Quantitative Aptitude

Directions (Q. 1 - 5)

In a college, 150 students of MBA are enrolled. The ratio of boys to girls is 7 : 8. There are three disciplines, namely Marketing, HR and Finance, in the college. In Marketing discipline there are 50% girls of their total number and the boys are 40% of their total number. In HR discipline, girls are 30% of their total number while boys are 30% of their total number. Finance discipline has girls 20% of their total number and the boys are 30% of their total number. 7 boys and 9 girls are in HR and Marketing both. 6 boys and 7 girls are in HR and Finance both. 5 boys and 8 girls are in Marketing and Finance both. 2 boys and 3 girls are enrolled in all three disciplines.

1. What percentage of students are enrolled in all three disciplines?
1) 3.3%
2) 7.2%
3) 8.5%
4) 9.32%
5) None of these

Ans.1
Reqd % = 5150 × 100 = 3.33%

2. What is the ratio of boys to girls only in Marketing discipline?
1)13 : 9
2) 9 : 13
3) 9 : 11
4) 11 : 9
5) None of these

Ans.2
Reqd ratio = 18 : 26 = 9 : 13

3. The ratio of the number of boys in Marketing and Finance both to that of girls only in Financeis
1 ) 5 : 3
2) 3 : 5
3) 5 : 4
4) 4 : 7
5) None of these

Ans.3
Reqd ratio = 5 : 4

4. By what per cent is the number of boys in Marketing discipline more than the number of girls in HR discipline?
1) 1313 %
2) 1413 %
3) 1423 %
4) 1623 %
5) None of these

Ans.4

$\frac{28\; -\;24}{24}\times 100\;\frac{4}{24}\times 100 =16\frac{2}{3}\%$

5. The ratio of boys to girls enrolled only in HR discipline is
1) 10 : 11
2) 9 : 10
3) 7 : 5
4) 5 : 7
5) None of these

Ans.1
Reqd ratio = 10 : 11
Directions (Q. 6 - 10)
Each of the following questions consists of a question followed by three statements I, II and III. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

6. What is the speed of a boat in still water?
I. The boat covers 12 km in 2 hours downstream.
II. The boat covers the same distance in 4 hours upstream.
III.The speed of the stream is one-third that of the boat in still water.
1) Both I and II
2) I and either II or III
3) All I, II and III
4) The question cannot be answered even with the information in all three statements.
5) None of these

Ans.2
Let the speed of the boat be u and that of the stream be v.
Then speed of boat downstream = u + v

From statement I.

From statement I.

v + u = 122 = 6 kmph … (i)

And speed of boat upstream = u – v

From statement II.

u – v = 124 = 3 kmph … (ii)

From statement III.

v = u3… (iii)

From statement I and II

$\frac{\begin{matrix} u \; + \; v \; = \; 6 \\ u \; ? \; v \; = \; 3 \end{matrix}}{2u \; = \; 9}$

∴ u = 92 = 4.5 kmph

From statement I and III.

Again, from eqn (i) and (iii), we get
u + 3u3 = 6 or, 4u = 18

4u = 184 = 4.5 kmph

Hence, statement I and either II or III is sufficient to answer the question

7. What is the speed of a train?
I. The length of the train is 240 metres.
II. The train crosses a pole in 24 seconds.
III.The train crosses a platform in 48 seconds.
1) Both I and III
2) Both I and II
3) Both II and III
4) Any two of the three
5) None of these

Ans.2
From statement I. The length of the train = 240 m. Again, time is not given in the statement. Hence, I
alone is not sufficient. From

II. Time taken by the train to cross a pole is 24 seconds. But the length (distance) is not given in the statement. Hence, statement II alone is not sufficient.

From III. Time taken by the train to cross the platform is 48 seconds. But the lengths of the train and the platform are not given. Therefore, statement III alone is not sufficient.
Now, on combining statements I and II, we get

Speed of the train = 24024 = 10 m/s

Hence, both I and II together are sufficient to answer
the question.

8. What is the age of a class teacher ?
I. There are 11 students in the class.
II. The average age of the students and the teacher is 14 years.
III.The average age of the teacher and the students is 3 years more than that of the students.
1) Both I and III
2) Both I and II
3) II and either I or III
4) All I, II and III
5) None of these

Ans.4
From I. There are 11 students in the class.

