@pyashraj - Which edition of Arun Sharma r u having? Mine is 2nd edition....ans is given option (b) in my book..
okk..then the ans is wrong in my edition..Arun Sharma has rectified the mistake in the later editions...:) 😃
A natural number x leaves a remainder 1 when divided by p. The resultant quotient, when divided by q, leaves a remainder 2. The resultant quotient, when divided by r, leaves a remainder 3 and the quotient, thus obtained, is exactly divisible by 5. If p, q and r are all natural numbers, which of the following is the least possible value of x?
If a man lies 1 out of 4 times throws a dice and reports a 6. What is the probability of it actually being a six?
@saurav.kgp said:The difference between simple and compound interest on a sum of money at 5% per annum is Rs 25. What is the sum?(a) Rs 5,000 (b) Rs 10,000 (c) Rs 4,000 (d) Data insufficient.My ans came out to be option (d) but in Arun Sharma book ans is option (b).
Question ain't complete. :)
If this is what is given, then it should be Option D - Data Insufficient. We need to No. Of Years (Time Period) too. :splat:
@shattereddream said:A natural number x leaves a remainder 1 when divided by p. The resultant quotient, when divided by q, leaves a remainder 2. The resultant quotient, when divided by r, leaves a remainder 3 and the quotient, thus obtained, is exactly divisible by 5. If p, q and r are all natural numbers, which of the following is the least possible value of x?
We can easily find the General Term for the Number.
X = p [ q { r (5n) + 3 } + 2 ] + 1
p, q and r are natural numbers and we need to minimise X.
Taking p = 2 and not 1 because remainder with p = 1. Hence, p > 1.
Similarly for q and r.
So, putting n = 0 and p, q, r as 2, 3 and 4 respectively.
X = 2*[ 3*{ 4* (5*0) + 3 } + 2 ] + 1 = 2*[3*{3} + 2 ] + 1 = 23.
@shattereddream said:If a man lies 1 out of 4 times throws a dice and reports a 6. What is the probability of it actually being a six?
It actually being a Six => A Six turns up and the man speaks the Truth.
Now, Probability that man speaks the Truth = 1 - 1/4 = 3/4 [Answer]
@Estallar12 said:We can easily find the General Term for the Number.
@Estallar12 said:It actually being a Six => A Six turns up and the man speaks the Truth.Now, Probability that man speaks the Truth = 1 - 1/4 = 3/4 [Answer]
@bs0409 said:OA=5..............A starts from a point P on a circular track ,at 6:00 am and runs around the track in clockwise direction .At 6:15 am ,B starts from the same point P and runs around the track in counter clockwise direction and meets A for the first time at 7:09 am.If B started at 6 am then he would have met A for the first time at 7 am.If both A & B start from P at 7:00 am and run in the opposite direction,then find the time at which they would meet at the starting point for the first time?
12 noon
can someone please explain me chinese remainder thoerum. and how does it apply to the following question -
Ques-
(201* 202 * 203* 204* 246 * 247 * 248 * 249)^2 Last 2 digits????
Soln-
Soln-
No actually the last two digits are calculated when remainder with 100 is taken
what is 100?
100 = 4*25
since the above term is already divisible by 4, we can directly take the remainder by 25 because when you apply chinese remainder theorem, it boils down to the same
what is 100?
100 = 4*25
since the above term is already divisible by 4, we can directly take the remainder by 25 because when you apply chinese remainder theorem, it boils down to the same
@Logrhythm @Estallar12 please help!
@shattereddream said:A natural number x leaves a remainder 1 when divided by p. The resultant quotient, when divided by q, leaves a remainder 2. The resultant quotient, when divided by r, leaves a remainder 3 and the quotient, thus obtained, is exactly divisible by 5. If p, q and r are all natural numbers, which of the following is the least possible value of x?
23..?
What is the probablity of two persons
among the four having birthday in he same month?
A. 75%
B. 50%
C. 33%
@rayus said:can someone please explain me chinese remainder thoerum. and how does it apply to the following question -Ques-(201* 202 * 203* 204* 246 * 247 * 248 * 249)^2 Last 2 digits????Soln-No actually the last two digits are calculated when remainder with 100 is takenwhat is 100?100 = 4*25since the above term is already divisible by 4, we can directly take the remainder by 25 because when you apply chinese remainder theorem, it boils down to the same@Logrhythm@Estallar12 please help!
4N=25*M+6
so M is 2 and N is 16
remainder is 56
correct me if i am wrong :))
so M is 2 and N is 16
remainder is 56
correct me if i am wrong :))
@shattereddream said:A natural number x leaves a remainder 1 when divided by p. The resultant quotient, when divided by q, leaves a remainder 2. The resultant quotient, when divided by r, leaves a remainder 3 and the quotient, thus obtained, is exactly divisible by 5. If p, q and r are all natural numbers, which of the following is the least possible value of x?
23
@rayus said:can someone please explain me chinese remainder thoerum. and how does it apply to the following question -Ques-(201* 202 * 203* 204* 246 * 247 * 248 * 249)^2 Last 2 digits????Soln-No actually the last two digits are calculated when remainder with 100 is takenwhat is 100?100 = 4*25since the above term is already divisible by 4, we can directly take the remainder by 25 because when you apply chinese remainder theorem, it boils down to the same@Logrhythm@Estallar12 please help!
As you have asked Chinese Remainder, I'm explaining that with an Example. See -
You need to find last 2 digits of 37^1111
For last two digits, we find remainder by 100.
100 = 4*25
Chinese Remainder says that you can factorise the number (divisor) into 2 or more coprime factors and then find the remainder with them individually like this -
37^1111 mod 4 = 1^1111 mod 4 = 1.
37^1111 mod 25 = 12^1111 mod 25.
12^3 mod 25 = 3 => (12^3)^370 mod 25 = 12^1110 mod 25 = 3
=> 12^1111 mod 25 = 3*12 = 36 mod 25 = 11.
Now, We know 25*a + 11 = R = 4*b + 1
Equate the two and go for the lowest value when 25a + 11 = 4b + 1
So, a = 2 and b = 15. Remainder R = 61.
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P.S. This is Chinese Rem. in Layman Terms and not the actual theorem in words. Will Put up a post after this for CRT and Inverse CRT. :)
@ayushverma said:What is the probablity of two personsamong the four having birthday in he same month?A. 75%B. 50%C. 33%
It is 2 out of four so directly 1/2 = 50%.