Cat 2009 Quant Test 50

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Quant Test 50

1. Three men are gambling in Casino Royal. They start with sums of money in the ratio 7 : 6 : 5 and finish with sums of money in the ratio 6 : 5 : 4, in the same order as before. One of them won $ 12. How many dollars did he start with ? [The three men gambled amongst each other, only]

j $1080 k l m n j $420 k l m n j $210 k l m n j $108 k l m n j None of these k l m n i Skip this question j k l m n

2. Two boats start from the opposite banks of a river simultaneously. They meet at a distance of 410 m from one of the banks and continue sailing further till they reach the opposite banks. They take rest for 1 hr each and start off the return journey. Now they meet at a distance of 230 m from the other bank. Find the distance between the two banks. Note: (Assume that river water is almost still)

j 750 m k l m n j 840 m k l m n j 1100 m k l m n j 1200 m k l m n j 1000 m k l m n i Skip this question j k l m n

3. An ‘n’ digit number is formed using the digits 3, 4, 5 and 6 where repetition of the digits is allowed. If the number of all such possible ‘n’ digits numbers exceeds 10000, then what is the minimum value of n?

j 5 k l m n j 6 k l m n j 7 k l m n j 8 k l m n j 9 k l m n i Skip this question j k l m n

4. ABCD is a rectangle with AB and BC equal to 4 units and 4 3units respectively. On every side an equilateral triangle is drawn as shown in the figure. Points G, O, H and also points E, O, F are collinear. Find the area of the shaded region in square units.

j 12/sqrt3 k l m n

j 13/sqrt3 k l m n j 14/sqrt3 k l m n j 15/sqrt3 k l m n j 16/sqrt3 k l m n i Skip this question j k l m n

5. If a2 b 3 c = 256/27 then find the minimum value of (a + b + c), where a, b and c are positive real numbers.

j 3 k l m n j 4 k l m n j 6 k l m n j 9 k l m n j 12 k l m n i Skip this question j k l m n

6. What is the remainder when 3 6001 is divided by 13?

j 9 k l m n j 10 k l m n j 4 k l m n j 3 k l m n j 6 k l m n i Skip this question j k l m n

7. Three triangular pyramid shaped dice, each having the faces numbered 1, 2, 3 and 4 were rolled simultaneously. What is the probability that the sum of the numbers on the three faces appearing at the bottom is at least 8?

j 35/ 64 k l m n j 29/ 64 k l m n j 1 /2 k l m n j 33 /64 k l m n j 15 /32 k l m n i Skip this question j k l m n

8. Four digit numbers are formed using digits 3, 5, 6 and 8 without any repetition of digit in any number. Out of all such numbers formed, how many are divisible by 4 but neither divisible by 8 nor by 11?

j 2 k l m n j 3 k l m n j 4 k l m n j 5 k l m n j 6 k l m n i Skip this question j k l m n

9. A person used to save 20% of his income. Since his income has increased by 20%, he started giving 10% of the income to a charity. Now he is saving16(2/3)% of his net income (after donation to the charity). Find the percentage change in his “Saving percent”. [“Saving percent” is defined as the savings of the person as a percentage of his income]

j 10% k l m n j 15% k l m n j 22.22% k l m n j 25% k l m n

j 20% k l m n i Skip this question j k l m n

10. Himesh said to Reshamiya “My wife is six years older than your daughter who is one-sixth the age my great-grandfather lived upto, but your eldest son is eight years younger than your second wife.” Reshamiya said to Himesh “My second wife is eight-seventh times the age of your wife. My eldest son is one-sixth the age of your great-grand father would have been today, had he not died six years ago.” What would Himesh’s great-grand father’s age have been at the time of conversation?

j 84 years k l m n j 90 years k l m n j 96 years k l m n j 102 years k l m n j 108 years k l m n i Skip this question j k l m n

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