Question Bank (3)  Quant Mixed Bag  Shashank Prabhu, CAT 100 Percentiler

2 + 4 + 6 ... + 2k = 2 (1 + 2 + ... k)
= 2k (k + 1)/2
= k (k + 1)
= 79 * 80.
So, k = 79, 2k=158 and because it is an odd number greater than 158, it will be 159

Q94) A yearly payment to the servant is Rs. 90 plus one turban. The servant leaves the job after 9 months and receives Rs. 65 and a turban. Then find the price of the turban.
[OA: 10]

Q95) Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed of 4 km/hr. While the other man travelled with varying speed as follows: in the first hour his speed was 2 km/hr, in the second hour it was 2.5 km/hr, in the third hour it was 3 km/hr, and so on. Which of the following will be true about the meeting point when they meet each other?
a. Meet after 7 hrs
b. Meet after 10 hrs
c. Meet at 35 km from A
d. Meet midway between A and B[OA: Option d]

Have to check the meeting point. Can do it using AP/sum of integers but i guess manual calculation would be far quicker in this context. In the first hour, 6 km, in the second hour, 6.5 km, third hour, 7 km and so on.
6 + 6.5 + 7 + 7.5 + 8 + 8.5 + 9 + 9.5 + 10.
They meet after 9 hours. A would have covered 36 km in 9 hours, so B would have covered the same distance as well.

Q96) Three wheels can complete 60, 36 and 24 revolutions per minute. There is a red spot on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again?
[OA: 5 seconds]

LCM (60/60,60/36,60/24)
LCM (1,5/3,5/2) = 5 seconds

Q97) One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survive and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?
[OA: 1 million]

Q98) Three circles, each of radius 20, have centres at P, Q and R. Further, AB = 5, CD = 10 and EF = 12. What is the perimeter of ΔPQR?
[OA: 93]

Q99) (BE)^2 = MPB, where B, E, M and P are distinct integers. Then M = ?
[OA: 3]

Q100) A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.
[OA: 5]