From II. The average age of students and class teacher is 14 years.

From III. The average age of class teacher is 3 years more than that of students.
Now, combining all three statements, we have
Average age of (students + teacher) = 14 × 12 = 168
years
Average age of 11 students = 14 – 3 = 11 years
Total age of 11 students = 11 × 11 = 121 years
∴ Teacher’s age = 168 – 121 = 47 years

9. Sri Gupta borrowed a sum at compound interest. What is the amount returned in 2 years ?
I. The rate of interest is 5% per annum.
II. The simple interest incurred on the sum in 1 year is 600.
III.The borrowed sum is ten times the amount earned at simple interest in two years.
1) Only I
2) Only III
3) Both II and III
4) Either I or III
5) All I, II and III

Ans.3
From I. R = 5% per annum

From II. SI for 1 year = 600 SI for 2 years = 600 × 2 = 1200

From III. P = 10 × SI = 10 × 1200 = 12000

Now, from II and III, we get

$\frac{SI\;\times \;100 }{P\;\times T}=\frac{1200\;\times 100}{12000\;\times 2}=\;5\%$

∴ Amount = P 1100 = 12000 × 1.05 × 1.05

= 13230 is the amount which Gupta returned after two years.
Hence, II and III are sufficient.

10. What is the area of a given right-angled triangle?
I. The length of the hypotenuse is 5 cm.
II. The perimeter of the triangle is four times that of its base.
III.One of the angles of the triangle is 60°.
1) Only II
2) Only III
3) Either II or III
4) Both I and III
5) Question cannot be answered even with the information in all three statements

Ans.4
From I. AC = 5 cm
From II. Perimeter = 4 × base
From III. One of the angles of the triangle, say ∠C, be 60°
From I and III. cos 60° = $\frac{BC}{AC}$

or, BC = AC × cos 60°= 52

a = 52, b = 5 (∴ AC = b)

Now, area of the triangle ABC = ab$\sin \Theta$

12 × 52 × sin 60°

$\frac{5}{4}\times\frac{\sqrt{3}}{2}=\frac{25}{8}\sqrt{3}\; cm^{2}$

Hence, statement I and III are sufficient to answer the question.

Directions (Q. 11 - 15)
Study the following graph carefully to answer the questions given below:

Number of selected employees in different grades/ ranks by three companies during 2012

11. What is the average number of selected employees by Company A in all grades taken together?
1) 450
2) 460
3) 475
4) 375
5) None of these

Ans.1
Average number of selected employees by Company A

$\frac{150+300+300+500+650+800}{6}=\frac{2700}{6}=450$

12. What is the ratio of selected employees for the post of Assistant IT Managers by Companies A, B and respectively?
1) 8 : 10 : 11
2) 10 : 8 : 11
3) 11 : 10 : 8
4) 10 : 11 : 8
5) None of these

Ans.2
Reqd ratio = 500 : 400 : 550 = 10 : 8 : 11

13. By what per cent is the number of selected employees for Finance Managers by Company C more than that of the selected employees by Company B for the same post?
1) 35%
2) 30%
3) 25%
4) 40%
5) None of these

Ans.3
The number of selected employees for Finance Manager by Company C = 250 And the number of selected employees for Finance Manager by Company B = 200
∴ Reqd % = $\frac{250-200}{200}\times 100\frac{50}{200}\times 100=25\%$

14. What is the average number of selected employees for the post of Assistant Marketing Managers by all companies taken together?
1) 570
2) 520
3) 620
4) 720
5) None of these

Ans.4
Reqd average =$\frac{800+700+660}{3}=\frac{2160}{3}=720$

15. What is the ratio of selected employees for IT Managers by all Companies A, B and C?
1) 6 : 4 : 7
2) 5 : 3 :7
3) 4 : 7 : 9
4) 8 : 7 : 6
5) None of these

Ans.1
Reqd ratio = 300 : 200 : 350 = 30 : 20 : 35 = 6 : 4 : 7
Directions (Question.16)
16. Three men A, B and C start a business together. They invest 30000, 24000 and 42000 respectively in the beginning. After 4 months, B took out 6000 and C took out 10000. They get a profit of 11960 at the end of the year. B’s share in the profit is
l) 2700
2) 2803
3) 2900
4) 2785
5) None of these

