Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

At what time do Ram and Shyam first meet each other?
(a) 10 a.m.
(b) 10:10 a.m.
(c) 10:20 a.m.
(d) 10:30 a.m.

At what time does Shyam overtake Ram?
(a) 10:20 a.m.
(b) 10:30 a.m.
(c) 10:40 a.m.
(d) 10:50 a.m.

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of the white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :
(a) 10
(b) 12
(c) 14
(d) 16

Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number 9 appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed?
a. 10,000
b. 2,430
c. 3,402
d. 3,006

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.
• A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR
project alone. is equal to the volunteers having additional involvement in the ER project.
• The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
• 17 volunteers are involved in the TR project. ,
• The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project
alone.
• Ten volunteers involved in the TR project are also involved in at least one more project.

Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:
(a) 1
(b) 3
(c) 4
(d) 5

Which of the following additional information would enable to find the exact number of volunteers involved in various projects?
(a) Twenty volunteers are involved in FR.
(b) Four volunteers are involved in all the three projects.
(c) Twenty three volunteers are involved in exactly one project.
(d) No need for any additional information.

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?
(a) The lowest number of volunteers is now in TR project.
(b) More volunteers are now in FR project as compared to ER project.
(c) More volunteers are now in TR project as compared to ER project.
(d) None of the above.

After the withdrawal of volunteers, as indicated in the above question, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?
(a) ER
(b) FR
(c) TR
(d) Cannot be determined

Five boys — A, B, C, D and E — went on a shopping trip. Before shopping, one boy had Rs. 400, one had Rs. 300, two boys had Rs. 200 each and one had Rs. 100. While shopping they did not lend or borrow from each other. After the shopping was over, it was observed that they were left with Rs. 165, Rs. 95, Rs. 70, Rs. 40 and Rs. 10, not necessarily in this order. Further, the following is known about the money they started with, they spent, or they were left with.
I. A started with more money than D.
II. B spent Rs. 15 more than C.
III. E started with more money than just one another person of the group.
IV. A spent the most but did not end with the least.
V. C started with 66.66% of the money that B started with.
VI. D spent the least and ended with more than A and C.
VII. E spent Rs. 35.

Who ended with the maximum amount of money?
a. A
b. B
c. C
d. E

How much money did A spend?
a. Rs. 205
b. Rs. 190
c. Rs. 35
d. Rs. 360

In ascending order of spending, E would rank at which position?
a. 1
b. 2
c. 4
d. 5

Who ended with Rs. 40?
a. A
b. B
c. C
d. D

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is
(a) 200

(b) 216

(c) 235

(d) 256

There are three cities: A, B and C. Each of these cities is connected with the other two cities by at least one direct road. If a traveller wants to go from one city (origin) to another city (destination), she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B (including those via C). Similarly, there are 23 routes from B to C (including those via A). How many roads are there from A to C directly?
a. 6
b. 3
c. 5
d. 10