Q.46.

[Manish Salian]

Hi,

Well! Well! Piyush is answering like anything!! After the answers to questions 49 and 48 have been revealed, here are the standings:

Anil: 24 points (-5 for Q.64 & Q.62 and -2 for Q.59)
Rishabh: 19 points (-2 for Q.64)
Minnat: 18 points (-2 for Q.62, -2 for Q.61)
Robin: 18 points
Abhinav: 11 points
Piyush: +5 (-2 for Q.62)
Ruchira: 3 points (-2 for Q.54)
Lajja: 2 points
Ankita: 2 points (-5 for Q.54)
Mohammed: 0 points (-2 for Q.52)
Nisha: 0 points (-5 for Q.63)

And here is today's question:

Q.46.

Ruchira and Shweta want to visit Ankita for Janmashthami celeberations! They all live on the same street yet neither Ruchira, not Shweta knows where Ankita lives. The houses on this street are numbered 1 to 99. Since the three of them love maths, they decide to figure out Ankita's house by asking a series of math questions. :confused:

On phone Ruchira asks Ankita, "Is your house number a perfect square?". She answers.
Then Ruchira asks, "Is it greater than 50?". She answers again.

Ruchira thinks she knows the house number, and decides to visit on her own. However, when she gets there she finds out that she is wrong! :mad:

This is not surprising, as Ankita decides to make the matters interesting by only answering the second question truthfully.

Shweta, unaware of Ruchira's conversation, asks Ankita two new questions. "Is your house number a perfect cube?". She answers.
Shweta then asks, "Is it greater than 25?". She answers again.

Shweta thinks she knows where Ankita lives, and decides to pay her a visit.
She too is mistaken as Ankita once again answered only the second question truthfully.

If I tell you that Ankita's house number is less than Ruchira's or Shweta's and the sum of the house numbers of the three of them is twice a perfect square, you should be able to figure out their house numbers.

Can you help me figure out their house numbers?

;) PS: In case you are confused, just call them up and ask the house number directly instead of beating around the bush!! ;)

I guess two days should be enough to figure out their house numbers. Deadline for this question is Thursday midnight.

Regards,

Manish sir

[PiyushTantia]

hello sir,

Their house no.s are 81, 54, 27
In the beginning 2 questions were asked by ruchira.
And the only possible answers to the 1st questions would be yes because in case the answer was no ruchira would’nt be confident enough to guess the right answer as the number of options to choose from would be many. But if her house no was a perfect square then ruchira would have proceeded to the next question. And again the answer to the next question would be yes because if it would be no then the options to choose from would be 1,4,9,16,25,36,49 i.e. 8 and more than 50 is only 2 i.e. 64 and 81

Similarly with shweta’s case the options to choose from is 2 i.e. 27 and 64.

since ankita's answer to the second question is correct it is greater than 50 and her house no. is definitely not a perfect square and a perfect cube

Both of them were confident to reach ankita’s house only in a case where they themselves stay in one of the two options.

Since both of them land up in the wrong house and the number common between them is 64 it can be safely assumed that they both landed up in house no, 64. that means they stay in house no. 81 and and 27 respectively.

Assuming ruchira and shweta they stay in 81 and 27 respectively and the sum of the three is twice a perfect square the only possibilities are 128, 162, 200, …. Out of these options the only option which is more than 50 and less than any one, we take it as it is less than 81 and more than 27, we can consider only 162 out of 128, 162 and 200

if we take 128 then her house no. is less than both of them and if we take 200 then her house no. is greater tyhan both of them.

So 81 + 27 + x = 2[81] which is a perfect square
i.e. x = 54

hurray

by trying other combinations all the conditions of the questions are not satisfied. So 54 is the house no. in which ankita stays.

is is correct sir, i'm sure it is.

[AnilkumarBDaga]

Back after a long time.....

BTW an amazing question.

The ages of Ruchira, Shweta and Ankita are 81, 64 and 55 respectively.

Solution:

According to Puish's explanation above - the answers to second questions posed by Ruchira and Shweta should be correct.

So the first set of questions gives us two possibilities of house number of Ruchira which are 64 and 81.

And the second set of questions gives us two possibilities of house number of Shweta which are 64 and 27.

So in all, as of now, there are two sets of answers for house numbers of Ruchira and Shweta. They are:

64 & 81 respectively
OR
27 & 64 respectively

We further know that:

The house number of Ankita is more than 50 - since the answers to both the second questions posed are correct and are Yes.

Also there is a condition that the house number of Ankita is lower than that of Ruchira as well as Shweta.

The above two simply removes the possibility of 64 and 27 being Ruchira and Shweta's house numbers.

Adding to the above the last condition being that the sum of their house numbers is double a perfect square.

Goes without saying that the number is not a perfect square or a cube.

Hence the only option is 55 for Ankita.

This should fetch me 5 points after a long time .......... hope so.

Thanks & Regards,
Anil Daga

[PiyushTantia]

Duh! i think u got it wrong this time. coz.. its clearly written ankita's house no. is less than Ruchira's or shweta's and not both of them.


.

[PiyushTantia]

Hello Sir,
i think you forgot to add points for my answer to the question for converting ONE to TWO.

.

[AnilkumarBDaga]

Hi Puish,

I got your point. But that seems to be the only possible answer.

If you agree that the two possibilities are 64 and 81 from first set of questions and 27 and 64 from second set of questions - apart from the one which you have mentioned.

We can make only three conditions out of it (one of which you have mentioned the other two being) 64 & 27 OR 81 and 64 respectively. The condition 64, 27 and any other number does not fulfill the condition of the sum of the 3 numbers being double the square and hence is ruled out.

