quantitative aptitude 12

OBJECTIVE-TYPE QUESTIONS

767 ■ MARCH 2002 ■ THE COMPETITION MASTER

Quantitative Aptitude1. If x * y = (x + 2)2 (y – 2), then the value of 7 * 5 is:(a) 175(b) 205(c) 213(d) 2432. The H.C.F. of three numbers is 12. If they are in the

ratio 1 : 2 : 3, the numbers are:(a) 12, 24, 36(b) 10, 20, 30(c) 6, 12, 18(d) 24, 48, 723. If m and n (n > 1) are whole numbers, such that

mn = 121, the value of (m – 1)n + 1 is:(a) 1(b) 10(c) 121(d) 1000

4. If xy

= 34

, the value of 67

+−+

FHG

IKJ

y xy x is:

(a) 117

(b)57

(c) 1(d) 25. If 76 is divided into four parts proportional to 7, 5, 3

and 4, the smallest part is:(a) 12(b) 15(c) 16(d) 196. The sum of three numbers is 98. If the ratio of the

first to the second is 2 : 3 and that of the second to the thirdis 5 : 8, then the second number is:

(a) 20(b) 30(c) 48(d) 58

7. A fraction, which bears the same ratio to 127

, that 311

does to 59

, is equal to:

(a)155

(b) 55

(c)111

(d)311

8. If x : y : : 5 : 2, the value of: 8x + 9y : 8x + 2y is:

(a) 22 : 29(b) 29 : 22(c) 61 : 26(d) 26 : 61

9. The prices of scooter and T.V. set are in the ratio 5 : 4.If a scooter costs Rs 4,000 more than the T.V. set, the price ofthe T.V. set (in rupees) is:

(a) 12,000(b) 14,000(c) 16,000(d) 20,000

10. How many numbers lying between 200 and 600 aredivisible by 4, 5 and 6?

(a) 5(b) 6(c) 7(d) 8

11. A number, when divided by 119, leaves a remainderof 19. If it is divided by 17, it will leave a remainder of:

(a) 19(b) 10(c) 7(d) 2

12. The average of the first 50 natural numbers is:(a) 12.25(b) 21.25(c) 25.00(d) 25.50

13. The average weight of 8 men is increased by 1.5 kg.When one of the men who weighs 65 kg is replaced by a newman, the weight of new man is:

(a) 76 kg(b) 76.5 kg(c) 76.7 kg(d) 77 kg

14. The average of 11 observations is 60. If the average offirst five observations is 58 and that of the last five is 56, thenthe sixth observation is:

Solved Paper of Staff Selection Commission Section Officer Exam held on July 24, 2001



(a) 90(b) 110(c) 85 (d) 100

15. The average age of 25 students is 10 years. If theteacher ’s age is also included, the average age increases byone year. The age of the teacher is:

(a) 26 years(b) 36 years(c) 46 years(d) 25 years16. The average age of 40 students of a class is 15 years.

When 10 new students are admitted, the average is increasedby 0.2 year. The average age of the new students is:

(a) 15.2 years(b) 16 years(c) 16.2 years(d) 16.4 years

17. A tin of oil was 45

full. When six bottles of oil were

taken out and four bottles of oil poured into it, it was 34

full.

How many bottles of oil can the tin contain?(a) 10(b) 20(c) 30(d) 40

18. The length of the bridge which a train, 130 metreslong and travelling at 45 km per hour, can cross in 30 seconds,is:

(a) 200 m(b) 225 m(c) 245 m(d) 250 m

19. A man walking at the rate of 4 km per hour crossesa square field diagonally in 3 minutes. The area of the field is:

(a) 20,000 m2

(b) 25,000 m2

(c) 18,000 m2

(d) 19,000 m2

20. The rate at which a sum becomes four times of itselfin 15 years at simple interest will be:

(a) 25%(b) 20%

(c) 1712

%

(d) 15%21. A sum of money at simple interest amounts to Rs 815

in 3 years and to Rs 854 in 4 years. The sum is:(a) Rs 700(b) Rs 698(c) Rs 690

(d) Rs 65022. In how many years will a sum of Rs 800 at 10% per

annum compounded semi-annually becomes Rs 926.10?

