Cat 2009 Quant Test 75

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Quant Test 75

1. The value of (222)X in base ‘X’ when converted to base 10 is ‘P’. The value of (222)Y in base ‘Y’ when converted to base 10 is Q. If (P – Q)10 = 28, then what is the value of (Q – X)10 ?

j 80 k l m n j 108 k l m n j 92 k l m n j 79 k l m n j Cannot be determined k l m n i Skip this question j k l m n

2. If ‘a’ is an odd number and ‘b’ is an even number, then what is the total number of solutions of the equation (ab + 2 = 2a + b + 600)?

j 16 k l m n j 12 k l m n j 5 k l m n j 6 k l m n j 8 k l m n i Skip this question j k l m n

3. Two numbers ‘p’ and ‘q’ are randomly chosen from the set S = (1, 3, 5, 6, 7, 9). What is the product of all the possible values of p/q ?

j 5670 k l m n j 1 / 5670 k l m n j 45 / 126 k l m n j 1 k l m n j 1/2 k l m n i Skip this question j k l m n

4. The age of the four friends namely Abhishek, Aman, Deepak and Dilshan is (x – 2), (3x + 3), (x – 5) and (11 – x) respectively. The average age (in years) of the 4 mentioned friends is ‘y’. How many integral values of ‘y’ are possible?

j Infinite k l m n j 1 k l m n j 3 k l m n j 4 k l m n j 6 k l m n i Skip this question j k l m n

5. ABCDEF is a regular hexagon of side a. P is a point inside the hexagon. If PG, PH, PI, PJ, PK, PL are drawn perpendicular to the sides AB, BC, CD, DE, EF, FA, respectively, then the value of PG + PH + PI + PJ + PK + PL is equal to

j 6Sqrt(3)a k l m n j 3Sqrt(3)a k l m n

j 3a k l m n j 6a k l m n j None of these k l m n i Skip this question j k l m n

6. There are nine distinct numbers of which five numbers are positive and four numbers are negative. Three numbers are chosen at random and the product of these numbers is found. How many of these products are positive?

j 48 k l m n j 300 k l m n j 40 k l m n j 90 k l m n j None of these k l m n i Skip this question j k l m n Directions for Questions from 7 to 8: Answer the questions on the basis of the information given below. A natural number ‘N’ less than 1000 exists such that when the units digit of ‘N’ is erased, the resulting number is the factor of ‘N’

7. How many values of ‘N’ are possible such that ‘N’ is a three-digit number?

j 100 k l m n j 101 k l m n j 90 k l m n j 91 k l m n j None of these k l m n i Skip this question j k l m n

8. What is the sum of all the possible value of ‘N’ such that ‘N’ is a two-digit number more than 35?

j 942 k l m n j 968 k l m n j 934 k l m n j 994 k l m n j 912 k l m n i Skip this question j k l m n Directions for Questions from 9 to 10: Answer the questions on the basis of the information given below. A basket containing a certain number of oranges and apples costs Rs. 248. If 1 apple is added to the basket, the average cost per fruit in the basket increases by Rs. 2 and if 1 orange is added to the basket, the average cost per fruit in the basket decreases by Rs. 1. It is also known that if 2 apples are replaced with 2 oranges, the average cost per fruit in the basket becomes Rs. 16.

9. Find the average cost per fruit in the basket after an apple is replaced by an orange.

j Rs. 22.18 k l m n j Rs. 18.48 k l m n j Rs. 25.81 k l m n j Rs. 19.27 k l m n j 16.45 k l m n i Skip this question j k l m n

10. Find the total number of fruits in the basket initially.

j 10 k l m n j 11 k l m n

j 12 k l m n j 13 k l m n j 14 k l m n i Skip this question j k l m n

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