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**ganesh****Moderator**- Registered: 2005-06-28
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Thanks for the information, JaneFairfax! I wasn't aware of it.

#256. What is the remainder obtained when

is divided by 19?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 #255, and #256:-

Answer to #256 is perfectly right!**Very well done!!!**

Answer to #255:- You made a minor mistake in the calculation. Please try again!

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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Answer to #255:-**Correct, JaneFairfax! Very good!!!**

#257. For a positive integer n, let

denote the product of the digits of n, and denote the sum of the digits of n. What is the number of integers between 10 and 1000 for which ?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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Answer to #257.**Perfectly right, JaneFairfax! Very well done!!!**

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#258. Four points A, B, C, and D lie on a straight line, such that AB = BC = CD, and the length of AB is 1 meter. An ant at A intends reaching a sugar particle at D. But there are insect repellants kept at points B and C. The ant would not go within 1 meter of the insect repellants. What is the minimum distance in meters that the ant must traverse in order to reach the sugar particle?

#259. In the XOY plane, what is the area of the reegion bounded by the graph of |x+y| + |x-y| = 4?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#260. Let n! = 1 x 2 x 3 x 4 x ....n for n≥1. If

then what is the remainder when p+2 is divided by ?

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 #258, #259, and #260:

#258 and #260 are correct!**Excellent!**

Answer to #259: Please check your answer. I get a different answer. I too shall check.

#261. The digits of a three-digit number A are written in the reverse order to form another three digit number B. If B>A, and B-A is perfectly divisible by 7, then which of the following is necessarily true?

(1) 100<A<299

(2) 106<A<305

(3) 112<A<311

(4) 118<A<317

#262. A new flag is to be designed with six vertical stripes using some or all of the colors yellow, blue, gree, and red. What is the number of ways this can be done such that no two adjacent stripes are of the same color?

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 think I may have visualized the wrong figure for #259.

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**ganesh****Moderator**- Registered: 2005-06-28
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#263. What are the values between which p can lie if

and f(0) and f(1) are of opposite signs?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#264. Let

where x is a real number. Then, what is the number of solution(s) the equation has?#265. In the figure below, the lines represent one-way roads allowing travel only Northwards or Westwards. Along how many distinct routes can a person from point A reach point B?

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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Answer to #263:

Well done, JaneFairfax!!!

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 #264 and #265:-

Both correct, JaneFairfax!

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#266. Let S be the set of five digit numbers formed with the digits 1, 2, 3, 4, and 5, using each digit exactly once such that exactly two odd positions are occupied by odd digits. What is the sum of the digits in the unit's place of the numbers in S?

#267. What is the value of x if

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**ganesh****Moderator**- Registered: 2005-06-28
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#268. If

where n = 1,2,3,4, ...., then what is equal to?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 #266, and #268:-

Both answers are correct, JaneFairfax!

For #268, it would've sufficed if you'd given

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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#269. In a sequence of seven consecutive integers, he average of the first five integers is n. What is the average of all the seven integers?

#270. One Red flag, three White flags, and two Blue flags are arranged in a line such that no two adjacent flags are of the same color and the flags at the two ends of the line are of different colors. In how many different ways can the flags be arranged?

#271. The integers 34041 and 32506 when divided by a three digit number n leave the same remainder. What is n?

#272. Let S be the set of integers x such that

Character is who you are when no one is looking.

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