Ans.2
Ratio of capital
= 30000 × 12 : (24000 × 4 + 18000 × 8) : (42000 × 4 + 32000 × 8)

= 36000 : (96000 + 144000) : (168000 + 256000)

= 360000 : 240000 : 424000

= 360 : 240 : 424 = 45 : 30 : 53

Sum of ratios = 45 + 30 + 53 = 128

Now, B’share = 30128 × 11960 = 2803.125 ≈ 2803

Directions (Question.17)
17. The edge of an ice cube is 14 cm. The volume of the largest cylindrical ice cube that can be formed out of it is
1) 2200 cu cm
2) 2000 cu cm
3) 2156 cu cm
4) 2400 cu cm
5) None of these

Ans.3
Here the edge of an ice cube is 14 cm.

Radius of the cylinder = 142 = 7 cm

Height of the cylinder = 14 cm

∴ Volume of the largest cylinder = π22 h

= 227 × 7 × 7 × 14 = 2156 cu cm

Directions (Question.18)
18. A sum of 16800 is divided into two parts. One part is lent at the simple rate of interest 6% per annum and the other at 8% per annum. After 2 years the total sum received is 19000. The sum lent at the rate of 6% simple interest is
1) 12200
2) 12000
3) 11000
4) 10000
5) None of these

Ans.1
Let the sum lent at 6% rate of interest be x.

Then, (1680 – x) is lent at 8% rate of interest.

Then, SI = 19000 – 16800 = 2200

$\frac{x\;\times 6\;\times 2 }{100} +\frac{(16800\;-\;x)\;\times 2\;\times 8}{100}=2200$

or, 12x + 268800 – 16x = 2200 × 100

or, 268800 – 220000 = 4x

or x = 488004 = 12200

Directions (Question.19)
19. The present age of Romila is one-fourth that of her father. After 6 years the father’s age will be twice the age of Kapil. If Kapil celebrated fifth birthday 8 years ago, what is Romil’s present age?
1) 7 years
2) 7.5 years
3) 8 years
4) 8.5 years
5) None of these

Ans.2
Kapil’s present age = (8 + 5 – 1) = 12 years

Kapil’s age after 6 years = 12 + 6 = 18 years

Now, Romila’s father’s age = 2 × Kapil’s age = 2 × 18 = 36 years

Father’s present age = 36 – 6 = 30 years

Romila’s present age = 14 × father’s present age

= 14 × 30 = 7.5 years

Directions (Question.20)
20. In an examination, 30% of the total students failed in Hindi, 45% failed in English and 20% failed in both the subjects. Find the percentage of those who passed in both the subjects.
1) 35.7%
2) 35%
3) 40%
4) 45%
5) 44%

Ans.4
Let the number of students be 100. Number of
students who failed in Hindi is 30%.
n(H) = 30
Number of students who failed in English is 45%
∴ n(E) = 45
Number of students who failed in both the subjects is 20%
n(H∩E) = 20
Applying the rule,
n(H∪E) = n(H) + n(E) – n(H∩E) = 30 + 45 – 20 = 55
Percentage of students who failed in Hindi or English
or both the subjects = 55%
Number of students who passed in both the subjects = 100 – 55 = 45%
Directions (Q. 21-25)
The following questions are based on the pie-charts given below:

Percentage-wise distribution of students studying in Arts and Commerce in seven different institutions
Different institutions – A, B, C, D, E, F and G Total number of students studying Arts = 3800
Percentage-wise distribution of students studying in Arts and Commerce in seven different institutions Different institutions – A, B, C, D, E, F and G

Total number of students studying Arts = 3800

Total number of students studying Commerce = 4200

21. What is the total number of students studying Arts in Institutes A and G together?
1) 1026
2) 1126
3) 1226
4) 1206
5) 1306

