# XAT 2010 Question Paper - QUANT

Instructions

For the following questions answer them individually

Question 62

Question 63

Question 64

Question 65

Question 66

Question 67

Question 68

## A manufacturer has 200 litres of acid solution which has 15% acid content. How many litres of acid solution with 30% acid content may be added so that acid content in the resulting mixture will be more than 20% but less than 25%?

Instructions

Answer questions based on the following information:

An automobiles company’s annual sales of its small cars depends on the state of the economy as well as on whether the company uses some high profile individual as its brand ambassador in advertisements of its product. The state of the economy is “good”, “okay” and “bad” with probabilities 0.3, 0.4 and 0.3 respectively. The company may choose a high profile individual as its brand ambassador in TV ads or may go for the TV ads without a high profile brand ambassador.

If the company fixes price at Rs. 3.5 lakh, the annual sales of its small cars for different states of the economy and for different kinds of TV ads are summarized in table 1. The figures in the first row are annual sales of the small cars when the company uses a high profile individual as its brand ambassador in its TV ads and the ones in the second row are that when the company does not use any brand ambassador in TV ads, for different states of the economy.
Table 1:

Without knowing what exactly will be the state of the company in the coming one year, the company will either have to sign a TV ad contract with some high profile individual, who will be the company’s brand ambassador for its small car for the next one year, or go for a TV ad without featuring any high profile individual. It incurs a cost of Rs. 3.45 lakh (excluding the payment to the brand ambassador) to put a car on the road.

When the company’s profit is uncertain, the company makes decisions on basis of its expected profit. If the company can earn a profit xi with probability pi (the probability depends on the state of economy), then the expected profit of the company is $$\sum_1XiPi$$

Question 69

Question 70

Question 71

## Mr. Khan a popular film actor, agrees to sign the contract to become the company’s brand ambassador for Rs. 9 crore. The cost to the company of putting a car on the road also got escalated by Rs. 1000. If the company signs the contract with Mr.Khan, its profit will

Instructions

For the following questions answer them individually

Question 72

Question 73

## The supervisor of a packaging unit of a milk plant is being pressurised to finish the job closer to the distribution time, thus giving the production staff more leeway to cater to last minute demand. He has the option of running the unit at normal speed or at 110% of normal - “fast speed”. He estimates that he will be able to run at the higher speed for 60% of the time. The packet is twice as likely to be damaged at the higher speed which would mean temporarily stopping the process. If a packet on a randomly selected packaging runs has probability of 0.112 of damage, what is the probability that the packet will not be damaged at normal speed?

Instructions

Let $$A_{1},A_{2},.....A_{n}$$ be then points on the straight - line y = px + q. The coordinates of $$A_{k}is(X_{k},Y_{k})$$, where k = 1, 2, ...n such that $$X_{1},X_{2}....X_{n}$$ are in arithmetic progression. The coordinates of $$A_{2}$$ is (2,–2) and $$A_{24}$$ is (68, 31).

Question 74

Question 75

## The number of point(s) satisfying the above mentioned characteristics and not in the first quadrant is/are

Instructions

For the following questions answer them individually

Question 76

Question 77

Question 78

Question 79

## In a clock having a circular scale of twelve hours, when time changes from 7:45 A.M. to 7:47 A.M., by how many degrees the angle formed by the hour hand and minute hand changes?

Instructions

Questions are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:
A. Statement I alone is sufficient to answer the question.
B. Statement II alone is sufficient to answer the question.
C. Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.
D. Either Statement I or Statement II alone is sufficient to answer the question.
E. Both Statement I and Statement II are insufficient to answer the question

Question 80

Question 81

## A sequence of positive integer is defined as $$A_{n+1}=A_{n}^{2}+1$$ for each n ≥ 0. What is the value of Greatest Common Divisor of $$A_{900}$$ and $$A_{1000}$$ ?I. $$A_{0} = 1$$II. $$A_{1} = 2$$

Instructions

For the following questions answer them individually

Question 82

## a,  b,  c,  d and  e are integers such that 1 ≤ a < b < c < d < e. If a, b, c, d and e are geometric progression and lcm (m , n) is the least common multiple of m and n, then the maximum value of $$\frac{1}{lcm(a,b)}+\frac{1}{lcm(b,c)}+\frac{1}{lcm(c,d)}+\frac{1}{lcm(d,e)}$$ is

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Books and More sells books, music CDs and film DVDs. In December 2009, they earned 40% profit in music CDs and 25% profit in books. Music CDs contributed 35% towards their total sales in rupees. At the same time total sales in rupees from books is 50% more than that of music CDs.

