#234. Let S be a set of positive integers such that every elemnt n of S satisfies the conditions
(i)

(ii) every digit in n is odd.
How many elements of S are divisible by 3?

#235. A string of three English letters is formed as per the following rules:
(a) The first letter is any vowel.
(b) The second letter is m, n, or p.
(c) If the second letter is m, then the third letter is any vowel which is different from the first letter.
(d) If the second letter is n, the third letter is e or u.
(e) If the second letter is p, then the third letter is the same as the first letter.

Question(I) : How many strings of letters can possibly be formed using the above rules?
Question (II) : How many strings of letters can possibly be formed using the above rules such that the third letter of the string is e?

#236. Stephen and Martin run a race between two points A and B 5 kilometers apart. Stephen starts at 9 am at a speed of 5 km/hour, reaches B, and returns to A at the same speed. Martin starts at 9.45 am from A at a speed of 10 km/hour, reaches B and returns to A at the same speed.
Question (I) : At what time do Stephen and Martin first meet each other?
Question (II) : At what time does Martin overtake Stephen?

I would much appreciate it if you could state your question carefully. “How much faster than” does not sound to me like asking for a ratio.

Answers to #234, #235, #236:
Answers to #234, and #236 are correct, JaneFairfax. The first part of answer to #235 is correct too!

#240. P, Q, S, and R are points on the circumference of a circle of radis r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimter of the quadrilateral PQSR?

#241. Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets through telephonic conversations, so that eventually each person knows all the six secrets. A telephone call can be used to share a secret between one person and another only. None of the Frenchmen know English, and only one Englishman knows French. What is the minimum number of telephone calls required to be made for the above purpose?

#242. 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 white tiles is the same as the number of red tiles. What is the minimum number of white tiles required to fulfill these conditions?

Answers to #237, #240, #241, and #242:
Answers #237, #240, and #242 are correct, JaneFairfax!
Regarding #241, I get more number of calls required. Please check your answer.

#245. A milkman mixes 20 liters of water with 80 liters of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he has sold. What is the proportion of water to milk after the addition of water the second time?

#246. What is the total number of integer pairs (x,y) satisfying the equation x + y = xy?

#247. Each family in a locality has at most two adults, and no family has fewer than three children. Considering all the families together, there are more adults than boys, more boys than girls and more girls than the number of families. What is the minimum possible number of families in the locality?

Answers to #245, and #246:-

#251. Assume that an equal number of people are born on each day. Find the percentage (to three places after the decimal) of people whose birthday would fall on February 29?   

#252. 139 persons have enrolled for a tournament being cnducted on elimination basis. All players are paired for the first round, but since 139 is an odd number, one player gets a bye, which promotes him/her to the next round. This way, at every stage the participants are paired, with a bye to any player left over. If the schedule is planned such that  minimum number of games are played, what is the number of games that has to be played to decide the winner?

Last edited by JaneFairfax (2009-02-02 00:14:36)

#255. If you use \dfrac instead of just \frac, you can make it look better. And use \ldots for three baseline dots (called an ellipsis).