(a) 212

(b) 112

(c) 213

(d) 113

23. If a sum of money at simple interest doubles itself in6 years, it will become 4 times in:

(a) 14 years(b) 12 years(c) 18 years(d) 16 years24. A man gains 10% by selling a certain article for a

certain price. If he sells it at double the price, the profit madeis:

(a) 20%(b) 60%(c) 100%(d) 120%25. An electric iron was sold at a proift of 15%. Had it

been sold for Rs 600, the profit would have been 20%. Theformer selling price of the electric iron is:

(a) Rs 500(b) Rs 540(c) Rs 575(d) Rs 60026. If the cost price of 12 tables is equal to selling price

of 16 tables, the loss per cent is:(a) 15% (b) 20%(c) 25% (d) 30%27. A man sells 2 horses at the same price, on one he

makes a profit of 10% and on the other he makes a loss of10%. On the whole he:

(a) makes no profit no loss(b) makes a profit of 1%(c) suffers a loss of 1%(d) suffers a loss of 2%28. Rahim buys 3 kg mangoes for Rs 21 and sells them at

5 kg for Rs 50. To earn Rs 102 as profit, the mangoes to be soldby him should be:

(a) 34 kg(b) 52 kg(c) 26 kg(d) 32 kg29. The difference between the circumference and radius



of a circle is 37 cm. (use π = 227

). The diameter of the circle is:

(a) 7 cm(b) 14 cm

(c) 3367

cm

(d) 37 cm30. The area of the largest triangle that can be inscribed

in a semi-circle of radius r is:(a) r2 (b) r3 (c) 2r2 (d) 2r3

31. The areas of the three adjacent faces of a rectangularbox which meet in a point are known. The product of theseareas is equal to:

(a) the volume of the box(b) twice the volume of the box(c) the square of the volume of the box(d) cube root of its volume32. A copper sphere of radius 3 cm is beaten and drawn

into a wire of diameter 0.2 cm. The length of the wire is:(a) 9 m (b) 12 m (c) 18 m (d) 36 m33. The diagonal of a square field is 110 m. Its area is:(a) 6050 m2

(b) 12100 m2

(c) 6000 m2

(d) 1200 m2

Direction: The table here is a blue print for the unit test onfractions and decimals-class-VII. Study the table and answerquestions 34 to 38.

34. Maximum marks for the unit test are:(a) 40 (b) 80 (c) 100 (d) 20035. The number of marks that test the understanding of

the concepts is:(a) 3 (b) 10 (c) 12 (d) 2236. Marks allotted for higher mental abilities, i.e.,

understanding and application are:(a) 52 (b) 50 (c) 40 (d) 1537. How many per cent of the marks have been allotted

for word problems?(a) 3 (b) 5 (c) 10 (d) 1538. What per cent of total marks test computational and

other skills in four fundamental operations?(a) 2 (b) 4 (c) 6 (d) 8

39. The H.C.F. of two numbers is 11 and their L.C.M. is7700. If one of the numbers is 275, the other is:

(a) 279 (b) 283 (c) 308 (d) 31840. The sum of 2 75. and 3 78. is:

(a) 5.53 (b) 4.53 (c) 1.53 (d) 1 03.

41.7 57 5

+− is equal to:

(a) 6 + 35 (b) 6 – 35

(c) 2 (d) 142. If log 27 = 1.431, then the value of log 9 is:

(a) 0.934(b) 0.945(c) 0.954(d) 0.958

43. The value of: (3.75 × 3.75 – 2 × 3.75 × 2.75 + 2.75 × 2.75) is:

(a) 1.00(b) 1.75(c) 4.75(d) 6.50

44. The total number of three digit numbers which areexactly divisible by 6 is:

(a) 149(b) 150(c) 151(d) 166

45. If the side of a square is increased by 25%, then itsarea is increased by:

(a) 25%(b) 55%(c) 40.5%(d) 56.25%

46. If A’s height is 10% more than B’s, how much percent less is B’s height than that of A?

(a) 10%

(b) 1019

%

Objective

Content

Concepts 15 3 — 4 22

Addition and 10 6 2 2 20Subtraction

Multiplication 10 6 4 4 24and Division

Conversion of 5 10 4 — 19fraction intodecimals andvice versa

Word Problems — 5 — 10 15

Total 40 30 10 20 100

Kno

wle

dge

Und

erst

andi

ng

Skill

App

lica

tion

Total

Note: Cells contain number of marks allotted.



