CAT1997 Related Question Answers
51. P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q?
52. The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.
53. If the roots $$x_1$$ and $$x_2$$ are the roots of the quadratic equation $$x^2 -2x+c=0$$ also satisfy the equation $$7x_2 - 4x_1 = 47$$, then which of the following is true?
54. The sum of the areas of two circles, which touch each other externally, is $$153\pi$$. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.
56.
A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.What is the maximum percentage of people who can watch all the three channels?
57.
A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.If 5% of people watched DD and CNN, 10% watched DD and BBC, then what percentage of people watched BBC and CNN only?
58.
A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.Referring to the previous question, what percentage of people watched all the three channels?
59. A man earns x% on the first Rs. 2,000 and y% on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from if his income is Rs. 5,000, find x%.
60. 
AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm, AC is 12 cm and BD is 9 cm, find the area of the quadrilateral ACBD.
61. P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is 3 less than two times R, find the value of R.
62.
For these questions the following functions have been defined.
$$la(x, y, z) = min (x+y, y+z)$$
$$le(x, y, z) = max(x -y, y-z)$$
$$ma (x, y, z) = \frac{1}{2} (le (x, y, z) + la (x, y, z))$$Given that $$x >y> z> 0$$. Which of the following is necessarily true?
63.
For these questions the following functions have been defined.
$$la(x, y, z) = min (x+y, y+z)$$
$$le(x, y, z) = max(x -y, y-z)$$
$$ma (x, y, z) = \frac{1}{2} (le (x, y, z) + la (x, y, z))$$What is the value of ma(10, 4, le((la10, 5, 3), 5, 3))?
64.
For these questions the following functions have been defined.
$$la(x, y, z) = min (x+y, y+z)$$
$$le(x, y, z) = max(x -y, y-z)$$
$$ma (x, y, z) = \frac{1}{2} (le (x, y, z) + la (x, y, z))$$For x=15, y=10 and z=9 , find the value of le(x, min(y, x-z), le(9, 8, ma(x, y, z)).
65. ABC is a three-digit number in which A > 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?
66. The adjoining figure shows a set of concentric squares. If the diagonal of the innermost square is 2 units, and if the distance between the corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and the seventh squares, counting from the innermost square. 
67. A, B and C are defined as follows.A=$$( 2.000004) \div ((2.000004)^2+ 4.000008)$$ ;B = $$(3.000003) \div ((3.000003)^2+9.000009)$$C= $$(4.000002) \div ((4.000002)^2 + 8.000004)$$ Which of the following is true about the values of the above three expressions?
68. The value of each of a set of coins varies as the square of its diameter, if its thickness remains constant, and it varies as the thickness, if the diameter remains constant. If the diameter of two coins are in the ratio 4 : 3, what should be the ratio of their thickness' be if the value of the first is four times that of the second?
69. In ABC, points P, Q and R are the mid-points of sides AB, BC and CA respectively. If area of ABC is 20 sq. units, find the area of PQR.
70. In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?
71.
The Weirdo Holiday Resort follows a particular system of holidays for its employees. People are given holidays on the days where the first letter of the day of the week is the same as the first letter of their names. All employees work at the same rate.Raja starts working on February 25(Sunday), 1996, and finishes the job on March 2, 1996. How much time would T and J take to finish the same job if both start on the same day as Raja?
72. Starting on February 25, 1996 (Sunday), if Raja had finished his job on April 2, 1996, when would T and S together likely to have completed the job, had they started on the same day as Raja?
73.
Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1hr less than his previous halt there. He then proceeds to Frankfurt.If his journey, including stoppage, is covered at an average speed of 180 mph, what is the distance between Frankfurt and India?
74. If X had started the return journey from India at 2.55 a.m. on the same day that he reached there, after how much time would he reach Frankfurt?
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