@jain4444 said:How many 4-term geometric sequences have all four terms positive integers less than or equal to 100?
Distinct terms?
regards
scrabbler
regards
scrabbler
@scrabbler said:Hear, hear ___/\___ and let me add ATDH also to that list, since he is evidently too modest to do so himself
why so, nobody however great, is above learning :/
@scrabbler said:I have a feeling this will be white since there is an odd number of white ones initially.... whites can go out only when "both are white" so the number of whites can reduce by 2 at a time only and ek to bach hi jayega?regardsscrabbler
i go for WHITE too. one odd white ball saves the day -.-
@ankita14 said:why so, nobody however great, is above learning :/i go for WHITE too. one odd white ball saves the day -.-
jake K ka prepare karo, yaha toh hume practice karne ki zaroorat hai.... namak chidakne aa gayi hamare ghao pe?? 
PS: yeah i also think white is right...
adding a question so that this post is not deemed as spam
Q) anu writes integers from 1 to 9 in his notebook. if he writes m 8's and n 9's more, average becomes 7.3. What is the value of m + n ?
@pratskool said:jake K ka prepare karo, yaha toh hume practice karne ki zaroorat hai.... namak chidakne aa gayi hamare ghao pe??
Woh prep to idhar bhi ho sakta hai!
@pratskool said:PS: yeah i also think white is right...adding a question so that this post is not deemed as spamQ) anu writes integers from 1 to 9 in his notebook. if he writes m 8's and n 9's more, average becomes 7.3. What is the value of m + n ?
21....(6 9s and 15 8s) Adding an answer so that this post is not deemed as spam
regards
scrabbler
@ankita14 said:why so, nobody however great, is above learning :/
request you to read my statement once more please. I am no way stating or implying that anyone is above learning. What I referred above is, a culture of politeness in use words and respect for those who we know for sure are really good and have been so helpful to many on the forum.
I have learnt many things on this forum and I have shared a few things as well which others have appreciated, but in no case I will ever say that "let me teach you...xxxx". Politeness is a matter of personal choice and cannot be enforced but if I feel something that is not polite on the forum I will definitely point it atleast once.
you are entitled to your opinion if such a statement is impolite or not I am no one to question it or comment on it.
@ankita14 said:i go for WHITE too. one odd white ball saves the day -.-
@scrabbler @pratskool white is the correct answer.
ATDH
@anytomdickandhary said:request you to read my statement once more please. I am no way stating or implying that anyone is above learning. What I referred above is, a culture of politeness in use words and respect for those who we know for sure are really good and have been so helpful to many on the forum. I have learnt many things on this forum and I have shared a few things as well which others have appreciated, but in no case I will ever say that "let me teach you...xxxx". Politeness is a matter of personal choice and cannot be enforced but if I feel something that is not polite on the forum I will definitely point it atleast once.you are entitled to your opinion if such a statement is impolite or not I am no one to question it or comment on it. @scrabbler@pratskool white is the correct answer.ATDH
Well I found the statement funny rather than impolite 
Anyway, I see your point. Peace. :D
Anyway, I see your point. Peace. :D@pratskool said:jake K ka prepare karo, yaha toh hume practice karne ki zaroorat hai.... namak chidakne aa gayi hamare ghao pe??PS: yeah i also think white is right...adding a question so that this post is not deemed as spamQ) anu writes integers from 1 to 9 in his notebook. if he writes m 8's and n 9's more, average becomes 7.3. What is the value of m + n ?
15+6=21
@anytomdickandhary said:@bodhi_vriksha it is we who learn from the Chillfactor and Jain Bhai..... i think we should be very careful before we decide that we can claim that we can teach these guys. I have been on this forum for just less than 10 years and I can say that Chillfactor is undoubtedly the most talented on the Quant forum, anyone who knows him just bows down to him for what we all have learned from him. Jain Bhai too is held in very high regards on the forum.Not really blaming you for anything but just pointing it to you in case you are not aware, so that we can be more respectful to the members who are respected by one and all.ATDH.
Dear ATDH
The post was not derogatory in any respect. And I know all of the persons mentioned very well. So rest assured that they will remain as honorable as they are. :)
Knowledge and Learning is a continuous effort. I, personally feel that even after teaching for years, am learning daily from my students. And in fact many of my students are teaching in various big institutes.
