Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

Thanks for the information, JaneFairfax! I wasn't aware of it.

#256. What is the remainder obtained when

is divided by 19?It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

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!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

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 ?It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

Answer to #257.**Perfectly right, JaneFairfax! Very well done!!!**

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

#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?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

#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 ?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

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?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

#263. What are the values between which p can lie if

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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

#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?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

Answer to #263:

Well done, JaneFairfax!!!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

Answers to #264 and #265:-

Both correct, JaneFairfax!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

#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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

#268. If

where n = 1,2,3,4, ...., then what is equal to?Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

Answers to #266, and #268:-

Both answers are correct, JaneFairfax!

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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,769

#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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Offline