BTW, according to the principles of set theory OR also includes AND. i.e Union includes Intersection.. To add to it Set theory is based on normal rational logic and is not derived from any other specific stream or body of knowledge. Hence what is true as per set theory should hold true in any set of rational circumstances. Isn't it Sir.

So in this case technically speaking we could be having two answers - and hence the answer could be cannot be determined as well.

For more information you can visit this link - http://en.wikipedia.org/wiki/Union_%28set_theory%29

Thanks & Regards,
Anil Daga

[PiyushTantia]

Hey Anil,

Firstly my name is Piyush and not Puis or sumthing.

Secondly even i agree wid you that there can be 2 or more possibilities but again i went wid the best possible answer. If there's an option of cannot be determined i wud have definitely gone wid that.

.

[AnilkumarBDaga]

Hi Piyush,

Regret the goof-up.

If you also agree that there are two possibilities then I do not know how can you claim your answer to be the best possible one.

(Because it is not a case of we having the answer options and "cannot be determined" is not present in any option).

So in this case "Cannot be determined" should be the mathematically and logically correct (no question of best or not) answer.

Thanks,
Anil Daga

[PiyushTantia]

Hey Anil,
Actually i din get completely what u wer trying to explain. So cant comment on it. But i'll stick to my answer and my explanation.

[IshanGupta]

i'd rather go with piyush's ans but thats based on my understanding of the word 'or' in the english language..according to my understanding, if we go with the set thoery, there would be no difference between putting and 'and' or an 'or' in the question.. if the rules of the set theory are to be applied well then anil's ans the way to go.. but i place my bets on piyush's ans..

[AnilkumarBDaga]

:confused: :confused: :confused:

Sir,

Please ignore my answer to this question for evaluation purposes. Would like to play extremely safe.

Thanks & Regards,
Anil Daga

[Manish Salian]

Hi all of you!!

Rather than having a spat on this forum...why not wait for the quiz master to give the answer?? :)

Look what it is has done?? :) Anil has lost an opportunity to win 5 points

Ruchira asks Ankita, "Is your house number a perfect square?". She answers. Then Ruchira asks again "Is it greater than 50?". She answers again. Ruchira thinks she now knows the house number of Ankita and decides to visit.

Since Ruchira thinks she has enough information, we can deduce that Ankita answered "Yes" to both the questions, as otherwise there is no way Ruchira would be certain of house number!!

For example, If Ankita's house number is not a perfect square there are multiple options possible. Also if her house number is a perfect square but not greater than 50, then again multiple options are possible. Only in case Ankita's house number is a perfect square and greater than 50, would Ruchira have two possibilities viz. 64 and 81. And one of them would be Ruchira's house number itself, hence she believes she is certain of Ankita's house number.

But when She got there, she finds out that she is wrong. This is not surprising, considering Ankita answered only the second question truthfully!!

So, Ankita's house number is greater than 50 but not a perfect square and Ruchira's house number is either 64 or 81.

By the same logic, Ankita must have answered "Yes" to both of Shweta's questions as then she would have only 2 possibilities viz. 27 and 64. And, Shweta should be living in one of them, so she would be ceratin about Ankita's house number.

But when She got there, she finds out that she is wrong. This is not surprising, considering Ankita answered only the second question truthfully!!

So, Ankita's house number is greater than 25 (already fogured out from Ruchiras questions) but not a perfect cube and Shweta's house number is either 27 or 64.

From this point onwards, our question ceases to be Maths and takes the form of Verbal Logic:

Case 1: Ankita's house number is less than both Ruchira's and Shweta's

Since Ankita's house number is greater than 50, and Shweta's is even more, she should live in house numer 64. Assuming Shweta and Ruchira are not room mates (I was wondering why didn't someone put this angle to the question?? :confused: ), Ruchira must stay in house number 81.

Now we apply the constraint that the sum of their house numbers is twice a perfect square, Ankita's house number turns out to be 55. (as 55+64+81 = 200).

The answer is: Ankita: 55, Ruchira: 81 and Shweta: 64.

Anil cracked this one, but withdrew his candidature at the last minute...so no points for him!


Case 2: Ankita's house number is less than Ruchira's or Shweta's, but not both

This throws up two possibilities: Either Ruchira is house number 64 and Shweta is house number 27 or Ruchira is house number 81 and Shweta is house number 27, but not both.

If in the light of this we need to apply the constraints that the sum of their house numbers is a perfect square then the first possibility throws up Ankita's house number as 37 (as 64 + 27 + 37 = 128), while the second one throws up Ankita's house number as 54 (as 81 + 27 + 54 = 162).

Ankita's house number cannot be 37 (as we know it is greater than 50), hence it has to be 54.

The answer is: Ankita: 54, Ruchira: 81 and Shweta: 27.

Piyush got this one right. He gets 5 points.

Anil I think you should have held on to your fort!! You don't get any points out here...

See these are not CAT questions, hence multiple answers are possible as long as they are logically correct!!

PS: Piyush, "Ankita's house number is less than Ruhira's or Shweta's" does not mean it cannot be less than both. There are clearly two possibilities as the two you have listed down.

Ishaan I don't know what to make of your answer, as you were only a supposrt player out here. Infact had you taken a neutral stand (and not stated 'I put my bet on Piyush's answer') you could have won 5 points as your's was actually the first correct answer. Presently I will not give you any points!!

Congratulations Anil for the movie tickets!

Regards,

Manish sir