pa’. Hence, eitherstatements I & II or statement III can be dispensed with.

48. a Statement I gives Ani > Som > Roha. Combining it withstatement III, we get Mony is tallest person andtherefore, Roha is smallest person. Statement II givesSom > Mony. It is not useful. Hence, statement II can bedispensed with.

49. c Using statements II and III, since C is the wife of S andR is the brother of C. Therefore, R is the brother-in-law of S. Statement I is not useful. Hence, statement Ican be dispensed with.

50. b Statement II gives S is sitting in south direction. Hence,statements I and III can be dispensed with.

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