Practice Test

Q1) Rajat draws a 10 x 10 grid on the ground such that there are 100 identical squares numbered 1 to 100. If he has to place two identical stones on any two separate squares in the grid, how many distinct ways are possible ? Show Answer

Q2) Vaibhav wrote a certain number of positive prime numbers on a piece of paper. Vikram wrote down the product of all the possible triplets among those numbers. For every pair of numbers written by Vikram, Vishal wrote down the corresponding GCD. If 90 of the numbers written by Vishal were prime, how many numbers did Vaibhav write ? Show Answer

Q3) Two cars A and B start from two points P and Q respectively towards each other simultaneously. After travelling some distance, at a point R, car A develops engine trouble. It continues to travel at 2/3rd of its usual speed to meet car B at a point S where PR = QS. if the engine trouble had occurred after car A had travelled double the distance it would have met car B at a point T where ST = SQ / 9. Find the ratio of speeds of A and B. Show Answer

Q4) There are two water drums in my house whose volumes are in the ratio 1 : 5. Every day the smaller drum is filled first and then the same pipe is used to fill the bigger drum. Normally by the time I return from my college, i.e.,at 1 : 30 pm, the smaller drum would just be full. But today I returned a little early and started drawing water from the well with the help of a bucket, poured one-third into the smaller drum and the remaining into the bigger drum. I continued this till the smaller drum was filled. Immediately after that, I shifted the pipe into the bigger drum and went for lunch. Today if the bigger drum was filled in 12 min before its normal time, when was the smaller drum full ? Show Answer

Q5) Rekha drew a circle of radius 2 cm on a graph paper of grid 1 cm X 1 cm. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained was d sq cm. less than the correct value, then find the maximum possible value of d ? Show Answer

Q6) Rekha drew a circle of radius 2 cm on a graph paper of grid 1 cm X 1 cm. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained was d sq cm. less than the correct value, then find the minimum possible value of d ? Show Answer