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questions
List of practice Questions
How many hours would P take to reach point B?
CAT - 1993
CAT
Quantitative Aptitude
Time, Speed and Distance
How many more hours would P take compared to Q to complete the journey?
CAT - 1993
CAT
Quantitative Aptitude
Time, Speed and Distance
P and Q start from opposite ends, with Q starting an hour later and at twice the speed. When P has covered 1/6th the distance, Q has also covered the same. Where do they meet?
CAT - 1993
CAT
Quantitative Aptitude
Algebra
The smallest number which when divided by 4, 6, or 7 leaves a remainder of 2 is
CAT - 1993
CAT
Quantitative Aptitude
Remainders and Factorials
A report has 20 sheets, each with 55 lines of 65 characters. It's retyped on pages of 65 lines and 70 characters per line. What is the percentage reduction in sheets?
CAT - 1993
CAT
Quantitative Aptitude
Percentage
From 5 points (4 vertices of a square + 1 intersection point of diagonals), how many triangles can be formed?
CAT - 1993
CAT
Quantitative Aptitude
Coordinate Geometry
If A = 2 and B = 4, what is the value of \(@(/(*(A, B), B), A)\)?
CAT - 1993
CAT
Quantitative Aptitude
Relations
In a locality of 100 families: 45 have radios, 75 have TVs, 25 have VCRs. 10 have all three. Every VCR owner has TV. 25 have radio only. How many families have only TV?
CAT - 1993
CAT
Quantitative Aptitude
Set Theory
Which expression gives the sum of A and B?
CAT - 1993
CAT
Quantitative Aptitude
Average
Which expression gives the sum of A, B, and C?
CAT - 1993
CAT
Quantitative Aptitude
Relations
A box contains 6 red, 7 green, and 5 blue balls (all distinct in size). What is the probability that the selected red ball is the smallest red ball?
CAT - 1993
CAT
Quantitative Aptitude
Probability
A group of workers starts a job. From Day 2 onward, 1 worker is removed each day. The job ends when the last worker is withdrawn. If all had worked full time, the work would’ve been done in 2/3 time. How many workers were initially in the group?
CAT - 1993
CAT
Quantitative Aptitude
Time and Work
A slab of ice 8 in × 11 in × 2 in is melted and recast into a cylinder of 8 in diameter. What is the length of the cylinder?
CAT - 1993
CAT
Quantitative Aptitude
Coordinate Geometry
ABC is an equilateral triangle with AB = AC, and B is 2 km north of A. A person walks from B parallel to AC, stops when directly east of C (point D). Where is D with respect to A?
CAT - 1993
CAT
Quantitative Aptitude
Coordinate Geometry
Find the maximum value of
\( y = \min\left(\frac{1}{2} - \frac{3x^2}{4}, \frac{5x^2}{4}\right) \) for \( 0<x<1 \)
CAT - 1993
CAT
Quantitative Aptitude
Functions
Let \( x<0.50 \), \( 0<y<1 \), \( z>1 \). What is the median of x, y, z?
CAT - 1993
CAT
Quantitative Aptitude
Number System
What is the total distance walked by the person (from B to D to E)?
CAT - 1993
CAT
Quantitative Aptitude
Coordinate Geometry
A five-digit number is formed using digits 1, 3, 5, 7, and 9 without repetition. What is the sum of all such possible numbers?
CAT - 1993
CAT
Quantitative Aptitude
Permutations and Combinations
How many positive integers less than or equal to 100 are not divisible by 2, 3, or 5?
CAT - 1993
CAT
Quantitative Aptitude
Number System
John bought 5 mangoes and 10 oranges for Rs. 40. He then returned 1 mango and got 2 oranges in exchange. What is the price of one orange?
CAT - 1993
CAT
Quantitative Aptitude
Algebra
Let \( u_0 = 0 \), and \( u_{n+1} = 2u_n + 1 \). What is the value of \( u_{10} \)? (nearest to)
CAT - 1993
CAT
Quantitative Aptitude
Relations
The function given by \( f(x) = |x|^3 \) is
CAT - 1993
CAT
Quantitative Aptitude
Relations
The sum of two odd functions
CAT - 1993
CAT
Quantitative Aptitude
Relations
85 children went to an amusement park with 3 rides. Each ride costs Re.1. 20 children took all 3 rides, 55 took at least 2 rides, and the total receipt was Rs.145. How many children did not take any rides?
CAT - 1993
CAT
Quantitative Aptitude
Algebra
Based on the same amusement park data, how many children took exactly one ride?
CAT - 1993
CAT
Quantitative Aptitude
Algebra
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