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# Analytical Skill Building 1

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Part A

Q1 Differentiate between Data Interpretation and Data Sufficiency.

Q2 Explain the process of construction of Pie Chart.

Q3 If the speed of a body and the radius of its circular path are made thrice by what factor the centripetal acceleration will change?

Q4 Define average angular acceleration.

Q5.In what ratio must rice at Rs 9.30 per Kg be mixed with rice at Rs 10.80 per Kg so that the mixture be worth Rs 10 per Kg?

Q6 .How much water must be added to 60 liters of milk at 11/2 liters for Rs 20 so as to have a mixture worth Rs 10 2/3 a liter?

Part B

Q1 The average weekly salary per head of the entire staff of a factory consisting of supervisors and the laborers is Rs 60.The average salary per head of the supervisors is Rs 400 and that of the laborers is Rs 56.Given that the number of supervisors is 12.Find the number of laborers in the factory.

Q2 : What is the value of X, if X and Y are two distinct integers and their product is 30?

(1) X is an odd integer

(2) X > Y

Q3 A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

A. 4 B. 5

C. 6 D. 10

CASE STUDY

The following pie-charts show the distribution of students of graduate and post-graduate levels in seven different institutes in a town.

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1. What is the total number of graduate and post-graduate level students is institute R?

A. 8320 B. 7916

C. 9116 D. 8099

2 What is the ratio between the number of students studying at post-graduate and graduate levels respectively from institute S?

A. 14 : 19 B. 19 : 21

C. 17 : 21 D. 19 : 14

3 How many students of institutes of M and S are studying at graduate level?

A. 7516 B. 8463

C. 9127 D. 9404

4 What is the ratio between the number of students studying at post-graduate level from institutes S and the number of students studying at graduate level from institute Q?

A. 13 : 19 B. 21 : 13

C. 13 : 8 D. 19 : 13

5 Total number of students studying at post-graduate level from institutes N and P is

A. 5601 B. 5944

C. 6669 D. 8372

Section C

1: If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?

121
B. 3267

C. 363

D. 33

E. None of the above

2: How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?

A. 6 B. 7
C. 5 D. 8
E. 18

Question 3: A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

A 13

B. 59

C. 35

D. 37

E. 12

Question 4: How many keystrokes are needed to type numbers from 1 to 1000?

A 3001 B 2893

C 2704 D 2890

E None of these

Question 5: When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?

A.11
B.17
C.13
D.23
E.None of these

Question 6: How many integral divisors does the number 120 have?

A.14
B.16
C.12
D.20
E.None of these

Question 7: How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?

A.25
B.8
C.6
D.5
E.2

Question 8: What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?

A.3
B.27
C.30
D.21
E.18

Question 9: Data Sufficiency : Is x3 > x2 ?
(1) x > 0
(2) x < 1 Question 10: Data Sufficiency : Is x/ya terminating decimal? (1) x is a multiple of 2 (2) y is a multiple of 3 1 1 The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? A. 8 : 9 B. 17 : 18 C. 21 : 22 D. Cannot be determined 12 Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary? A. Rs. 17,000 B. Rs. 20,000 C. Rs. 25,500 D. Rs. 38,000 13 If 0.75 : x :: 5 : 8, then x is equal to: A. 1.12 B. 1.2 C. 1.25 D. 1.30 14The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is: A. 20 B. 30 C. 48 D. 58 15If Rs. 782 be divided into three parts, proportional to 1-div-1by2: 1-div-2by3: 1-div-3by4, then the first part is: A. Rs. 182 B. Rs. 190 C. Rs. 196 D. Rs. 204 16 The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries? A. 3 : 3 : 10 B. 10 : 11 : 20 C. 23 : 33 : 60 D. Cannot be determined 1 7If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number? A. 2 : 5 B. 3 : 7 C. 5 : 3 D. 7 : 3 18The fourth proportional to 5, 8, 15 is: A. 18 B. 24 C. 19 D. 20 19Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is: A. 27 B. 33 C. 49 D. 55 20 In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there? A. 50 B. 100 C. 150 D. 200 21 Data Sufficiency : Is the positive integer X divisible by 21? (1) When X is divided by 14, the remainder is 4 (2) When X is divided by 15, the remainder is 5 22: Data Sufficiency : If x and y are positive integers, is y odd? (1) x is odd. (2) xy is odd. 23 Data Sufficiency : Is xy < 0? (1) (1) 5|x| + |y| = 0 (2) (2) |x| + 5|y| = 0 24 Is the two digit positive integer P a prime number? (1) (P + 2) and (P - 2) are prime. (2) (P - 4) and (P + 4) are prime. 25 Data Sufficiency : A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x? (1)The elements are in arithmetic progression (2) x is prime 26Data Sufficiency : Is the positive integer X divisible by 21? (1) When X is divided by 14, the remainder is 4 (2) When X is divided by 15, the remainder is 5 27 If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?
(1) m > a
(2) a + b + c + d = 0