Ans.1
Total number of students studying Arts in Institutes A and G together

$\frac{15\;+12 }{100}=38\;\times \frac{27}{100}=1026$

22. How many students from Institute B study Arts and Commerce?
1) 1180
2) 1108
3) 1018
4) 1208
5) 1408

Ans.3
Number of students studying Art in Institute

B = 3800 × 8100 = 304

Number of students studying Commerce in Institute

B = 4200 × 17100 = 714

∴ Total number of students = 304 + 714 = 1018

23. The ratio of the number of students studying Arts to that studying Commerce in Institute E is
1) 27 : 14
2) 19 : 27
3) 19 : 16
4) 19 : 28
5) None of these

Ans.2
Number of students studying Arts in Institute

E = 3800 × 14100 = 532

Number of students studying Commerce in Institute

E = 4200 × 18100 = 756

∴ Reqd ratio = 532 : 756 = 19 : 27

24. The ratio of the number of students studying Arts in Institute E to that studying commerce in Institute D is
1) 12 : 17
2) 12 : 7
3)19 : 21
4) 17 : 19
5) None of these

Ans.3
Number of students studying Arts in Institute E = 532

Number of students studying Commerce in Institute

D = 4200 14100 = 588

∴ Reqd ratio = 532588 = 19 : 21

25. How many students in institutes B and D together study commerce?
1) 1320
2) 1302
3) 1202
4) 1220
5) None of these

Ans.2
Total number of students studying Commerce in Institute B and D together

$3800\times\frac{17\;+14 } {100}$ = 42 × 31 = 1302
Directions (Q. 26-30)
In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer
1) if x < y 2) if x > y
3) if x = y
4) if x ≥ y5) if x ≤ y or no relationship can be established between x and y.

26. I. x2 – 24x + 144 = 0             II. y2 – 26y + 169 = 0

Ans.
I. x2 – 24x + 144 = 0

or, x2 – 12x – 12x + 144 = 0

or, x(x – 12) – 12(x – 12) = 0

or, (x – 12)2 = 0

∴ x = 12
II. y2 – 26y + 169 = 0

or, y2 – 13y – 13y + 169 = 0

or, y(y – 13) – 13(y – 13) = 0

or, (y – 13)2 = 0

∴ y = 13

Hence, x < y

27. I. 2x2 + 3x – 20 = 0               II. 2y2 +19y + 44 = 0

Ans.4
I. 2y2 + 3x – 20 = 0

or, 2x2 + 8x – 5x – 20 = 0

or, 2x(x + 4) – 5(x + 4) = 0

or, (2x – 5) (x + 4) = 0

or, x = 52, –4

II. 2y2 + 19y + 44 = 0

or, 2y2 + 11y + 8y + 44 = 0

or, 2y(2y + 11) + 4(2y + 11) = 0

or, (y + 4) (2y + 11) = 0

y = –4, 112

Hence, x ≥ y

28. I. 6x2 + 77x + 121 = 0           II. y2 + 9y – 22 = 0

Ans.5
I. 6x2 + 77x + 121 = 0

or, 6x2 + 66x + 11x + 121 = 0

or, 6x(x + 11) + 11(x + 11) = 0

or, (6x + 11) (x + 11) = 0

or, x = –116, –11

II. y2 + 9y – 22 = 0

or, y2 + 11y – 2y – 22 = 0

or, y(y + 11) – 2(y + 11)

or, (y – 2) (y + 11) = 0

or, y = 2, –11

Hence, no relationship can be established between x and y.

29. I. x2 – 6x = 7                          II. 2y2 + 13y + 15 = 0

Ans.2
I. x2 – 6x = 7

or, x2 – 6x – 7 = 0

or, x2 – 7x + x – 7 = 0

or, x(x – 7) + 1(x – 7) = 0

or, (x + 1) (x – 7) = 0

or, x = –1, 7

II. 2y2 + 13y + 15 = 0

or, 2y2 + 10y + 3y + 15 = 0

or, 2y(y + 5) + 3(y + 5) = 0

or, (2y + 3) (y + 5) = 0

or, y = –32, –5

Hence, x > y

30. I. 10x2 – 7x + 1 = 0              II. 35y2 – 12y + 1 = 0

Ans.4
I. 10x2 – 7x + 1 = 0

or, 10x2 – 5x – 2x + 1 = 0

or, 5x(2x – 1) – 1(2x – 1) = 0

or, (5x – 1) (2x – 1) = 0

or, x = 15, 12

II. 35y2 – 12y + 1 = 0

or, 35y2 – 7y + 5y + 1 = 0

or, 7y(5y – 1) – 1(5y – 1) = 0

or, (7y – 1) (5y – 1) = 0

or, y = 15, 17,

Hence, x ≥ y

Directions (Q. 31-35)
Study the following table carefully to answer these questions. Percentage of marks obtained by six students in six different subject