So just take it easy and let's learn together. :)
Team BV - Kamal Lohia
The post was not derogatory in any respect. And I know all of the persons mentioned very well. So rest assured that they will remain as honorable as they are. :)
Knowledge and Learning is a continuous effort. I, personally feel that even after teaching for years, am learning daily from my students. And in fact many of my students are teaching in various big institutes.
So just take it easy and let's learn together. :)
Team BV - Kamal Lohia
@jain4444 said:
How many 4-term geometric sequences have all four terms positive integers less than or equal to 100?
Assuming 4 distinct terms
a, 2a, 4a, 8a, a can vary from 1 to 12
a, 3a, 9a, 27a, a can vary from 1 to 3
a, 4a, 16a, 64a, a can only be 1
a, 3a/2, 9a/4, 27a/8, a has to be a multiple of 8 and less than 800/27 = 29, so possible values are 8, 16, 24
a, 4a/3, 16a/9, 64a/27, a can only be 27
So, 20 such GP's
@pratskool said:
Q) anu writes integers from 1 to 9 in his notebook. if he writes m 8's and n 9's more, average becomes 7.3. What is the value of m + n ?
45 + 8m + 9n = 7.3(m + n + 9)
0.7m + 1.7n = 20.7
7m + 17n = 207
(m, n) = (15, 6) is the only solution
2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
can somebody help me out on how to solve this question..
@iLoveTorres said:can somebody help me out on how to solve this question..
A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
Increased by 50% => multiplied by 3/2. So power of 3 increases by 1 and of 2 decreases by 1. Still same total factors => it could probably be of the form 2^(a+1)*3^a
When decreased by 25% i.e. divided by 2^2 -t becomes 2^(a-1)*3^a
Number of factors decreases by 33.33% => (a+2)*(a+1) = 3/2 * (a)*(a+1) which gives us a = 4.
Hence 2^5*3^4 will work.
Edit: Sorry it got posted prematurely!
regards
scrabbler
Increased by 50% => multiplied by 3/2. So power of 3 increases by 1 and of 2 decreases by 1. Still same total factors => it could probably be of the form 2^(a+1)*3^a
When decreased by 25% i.e. divided by 2^2 -t becomes 2^(a-1)*3^a
Number of factors decreases by 33.33% => (a+2)*(a+1) = 3/2 * (a)*(a+1) which gives us a = 4.
Hence 2^5*3^4 will work.
Edit: Sorry it got posted prematurely!
regards
scrabbler
@scrabbler said:
Woh prep to idhar bhi ho sakta hai!21....(6 9s and 15 8s) Adding an answer so that this post is not deemed as spamregardsscrabbler
@Dexian said:15+6=21
@chillfactor said:
45 + 8m + 9n = 7.3(m + n + 9)0.7m + 1.7n = 20.77m + 17n = 207(m, n) = (15, 6) is the only solution
Right !!
@scrabbler said:Woh prep to idhar bhi ho sakta hai!21....(6 9s and 15 8s) Adding an answer so that this post is not deemed as spamregardsscrabbler
Sir elaborate on how you arrived at this too 😃
@pratskool said:Q) anu writes integers from 1 to 9 in his notebook. if he writes m 8's and n 9's more, average becomes 7.3. What is the value of m + n ?
@iLoveTorres said:Sir elaborate on how you arrived at this too
Bear with me, it is a little long (much faster to actually do, but to write with explanations takes time and space....karne mein 75% orally ho gaya tha!)
Currently we have 9 numbers totalling 45, and the numbers added have to have an average between 8 and 9).
If the average has to come 7.3, the total number of numbers should be a multiple of 10.
