Brain Teasers

Jai Ganesh · 2009-02-01 02:06:19

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

#256. What is the remainder obtained when

is divided by 19?

JaneFairfax · 2009-02-01 02:36:25

Jai Ganesh · 2009-02-01 02:42:37

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!

JaneFairfax · 2009-02-01 02:47:54

Jai Ganesh · 2009-02-01 03:41:14

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 ?

JaneFairfax · 2009-02-01 04:18:56

Jai Ganesh · 2009-02-01 16:49:11

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

Jai Ganesh · 2009-02-02 03:59:01

#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?

Jai Ganesh · 2009-02-02 16:39:08

#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 ?

JaneFairfax · 2009-02-03 02:36:30

Jai Ganesh · 2009-02-03 04:12:45

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?

JaneFairfax · 2009-02-03 10:42:54

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

Jai Ganesh · 2009-02-03 16:30:36

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

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

Jai Ganesh · 2009-02-04 02:04:22

#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?

JaneFairfax · 2009-02-04 02:16:25

Jai Ganesh · 2009-02-04 02:31:33

Answer to #263:

Well done, JaneFairfax!!!

JaneFairfax · 2009-02-04 02:41:30

Jai Ganesh · 2009-02-04 02:46:04

Answers to #264 and #265:-
Both correct, JaneFairfax!

Jai Ganesh · 2009-02-04 02:59:45

#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

?

Jai Ganesh · 2009-02-04 03:31:34

#268. If

where n = 1,2,3,4, ...., then what is equal to?

JaneFairfax · 2009-02-04 03:57:51

Jai Ganesh · 2009-02-04 17:05:38

Answers to #266, and #268:-
Both answers are correct, JaneFairfax!
For #268, it would've sufficed if you'd given

.

JaneFairfax · 2009-02-04 22:03:14

Jai Ganesh · 2009-02-05 02:42:33

#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

, x is odd and is divisible by 3 but not by 7. How many elemnts does the set S contain?

JaneFairfax · 2009-02-05 09:44:38

Math Is Fun Forum

#351 2009-02-01 02:06:19

Re: Brain Teasers

#352 2009-02-01 02:36:25

Re: Brain Teasers

#353 2009-02-01 02:42:37

Re: Brain Teasers

#354 2009-02-01 02:47:54

Re: Brain Teasers

#355 2009-02-01 03:41:14

Re: Brain Teasers

#356 2009-02-01 04:18:56

Re: Brain Teasers

#357 2009-02-01 16:49:11

Re: Brain Teasers

#358 2009-02-02 03:59:01

Re: Brain Teasers

#359 2009-02-02 16:39:08

Re: Brain Teasers

#360 2009-02-03 02:36:30

Re: Brain Teasers

#361 2009-02-03 04:12:45

Re: Brain Teasers

#362 2009-02-03 10:42:54

Re: Brain Teasers

#363 2009-02-03 16:30:36

Re: Brain Teasers

#364 2009-02-04 02:04:22

Re: Brain Teasers

#365 2009-02-04 02:16:25

Re: Brain Teasers

#366 2009-02-04 02:31:33

Re: Brain Teasers

#367 2009-02-04 02:41:30

Re: Brain Teasers

#368 2009-02-04 02:46:04

Re: Brain Teasers

#369 2009-02-04 02:59:45

Re: Brain Teasers

#370 2009-02-04 03:31:34

Re: Brain Teasers

#371 2009-02-04 03:57:51

Re: Brain Teasers

#372 2009-02-04 17:05:38

Re: Brain Teasers

#373 2009-02-04 22:03:14

Re: Brain Teasers

#374 2009-02-05 02:42:33

Re: Brain Teasers

#375 2009-02-05 09:44:38

Re: Brain Teasers

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