(c) 101

11%

(d) 91

11%

47. If 75% of a number is added to 75, the result is thenumber itself, then the number is:

(a) 400(b) 300(c) 60(d) 50

48. A student has to secure 40% marks to pass. He gets178 marks and fails by 22 marks. The maximum marks are:

(a) 450(b) 500(c) 520(d) 600

49. A school has only three classes which contain 40, 50and 60 students respectively. The pass percentages of theseclasses are 10, 20 and 10 respectively. The pass percentage ofthe school is:

(a) 1313

(b) 15

(c) 1623

(d) 2050. If x and y are two digits of the number 653 xy

such that the number is divisible by 80, then x + y isequal to:

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

ANSWERS AND EXPLANATIONS

1. (d) 7 * 5 = (7 + 2)2 (5 – 2) = 243.2. (a) Nos. are 12 × 1, 12 × 2, 12 × 3 i.e. 12, 24, 363. (d) mn = 121 = 112

∴ m = 11, n = 2, (m – 1)n + 1 = (11 – 1)2 + 1 = 1000

4. (c)67

67

+−+

= +y xy x

yy

xy

yy

xy

−

+= +

−

+=6

7

134

134

1

5. (a) Smallest part = 3

7 5 3 476 12

+ + +× =

6. (b) I : II : III2 : 3

5 : 8= 10 : 15 : 24

7. (a) x x: :1

27311

59

311

95

127

155

= ⇒ = × × =

8. (b)8 98 2

8 9

8 2

852

9

852

2

2922

29 22x yx y

xyxy

++

=+

+=

× +

× += =

.

.:

9. (c) Let the costs of a scooter and T.V. are Rs 5x and 4x ∴ 5x – 4x = 4000 ∴ Price of a T.V. = 4 × 4000 = Rs 16000

10. (b) LCM of 4, 5, 6 = 60The nos. divisible by 60 and lying between 200 and

600 are 240, 300, .... 540 ∴ a = 240, tn = 540, d = 60

tn = a + (n – 1) d∴ 540 = 240 + (n – 1) 60 ⇒ n = 6

11. (d) No. = 119 × Q + 19 = 17 × 7 × Q + 17 + 2= 17 (7Q + 1) + 2

∴ Reqd. remainder = 2

12. (d) Reqd. average = 150

50 50 12

25( )

.50+L

NMOQP=

[ QSum of n natural nos.= n n( )+ 1

2

13. (d) Total increase in weight = 8 × 1.5 = 12.0∴ Weight of new man = 65 + 12 = 77 kg

14. (a) Sixth observation = 11 × 60 – (5 × 58 + 5 × 56) = 9015. (b) Teacher’s age = 26 × (10 + 1) – 25 × 10 = 36 yrs16. (b) Average age of new students

= 50 15 2 40 15

1016

× ×=

. yrs

17. (d)45

34

x x− = Capacity of 2 bottles

⇒ Capacity of 1 bottle = x40

∴ No. of bottles = xx40

40=

18. (c)130

455

18

30 245+

×= ⇒ =

xx m (T =

DS

)