Question 83

Question 84

## If Books and More made 50% loss in film DVDs, then overall they made

Instructions

For the following questions answer them individually

Question 85

## ABCD is a parallelogram with $$\angle$$ ABC = 60°. If the longer diagonal is of length 7 cm and the area of the parallelogram ABCD is $$15\frac{\sqrt{3}}{2}$$ sq.cm, then the perimeter of the parallelogram (in cm) is

Instructions

OABC is a square where O is the origin and AB = 1. Consider the set of points $$s = {(x_{i},y_{i})}$$ in the square such that $$x_{i}+y_{i}$$≤1. Let $$P (x_{1}, y_{1})$$ and $$Q (x_{2}, y_{2})$$ be two such points. Two operations addition (+) and multiplication (.) on S are defined as
$$P + Q = (x_{1}+x_{2} - x_{1}x_{2},y_{1}y_{2})$$
$$P.Q = (x_{1}x_{2},y_{1}+y_{2} - y_{1}y_{2})$$

Question 86

Question 87

## For a very large number n, nP + nQ is

Instructions

Answer thequestions based on the data given in table 2

Cost and price data for Portland cement manufactured by Paharpur Cement and Bahsin Cement, for four consecutive quarters, are given in table 2:

Sales Revenue = Price × Sales Quantity
Profit = Sales Revenue – Cost
Profit Rate = Profit / Sales Quantity

Question 88

Question 89

Question 90

## If between Apr - Jun 2009 and Jul - Sept 2009 sales of Paharpur Cement increased by 2.25%, its profit increased by

Instructions

Answer the questions based on the information given below:

Madhubala Devi, who works as a domestic help, received Rs. 2500 as Deepawali bonus from her employer. With that money she is contemplating purchase of one or more among 5 available government bonds - A, B, C, D and E.

To purchase a bond Madhubala Devi will have to pay the price of the bond. If she owns a bond she receives a stipulated amount of money every year (which is termed as the coupon payment) till the maturity of the bond. At the maturity of the bond she also receives the face value of the bond.
Price of a bond is given by: $$P=[\sum_{t=1}^T\frac{C}{(1+r)^{t}}]+\frac{F}{(1+r)^{t}}$$

where C is coupon payment on the bond. which is the amount of money the holder of the bond receives annually; F is the face value of the bond, which is the amount of money the holder of the bond receives when the bond matures (over and above the coupon payment for the year of maturity); T is the number of years in which the bond matures;
R = 0.25, which means the market rate of interest is 25%.

Among the 5 bonds the bond A and another two bonds mature in 2 years, one of the bonds matures in 3 years, and the bond D matures in 5 years.

The coupon payments on bonds A, E, B, D and C are in arithmetic progression, such that the coupon payment on bond A is twice the common difference, and the coupon payment on bond B is half the price of bond A.

The face value of bond B is twice the face value of bond E, but the price of bond B is 75% more than the price of bond E. The price of bond C is more than Rs. 1800 and its face value is same as the price of bond A. The face value of bond A is Rs. 1000.

Bond D has the largest face value among the five bonds.

Question 91

Question 92

Question 93

## The price of bond C must be

Instructions

For the following questions answer them individually

Question 94

Question 95

Question 96

Question 97

Question 98

## A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of same size. The number of boxes to be sent is 96 of brand A, 240 of brand B and 336 of brand C. These boxes are to be packed in cartons of same size containing equal number of boxes. Each carton should contain boxes of same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?

Instructions

based on the information given below.

The retail prices of flowers, consumer expenditure on flowers and sales of flowers for the calendar year 2009, in Phoolgaon, a small town with a population of 70000, is summarized in table 3:

Question 99

Question 100

Question 101