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**ganesh****Moderator**- Registered: 2005-06-28
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#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?

Character is who you are when no one is looking.

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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#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?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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Answers to #232 and #233:-

#232 is correct, #233 too is correct, but the answer expected was the ratio of the speeds, since the problem states that the two take the same time.

Character is who you are when no one is looking.

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**JaneFairfax****Member**- Registered: 2007-02-23
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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.

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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Answers to #234, #235, #236:

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

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#237. What is the sum of all the 4 digit numbers that can be formed by using the digits 2, 4, 6, and 8 if repetition is not allowed?

#238. What is the number of positive integers formed by using any number of digits from 0, 1, 2, 3, 4, and 5 but using each digit not more than once in each number?

#239. How many different number greater than 50,000 can be formed with the digits 1, 1, 5, 9, and 0?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#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?

Character is who you are when no one is looking.

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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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.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#243. The digit on the extreme right immediately before the zeros in

#244. Consider a traingle with vertices (41,0), (0,41), and (0,0) in the Cartesian plane. What is the number of points with integer coordinates inside the triangle excluding all points on the boundary?

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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That was a good attempt.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#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?

Character is who you are when no one is looking.

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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Answers to #245, and #246:-

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#248. If a man rides a bicycle at 10 km/hour, then he arrives at a certain place at 1 p.m. If he rides the bicycle at 15 km/hour, he reaches at 11 a.m. At what speed must he ride to get there at noon?

#249. A rectangular sheet of paper, when halved by folding it at the mid-point of its longer side, results in a rectangle whose longer side and shorter side are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2 units, what is the area of the smaller rectangle in square units?

#250. If n is an integer such that the sum of digits of n is 2, and

, what is the number of different values of n?Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#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?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#253. A young girl counted in the following manner with the fingers on her left hand. She started by calling the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, and the little finger 5; then reversed the direction, calling the ring finger 6, the middle finger 7, the index finger 8, the thumb 9, then back to the index finger for 10, middle finger for 11 and so on. She counted up to 1994. In which finger did she end?

#254. The set of Natural Numbers N is partitioned into subsets

What would be the sum of all the elements of the subset ?

*Last edited by ganesh (2009-02-01 01:01:01)*

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**JaneFairfax****Member**- Registered: 2007-02-23
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*Last edited by JaneFairfax (2009-02-01 01:14:36)*

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**ganesh****Moderator**- Registered: 2005-06-28
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Answer to #253:-

Absolutely right, JaneFairfax!

Answer to #254:-

The mistake has now been rectified. Thanks for pointing out! Please try again!!!

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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Answer to #254:

Perfect!

#255. What is the value of y if

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**JaneFairfax****Member**- Registered: 2007-02-23
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#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).

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