31. What is the approximate integral percentage of marks obtained by Umesh in all the subjects?
1) 80%
2) 84%
3) 86%
4) 78%
5) 77%

Ans.1
Total marks obtained by Umesh in all subjects
together = 50 × 82100 +50 × 67100 + 150 × 92100 + 100 × 87100 + 75 × 69100 + 75 × 76100

= 41 + 33.5 + 138 + 87 + 51.75 + 57 = 408.25

∴ Reqd % = 408.25500 × 100 = 81.65% ≈ 80%

32. What is the average percentage of marks obtained by all students in Hindi ? (approximated to two places of decimal)
1) 77.45%
2) 79.33%
3) 75.52%
4) 73.52%
5) None of these

Ans.2
Average percentage marks obtained by all the students in Hindi

$=\frac{ 88+ 92+ 76 +83 +65 +72}{6}=\frac{476}{6}=79.33\%$

33. What is the average marks of all the students in Mathematics?
1) 128
2) 112
3) 119
4) 138
5) 144

Ans.3
Average marks obtained by all the students in Mathematics

$\frac{150\times (69+ 85 +92_+ 78 +64+ 88)}{100\times 6}=\frac{150\times 476}{600}$ $\frac{476 }{4}=119$

34. What is the average marks obtained by all the students in Geography?
1) 38.26
2) 37.26
3) 37.16
4) 39.16
5) None of these

Ans.4
Average marks obtained by all the students in Geography

$\frac{50 \times (85 +80+ 67+ 72+ 79+ 87) }{100\times 6}$ $\frac{470\times 500 }{600}=\frac{235}{6}=36.16$

35. What is the total marks obtained by Ritesh in all the subjects taken together?
1) 401.75
2) 410.75
3) 402.75
4) 420.75
5) None of these

Ans.5
Total marks obtained by Ritesh in all the subjects

together = $50 \frac{79}{100}+\frac{50\times 87}{100}+\frac{88\times 150}{100}+\frac{93\times 100}{100}+\frac{72\times82}{100}+\frac{72\times75}{100}$ = 34.5 + 43.5 + 132 + 93 + 61.5 + 54 = 423.5

Directions (Q. 36-40)
What value will come in place of question mark(?) in the following questions? (You are not expected to calculate the exact value)

36. 21 + 3.9 × 2.9 + 8.99 = ?
1) 42
2) 46
3) 44
4) 34
5) 36

Ans.1
? = 21 + 3.9 × 2.9 + 8.99 ≈ 21 + 4 × 3 = 21 + 12 + 9 = 42

37. 22.9889 ÷ ? = 23
1) 23
2) 1
3) 232
4) 24
5) None of these

Ans.2
22.9889 ÷ ? = 23

or, 23? or, ? = 2323 = 1

38. $\sqrt{1000000.000001}$ = ?
1) 1000
2) 100
3) 1000.001
4) 10000
5) 999

Ans.1
? = $\sqrt{1000000.000001} ?\sqrt{1000\times 1000}=1000$

39. 134% of 3894 + 38.94 of 134 = ?
1) 11452
2) 10000
3) 10452
4) 1100
5) None of these

Ans.3
? = $\frac{134 \times 3894}{100} +38.94 \times 134$

= 38.94 × 134 + 38.94 × 134

≈ 2 × (39 × 134) = 78 × 134 = 10452

40. 103 × 1003 + 999999999 = 10? + 10?
1) 6
2) 9
3) 7
4) 10
5) 12

Ans.2
103 + 10? = 103 × 1003 + 999999999

= 103 × 106 + 1000000000

= 109 + 109

or, 2 × 10? = 2 × 109 ∴ ? = 9

Directions (Q. 41-45)
Study the following bar diagram and table carefully to answer the questions. Number of employees working in five different companies A B C D and D.