Hence it could be:
10 numbers total 73 (=> added 1 number totalling 28 => average 28 => not possible)
OR
20 numbers total 146 (=> added 11 numbers totalling 101 => average 9.xx => not possible)
OR
30 numbers total 219 (=> added 21 numbers totalling 174 => average 8.xx => possible)
OR
40 numbers total 292 (=> added 31 numbers totalling 247 => average 7.xx => not possible)
So only case is adding 21 numbers (either 8 or 9) totalling 174. Now if all of them had been "8"s total would be 168, each "9" gives an extra 1 so for 174 there must be 6 "9"s and the remaining 15 "8"s. (Not that we need to calculate this as the question only asks the total of m + n which is 21)
regards
scrabbler
@scrabbler said:Bear with me it is a little long (much faster to actually do, but to write with explanations takes time and space....karne mein 75% orally ho gaya tha!)Currently we have 9 numbers totalling 45, and the numbers added have to have an average between 8 and 9).If the average has to come 7.3, the total number of numbers should be a multiple of 10.Hence it could be:10 numbers total 73 (=> added 1 number totalling 28 => average 28 => not possible)OR20 numbers total 146 (=> added 11 numbers totalling 101 => average 9.xx => not possible)OR30 numbers total 219 (=> added 21 numbers totalling 174 => average 8.xx => possible)OR40 numbers total 292 (=> added 31 numbers totalling 247 => average 7.xx => not possible)So only case is adding 21 numbers (either 8 or 9) totalling 174. Now if all of them had been "8"s total would be 168, each "9" gives an extra 1 so for 174 there must be 6 "9"s and the remaining 15 "8"s. (Not that we need to calculate this as the question only asks the total of m + n which is 21)regardsscrabbler
what if the average was given as 7.975... then how do you decide what should be the total number?
@iLoveTorres said:what if the average was given as 7.975... then how do you decide what should be the total number?
Multiple of 40 as the "least count" is 25/1000 = 1/40 😃
But aisa nahin denge...don't worry. They are not being sadistic just for the sake of it (ok, not entirely!) 😁
regards
scrabbler
But aisa nahin denge...don't worry. They are not being sadistic just for the sake of it (ok, not entirely!) 😁
regards
scrabbler
@scrabbler said:Multiple of 40 as the "least count" is 25/1000 = 1/40 But aisa nahin denge...don't worry. They are not being sadistic just for the sake of it (ok, not entirely!) regardsscrabbler
yeh least count ka funda kya hai? pls elaborate
@scrabbler said:A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
Increased by 50% => multiplied by 3/2. So power of 3 increases by 1 and of 2 decreases by 1. Still same total factors => it could probably be of the form 2^(a+1)*3^a
When decreased by 25% i.e. divided by 2^2 -t becomes 2^(a-1)*3^a
Number of factors decreases by 33.33% => (a+2)*(a+1) = 3/2 * (a)*(a+1) which gives us a = 4.
Hence 2^5*3^4 will work.
Edit: Sorry it got posted prematurely!regardsscrabbler
is question me min value ka kya significance hai...
what will be the nxt number of this format..
@iLoveTorres said:yeh least count ka funda kya hai? pls elaborate
Arre....couldn't find an appropriate word for it so used "Least Count" what I meant was....aila how to explain....
OK....different approach....let's start from the top again.
Suppose we had average 7.6 we could write it as 76 / 10 = 38 / 5. Can't reduce further so can be sure total objects = 5n
If 7.7 we write 77/10 which cannot be further reduced so total objects = 10n
If 7.82 then 782 / 100 = 391 / 50 cannot reduce, so 50n
If 7.975 then 7975/1000 = 319/40 cannot reduce, so 40n
Making sense I hope?
regards
scrabbler
what I meant was....aila how to explain....OK....different approach....let's start from the top again.
Suppose we had average 7.6 we could write it as 76 / 10 = 38 / 5. Can't reduce further so can be sure total objects = 5n
If 7.7 we write 77/10 which cannot be further reduced so total objects = 10n
If 7.82 then 782 / 100 = 391 / 50 cannot reduce, so 50n
If 7.975 then 7975/1000 = 319/40 cannot reduce, so 40n
Making sense I hope?
regards
scrabbler
@Dexian said:is question me min value ka kya significance hai...what will be the nxt number of this format..
That is beyond the scope of this solver...I guess 2^5*3^4*5^1 but wouldn't swear to it :)
@chillfactor Sir @anytomdickandhary Sir ....please field this one....
regards
scrabbler
@chillfactor Sir @anytomdickandhary Sir ....please field this one....
regards
scrabbler