Practice Test

Q1) Find the minimum value of the expression (p+1/p); p > 0. Show Answer

Q2) In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey's side, while solving a quadratic equation, committed the following mistakes:
(i) One of them made a mistake in the constant term and got the roots as 5 and 9.
(ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4.
But in the meantime, they realized that they are wrong and they managed to get it right jointly. Find the quadratic equation. Show Answer

Q3) The sum of a fraction and its reciprocal equals 85/18. Find the fraction. Show Answer

Q4) A journey between Mumbai and Pune (192 km apart) takes two hours less by a car than by a truck. Determine the average speed of the car if the average speed of the truck is 16 km/h less than the car. Show Answer

Q5) Sardar was asked to calculate the arithmetic mean of ten positive integers each of which has two digits. By mistake be interchanged the two digits in one of the ten integers. As a result, his answer for the arithmetic mean became 1.8 more than what it should have been. Based on this information, find the value of b - a : Show Answer

Q6) Every ten years, the Indian government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri:
Chota Hazri has 4,522 fewer males than Mota Hazri.
Mota Hazri 4,020 more females than males.
Chota Hazri has twice as many females as males.
Chota Hazri has 2,910 fewer females than Mota Hazri.
What is the total number of males in Chota Hazri? Show Answer

Q7) At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place, it would cost Rs. 164.50 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries? Show Answer

Q8) For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of seventh and sixth terms of this sequence is 517, what is tenth term of this sequence? Show Answer

Q9) Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He roots as (3, 2). What will be the exact roots of the original quadratic equation? Show Answer

Q10) A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of coins is 300. The amount is Rs. 960. If the number of 1 rupee coins and the number of 2 rupee coins are interchanged, the value comes down by Rs. 40. The total number of 5 rupee coins is: Show Answer

Q11) The maximum number of coins collected by any one of them cannot exceed : Show Answer

Q12) If A collected 54 coins, then the difference in the number of coins between the one who collected maximum number of coins and the one who collected the second highest number of coins must be at least : Show Answer

Q13) If A collected 54 coins and B collected two more coins than twice the number of coins collected by C, then the number of coins collected by B could be : Show Answer

Q14) Let x, y and z be distinct integers that are odd and positive. Which one of the following statements cannot be true? Show Answer

Q15) Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all elements of S. With how many consecutive zeros will the product end? Show Answer

Q16) After executing a sequence of three instructions, bottle A contains two liters of water. The first and the third of these instructions are shown below.
First instruction : FILL (C, A)
Third instruction : FILL (C< A)
Then, which of the following statements about the instructions is true? Show Answer

Q17) Consider the same sequence of three instructions and the same initial state mentioned above. Three more instructions are added at the end of the above sequence to have A contain 8 L of water. In this total sequence of six instructions, the fourth one is DRAIN (A). This is the only DRAIN instruction in the entire sequence. At the end of the execution of the above sequence, how much water is contained in C? Show Answer

Q18) What is the amount of water contained in B? Show Answer

Q19) Let p, q and r be distinct positive integers satisfying p < q < r and p + q + r = k. What is the smallest value of k that does not determine p, q, r uniquely? Show Answer

Q20) Give odd positive integers p, q, and r which of the following is not necessarily true? Show Answer

Q21) Given that f (a) = a (a + 1) (a + 2) where a = 1, 2, 3, .... Then find S = f (1) + f (2) + f (3) + .... + f (10)?
Show Answer