41. What is the number of male employees, taking all the companies together?
1) 2084
2) 2048
3) 2064
4) 2046
5) 2066

Ans.1
Male employees

In Company A → 760 × 1319 = 520

In Company B → 840 × 47 = 480

In Company C → 720 × 715 = 336

In Company D → 640 × 1100 = 288

In Company E → 700 × 2335 = 460

∴ Total number of male employees = 520 + 480 + 336 + 288 + 460 = 2084

42. What is the approximate average number of female employees, taking all the companies together ?
1) 340
2) 315
3) 335
4) 325
5) 321

Ans.2
Female employees

In Company A → 760 × 619 = 240

In Company B → 840 × 37 = 360

In Company C → 720 × 815 = 384

In Company D → 640 × 1120 = 352

In Company E → 700 × 1235 = 240

∴ Average = $\frac{240 + 360 + 384 + 352 + 240}{5}$

= $\frac{1576}{5}$ = 315.2 ≈ 315

43. By what per cent is the number of male employees working in Company A and C more than that of female employees working in Company B and D?
1) 164
2) 146
3) 144
4) 154
5) 184

Ans.3
Male employees in Company A and B =520 +336 = 856
Female employees in Company B and D = 360 + 352 = 712

Difference = 876 – 712 = 144

44. What is the ratio of female employees working in Company D and E respectively?
1) 17 : 22
2) 22 : 17
3) 15 : 22
4) 22 : 15
5) None of these

Ans.4
Reqd ratio = 352240 22 : 15

45. By what per cent is the number of total employees of Company C more than that of Company D?
1) 12.5%
2) 16.5%
3) 21%
4) 20%
5) 16%

Ans.
Reqd % = $\frac{720-640}{640}\times 100=\frac{80}{640}\times 100=12.5\%$
Directions (Q. 46-47)
Study the following diagram to answer the questions.

46. If the diameter of each circle is 14 cm and DC = CE, the area of ΔBDE is
1) 784 sq cm
2) 748 sq cm
3) 874 sq cm
4) 441 sq cm
5) None of these

Ans.1
In ΔBDE

DC = 28cm (beacause diameter of each circle 14cm)

Now, DE = DC + CE = 28 + 28 + 56cm

And BC = 28cm

Again, area of ΔBDE,

= 12 × DE × BC = 12 × 56 × 28= 784 sq m

47. The area of the shaded region of square ABCD is
1) 186 sq cm
2) 168 sq cm
3) 188 sq cm
4) 441 sq cm
5) None of these

Ans.2
Area of the square = 28 × 28 784 sq cm

Area of four circles = 4πr2

= 4 × 227 × 7 × = 28 × 22 =616 sq cm

Directions (Question.48)
48. A pump can fill a tank with water in 2 hours. Because of a leak, it took 213

hours to fill the tank. The leak can drain all the water of the tank in
1) 413 4 hours
2) 7 hours
3) 8 hours
4) 14 hours
5) None of these

Ans.4
Park of thank emptied in 1 hour by leak = 1237 = 114

The leak will empty the tank in 14 hour.

Directions (Question.49)
49. A person travels from P to Q at a speed of 40 kmph and returns to Q by increasing his speed by 50%. What is his average speed for both the trips?
1) 36 kmph
2) 45 kmph
3) 48 kmph
4) 50 kmph
5) None of these

Ans.3
Speed of man for P to Q = 40 kmph

Speed of man for Q to P = $\frac{40\times 150}{100}=60 kmph$

∴ Average speed = $\frac{2\times40 \times600}{40+60}=40 kmph$

Directions (Question.50)
50. A shopkeeper sells two watches for `308 each. On one he gets 12% profit and on the other 12% loss. His profit or loss in the entire transaction was
1) 11125% loss
2) 11125% gain
3) 3225% loss
4) 3225% gain
5) None of these

Loss % = $\left ( \frac{Common \;gain \;or \;loss }{10} \right )^{2}=40 kmph$
12 – 12 = $\frac{12\times 12}{100}=\frac{144}{100}= -\frac{36}{50}= -1\frac{11}{25}\%$