19. (a) 2 a

∴ = × × × =2 3 60 45

18200a ( ) ( ) D = T × S

a2 = 200 200

2 220000

××

= m2

20. (b) If P = Rs x A = Rs 4x ∴ I = 4x – x = Rs 3x

IInd no. = 15

10 15 2498 30

+ +× =



R = IP T××100

= 3 100

1520

xx

××

=

21. (b) Int. for 1 year = 854 – 815 = Rs 39 Int for 3 yrs = 39 × 3 = Rs 117

∴ P = 815 – 117 = 698

22. (b) A = P ( )1100

+ R n , 926.10 = 800 (1 + 10

2 1003

×⇒ =)n n

n = 3 half years = 32

112

= years

23. (c) R = xx××

=100

6503

, T = 3 100

503

x

x

×

× = 18 years

24. (d) Let CP = Rs 100 ∴ S.P. = Rs 110If S.P. = Rs 110 × 2 = Rs 220Gain = 220 – 100 = Rs 120

Gain% = × =120100

100 120

25. (c) Let C.P. = Rs 100Gain = 20% S.P. = Rs 120If Gain = 15%, S.P. = Rs 115If S.P. = Rs 120, then actual S.P. = Rs 600

If S.P. = Rs 115, then actual S.P. = 600120

115 575× =

26. (c) C.P. of 12 tables = S.P. of 16 tablesLet C.P. of 1 table = Re 1 ∴ C.P. of 12 tables = Rs 12C.P. of 16 tables = Rs 16S.P. of 16 tables = Rs 12Loss = C.P. – S.P. = 16 – 12 = Rs 4

Loss % = 4

16100 25× =

27. (c) If S.P. is same in both cases, there is always a loss= x% of x x = 10= 10% of 10 = 1 x is a common gain & loss%

28. (a) L.C.M. of 3 and 5 = 15

CP = 213

15× = Rs 105

S.P. = 505

15× = Rs 150

Gain = 150 – 105 = Rs 45If P = Rs 45, then mangoes sold = 15 kg

If P = Rs 102, then mangoes sold = 1545

102 34× = kg

29. (b) 2 37 2227

1πr r x( )= ⇒ × − = 37 ⇒ r = 7, D = 14 cm

30. (a) Base of a ∆ = diameter = 2rHeight for largest ∆ = r

∴ Area = 12

2 2× × =r r r

31. (c) Area of three adjacent faces which meet in a pt. are lb, bh, hlProduct = lb × bh × hl = (lbh)2 = V2

32. (d) π(.

)22

2 × l = 43

π × 33 ⇒ l = 3600 cm = 36 m

(Vol. of wire = πr 2 l) (Vol. of a sphere = 43

3πr )

33. (a) d = 2 110 2a a⇒ =

∴ 2a2 = 1102 ⇒ a2 = 6050 m2

34. (c) 35. (a) 36. (b) 30 + 20 = 50 37. (d)38. (c)

39. (c) IInd No. = × = × =H C F L.C M

Ist No

. . . . .

.

11 7700275

308

40. (b) 2 75 3 78 2 75 3 78 5 1. . . ( ) . .53+ = − + + − + = − +

= –4 + .53 = 4.53

41. (a)7 57 5

7 57 5

+−

×+−

=7 5 2 35

7 56 35

+ +−

= +

42. (c) log 27 = 1.431 ⇒ log 33 = 1.431 ⇒ 3 log 3 = 1.431

log 3 = 1431

3477

.. ,= log 9 = log 32 = 2 log 3

= 2 × .477 = 0.95443. (a) (a – b)2 = a2 – 2ab + b2

Reqd. value = (3.75 – 2.75)2 = 144. (b) Three digit nos. divisible by 6 are 102, 108, ... 996

Tn = a + (n – 1) d∴ 996 = 102 + (n – 1) 6 ⇒ n = 150

45. (d) %increase in area = (125100

x) x

x100 56.25

2 2

2

−× =

46. (d) Let B’s height be 100 ∴ A’s height = 110If A’s height is 110, then B’s height is less by 10If A’s height is 100, then B’s height is less by

= 10110

100 9111

× =

47. (b) 75% of x + 75 = x ⇒ x = 30048. (b) 40% of x = 178 + 22 ⇒ x = 50049. (a) Pass% of school

= 40

10100

5020

10060

10100

40 50 6013

13

× + × + ×

+ +=

50. (a) As the no. is divided by 80, y must be 0 ∴ x should be 6, x + y = 6 + 0 = 6

quantitative aptitude 12

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