CAT PyQs Details

Rahul starts on his journey at 5 pm at a constant speed so that he reaches his

destination at 11 pm the same day. However, on his way, he stops for 20 minutes,

and after that, increases his speed by 3 km per hour to reach on time. If he had

stopped for 10 minutes more, he would have had to increase his speed by 5 km per

hour to reach on time. His initial speed, in km per hour, was

The ratio of the number of coins in boxes A and B was 17:7. After 108 coins were

shifted from box A to box B, this ratio became 37:20. The number of coins that

needs to be shifted further from A to B, to make this ratio 1:1, is

If (x² + 1/x²) = 25 and x > 0, then the value of (x⁷ + 1/x⁷) is

If f(x) = (x² + 3x)(x² + 3x + 2), then the sum of all real roots of the equation √(f(x) + 1) = 9701, is

For a 4-digit number (greater than 1000), sum of the digits in the

thousands, hundreds, and tens places is 15. Sum of the digits in the

hundreds, tens, and units places is 16. Also, the digit in the tens place is

6 more than the digit in the units place. The difference between the

largest and smallest possible value of the number is

Teams A, B, and C consist of five, eight, and ten members, respectively, such that

every member within a team is equally productive. Working separately, teams A, B,

and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively.

Two members from team A, three members from team B, and one member from

team C together start the job, and the member from team C leaves after 23 hours.

The number of additional member(s) from team B, that would be required to replace

the member from team C, to finish the job in the next one hour, is

The sum of all the digits of the number (10⁵⁰ + 10²⁵ – 123), is

A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of

the lengths, in cm, of all three altitudes of the triangle ABC is

ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is

In ΔABC, AB = AC = 12 cm and D is a point on side BC such that AD = 8 cm. If AD is extended to a point E such that ∠ACB = ∠AEB, then the length, in cm, of AE is

Ankita walks from A to C through B, and runs back through the same route at a

speed that is 40% more than her walking speed. She takes exactly 3 hours 30

minutes to walk from B to C as well as to run from B to A. The total time, in minutes,

she would take to walk from A to B and run from B to C, is

In a class of 150 students, 75 students chose physics, 111 students

chose mathematics and 40 students chose chemistry. All students

chose at least one of the three subjects and at least one student chose

all three subjects. The number of students who chose both physics and

chemistry is equal to the number of students who chose both chemistry

and mathematics, and this is half the number of students who chose

both physics and mathematics. The maximum possible number of

students who chose physics but not mathematics, is

The monthly sales of a product from January to April were 120, 135, 150 and 165

units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed

marked price was used for the product in all the four months. Discounts of 20%, 10%

and 5% were given on the marked price per unit in January, February and March,

respectively, while no discounts were given in April. If the total profit from January to

April was Rs. 138825, then the marked price per unit, in rupees, was

Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A

certain volume is taken out from A and poured into B. After stirring, the same

volume is taken out from B and poured into A. If the resultant ratio of alcohol and

water in A is 15 : 4, then the volume, in litres, initially taken out from A is

In a school with 1500 students, each student chooses any one of the streams out of

science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800,

respectively. The total fee paid by all the students is Rs 15,50,000. If the number of

science students is not more than the number of arts students, then the maximum

possible number of science students in the school is

In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and

the sum of the first fourteen terms is 497, then the sum of first five terms is

The average salary of 5 managers and 25 engineers in a company is 60000 rupees.

If each of the managers received 20% salary increase while the salary of the

engineers remained unchanged, the average salary of all 30 employees would have

increased by 5%. The average salary, in rupees, of the engineers is

For real values of x, the range of the function f(x) = (2x - 3) / (2x² + 4x - 6) is

Let p, q and r be three natural numbers such that their sum is 900, and r is a perfect

square whose value lies between 150 and 500. If p is not less than 0.3q and not

more than 0.7q, then the sum of the maximum and minimum possible values of p is

The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An

empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes

are used simultaneously to fill up this empty tank, the time, in minutes, required to

fill up the entire tank completely is nearest to

The sum of all possible real values of x for which log_x-3(x² - 9) = log_x-3(x + 1) + 2, is

If 12^12x × 4^24x+12 × 5^2y = 8^4z × 20^12x × 243^3x-6, where x, y and z are natural numbers, then x + y + z equals