Cat 2009 Quanttest 96

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Quant Test 96

1. A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fenceposts at six metre intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was five less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them eight metres apart. What is the length of the side of his property and how many posts did he buy?

j 100 metres, 15 k l m n j 100 metres, 16 k l m n j 120 metres, 15 k l m n j 120 metres, 16 k l m n j -nullk l m n i Skip this question j k l m n

2. What is the smallest possible positive integer such that the product of all its digits equals to 9!?

j 2578899 k l m n j 13856789 k l m n j 2345678 k l m n j 12345789 k l m n j None of these k l m n i Skip this question j k l m n

3. In the X-Y plane, P and Q are points on straight lines 4y = x and 3y = x respectively. If R(10, 3) is the midpoint of line segment PQ, then find the length of line segment PQ.

j 2sqrt( 5)units k l m n j 3 sqrt(5) units k l m n j 4 sqrt(2) units k l m n j 5 sqrt(2) units k l m n j None of these k l m n i Skip this question j k l m n

4. For which of the following values of ‘p’, (x + p)(x + 10) + q = (x + m)(x + n) + r for all values of x, where m, n are integers and q and r consecutive integers with q > r?

j 30 k l m n j 12 k l m n j 24 k l m n j 8 k l m n j Both (2) and (4) k l m n i Skip this question j k l m n

5. A store owner plans to sell two types of MP3 players. One type costs the store owner $200 each; the other type costs $400 each. The $200 models yield a profit of $25 dollars each and the $400 models a profit of $30 each. The store owner estimates that the total demand for the MP3 players will not exceed 300 units. The store owner can invest up to $80,000 on the inventory of MP3 players. The store owner sells some models of each type to maximize the profit. What is the value of the maximum possible profit the store owner can make?

j $8000 k l m n j $7000 k l m n j $9000 k l m n j $7500 k l m n j $6000 k l m n i Skip this question j k l m n

6. Find the sum of all the integers N > 1 such that the each prime factor of N is either 2, 3 or 7 and N is not divisible by any perfect cube greater than 1.

j 2820 k l m n j 4004 k l m n j 5186 k l m n j 3184 k l m n j 6186 k l m n i Skip this question j k l m n

7. There are 10 students out of which three are boys and seven are girls. In how many different ways can the students be paired such that no pair consists of two boys?

j 630 k l m n j 1260 k l m n j 105 k l m n j 210 k l m n j None k l m n i Skip this question j k l m n

8. Ajay, Vijay and Dhananjay purchased 1, 10 and 25 notebooks for a total of Rs.14, Rs.130 and Rs.300 respectively from a stationery shop. In his transaction with Ajay and Dhananjay, the shopkeeper made a profit of p% and q% respectively such that p = 2q. How much profit did the shopkeeper make in his transaction with Vijay?(Assume that the shopkeeper bought each note book at the same price)

j 22% k l m n j 25% k l m n j 28% k l m n j 30% k l m n j 27% k l m n i Skip this question j k l m n

9. In the figure given below PQ and RS are two chords of equal length such that PQ || RS. Another chord AD cuts the chords PQ and RS at B and C respectively. Given that PB: BQ = 3 : 1, RC : CS = 3 : 5 and AB : BC = 1 : 4. What is the ratio of area of the ΔABQ to the area of the ΔCDS?

j 3 : 10 k l m n j 1:3 k l m n j 1:4 k l m n j 2:5 k l m n j 1:2 k l m n

i Skip this question j k l m n Directions for Questions from 10 to 11: Answer the questions on the basis of the information given below. The employees of IHG Limited are given one out of the three different designations namely Executives, Analysts and Managers. Each executive has worked with exactly four analysts and exactly three managers. Each manager has worked with exactly two executives and exactly five analysts and each analyst has worked with exactly three managers.

10. If the total number of employees in IHG Limited is 920, then what is the number of executives in the company?

j 230 k l m n j 184 k l m n j 165 k l m n j 372 k l m n j Cannot be determined k l m n i Skip this question j k l m n

11. Which of the following can be the total number of executives and analysts in IHG Limited?

j 63 k l m n j 147 k l m n j 210 k l m n j 49 k l m n j 196 k l m n i Skip this question j k l m n

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