28 What is the speed of the train whose length is 210 metres?

I. The train crosses another train (Howrah Express/12869) of 300 metres length running in opposite direction in 10 seconds.

II. The train crosses another train (Howrah Express/12869) running in the same direction at the speed of 60 km/hr in 30 seconds.

A. I alone sufficient while II alone not sufficient to answer

B. II alone sufficient while I alone not sufficient to answer

C. Either I or II alone sufficient to answer

D. Both I and II are not sufficient to answer

E. Both I and II are necessary to answer

29 What is the length of a running train crossing another 180 metre long train running in the opposite direction?

I. The relative speed of the two trains was 150 kmph.

II. The trains took 9 seconds to cross each other.

A. I alone sufficient while II alone not sufficient to answer

B. II alone sufficient while I alone not sufficient to answer

C. Either I or II alone sufficient to answer

D. Both I and II are not sufficient to answer

E. Both I and II are necessary to answer

30 What is the length of a running train?

I. The train crosses a man in 9 seconds.

II. The train crosses a 240 metre long platform in 24 seconds.

A. I alone sufficient while II alone not sufficient to answer

B. II alone sufficient while I alone not sufficient to answer

C. Either I or II alone sufficient to answer

D. Both I and II are not sufficient to answer

E. Both I and II are necessary to answer

Q 31 The following bar chart shows the trends of foreign direct investments(FDI) into India from all over the world.

Trends of FDI in India

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31. What was the ratio of investment in 1997 over the investment in 1992 ?

A. 5.50 B. 5.36

C. 5.64 D. 5.75

32 What was absolute difference in the FDI to India in between 1996 and 1997 ?

A. 7.29 B. 7.13

C. 8.13 D. None of these

33 If India FDI from OPEC countries was proportionately the same in 1992 and 1997 as the total FDI from all over the world and if the FDI in 1992 from the OPEC countries was Euro 2 million. What was the amount of FDI from the OPEC countries in 1997 ?

A. 11 B. 10.72

C. 11.28 D. 11.5

34 Which year exhibited the highest growth in FDI in India over the period shown ?

A. 1993 B. 1994

C. 1995 D. 1996

35 What was India’s total FDI for the period shown in the figure ?

A. 93.82 B. 93.22

C. 93.19 D. None of these

The following chart represents the number of students who passed the CAT exam or the XAT exam or the CET exam or None of these exams. (Assume that there are no students who passed more than one exam.)

Number of students who qualified CAT/XAT/CET Exams

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36 Which year showed the best result in MBA entrance exams (in terms of percentage of students who cleared) ?

A. 2000 B. 2001

C. 2002 D. Cannot be determined

37 What was the percentage of students who succeeded in at least one of three exams in 2000 ?

A. 82.4 % B. 82.8 %

C. 82.35 % D. 83.3 %

38 What is the percentage increase in the number of students in 2002 over 2000 ?

A. 30 % B. 17.64 %

C. 117.6 % D. 85 %

39 What is the percentage of students who cleared CAT in 2000 ?

A. 19.56 % B. 12.65 %

C. 14.28 % D. 11.76 %

40 5Kg of rice at Rs 6 per Kg is mixed with 4 Kg of rice to get a mixture costing Rs 7 per Kg. Find the price
of the costlier rice?

A 8.25 B 6.75

C 5.25 D 7.25