CAT Infinite DILR - Set 461 | Melody Itni Chocolaty Kyu Hai? | Caselet

Ajouté : 2026-05-26

[00:00:00]Hello everyone, welcome to aptitude jam.

[00:00:03]This is a caselet which would look easy initially but is a tricky one. It says that there are five kids who went to attend a birthday party and received two candies eclair's and melody as return gifts. They were standing in a line in the in some order. The child first in the queue got the least number of melodies. The number of melodies or declares received by each child is a natural number from 6 to 14 including both with each number appearing at least once. So we are given a set of conditions and we need to solve that who is standing at what position in the queue and received how many melodies and eclairs right. So let us first uh look at the numbers right the total number of candies that are distributed. So it says the number of melodies or declares received by each child is a natural number from 6 to 14. Right? First of all there are five children.

[00:01:02]So we have to distribute total 10 candies. 10 means five five kind of aes and five numbers for melodies. Right? So total 10 numbers and 6 to 14 the count is nine numbers. Right? So there will be one repeat number one repeat. Right? So first thing is let us calculate the grand total of the number of candies. So when you add 6 to 14 the sum is nx2 a + l right sum of arithmetic progression. So 9 by 2 6 + 14 is 20 that is 90. So 90 candies are there and see each number appearing at least once. So that means there is one repeat. So the number of total number of candies could be 96 to 104. Right? That is the grand total of the number of candies. It can be from 96 to 104 because one of these numbers will repeat. Right? Now the next statement is very crucial. It says the total number of melodies is two more than the total number of the melodies is plus two.

[00:02:10]Now what does this indirectly tell us?

[00:02:12]Right? If you're good at logic, you will directly get that the total number of candies is even. How? Suppose is odd in number. Okay, odd plus two is an odd number. So, melody will be odd in number and odd plus odd is even, right? Second thing, suppose a clear is even in number. In that case, melody will also be even in number, right? And even plus even is an even number. So if you are good at mathematical logic without making these two scenarios you would directly get that the total has to be a even number right. So we were discussing that the totals could be 96 to 104. So these are the possible totals. So one of the numbers will repeat and these will be the total numbers. That means the repeating number has to be 6 8 10 12 or 14. Now once we have done this let us start filling the table. So we'll make a table that there are five children. So five children the order because they came in order of standing in a queue. So one second child, third child, fourth child and the fifth child.

[00:03:21]And second thing is melodies plus total.

[00:03:29]Okay. So this is the table that we need to fill. And now let us look at the conditions. The first condition from here says Carlos was in the middle of the line. So this is Carlos and uh he received the maximum number of candidates.

[00:03:46]So Carlos is the maximum. How much is it? We do not know yet. Emma received eight more melodies than Eclipse. Now it becomes quite simple. Eight more melodies than Eclipse. So that means 14 melodies and six because the difference is eight, right?

[00:04:04]So melodies and eclus that is 14 and six for Emma right now.

[00:04:12]Next uh let us put it this way so that we can put for others as well.

[00:04:21]14 melodies and sixclair. So total is 20.

[00:04:26]Now the next statement says the child who was last in the queue received 20 candies in all while Anthony received 15 candies. So Anthony has received 15 candies.

[00:04:38]Now one common mistake that people who people solving questions is they make this as Emma. Okay. Many people would put Emma and say that Emma received 20 candies. It is not written that no two people can receive the same number of candies. Right? So unless that is stated that all people receive different number of candies, we cannot put Emma here because there can be some other person also who can receive 20 candies. We know Emma has received 20 candies but not necessarily she is last in the queue. So we will just put 20 and this here. Ben is after Anthony but before Diana in the queue, right? So we have Anthony, Ben, Diana like this, right? So there could be people in between also. The number of melodies Ben received is equal to number of eclairs Anthony received. Right? So we do not know how many candies Ben received. But we know that the number of melodies Ben received. So let us say this number is X. So that is equal to X. Right? That is the repeating number. We said that there is one repeat number. So this number is X which is the number of Eclipse received by Anthony and melodies received by Ben. Now the next step is we will find out the value of X. Right? Now we know that the repeat number is an even number right because of this logic which we used previously. Now suppose X is six then what will happen?

[00:06:09]Right? So if X is six so six and six but six is already used right? Mi has received six layers so six is not possible.

[00:06:24]If you put X equal to 8 that is possible right?

[00:06:30]Uh in that case this will be 7 that is fine. However, if we take 10, suppose if we take x equal to 10, then this number will be five, which is not possible because minimum is 6 and maximum is 14.

[00:06:42]The range is 6 to 14. So, that means the only possible value is x= 8. So, Emma receives seven melodies and eight declares. The total number of candies is 100 sorry 98 and melodies is two more than so. So, there will be 48 and 50 melodies. So 50 melodies and 48 that's what we have got the total total is 98 and we have got the candies with these two people right okay the next statement says Ben received one more candy than Diana and one less than Carlos okay so we have got 20 + 15 35 grand total is 98us 35 is 63 now Ben received one more than Dina but one less than Carlos Carlos Ben and Dina Suppose Diana receives X candies. Ben will receive X + 1. Carlos will receive X + 2. If you are good with mathematical logic, you know that these are three consecutive numbers. And you can directly get the values because see 35 is with Emma and Anthony, right? And we can just get these numbers as 20, 21, and 22. So now we know the number of candies with all of these people, right?

[00:07:58]So, Diana is 20, Ben is 21 and Carlos is 22. So, Carlos will put 22. Now, we still do not know who is this. It could be Diana also. It could be Emma as well, right? Okay. Next condition says that the child second in the queue received an even number of eclairs and an even number of melodies. Right? So, this is even and even number. So, this total has to be even. So that means this child received 20 candies. Okay. And are we missing any of the statements? Let us uh just revisit it. They were standing in a line in some order. The child first in the queue got the least number of melodies. Okay, least number of melodies. Now how to find the least number of melodies? We know that the numbers are repeating from 6 to 14 with eight repeating.

[00:08:52]Okay, so these are the numbers. Six is already taken. Six is eclair's right so these cannot be the number of melodies we know that Anthony received seven melodies so this child must be Anthony this child is Anthony who received seven melodies which is the least number of melodies so seven melodies declares total 15 so Anthony is done we know this is Anthony right now we have to place these people uh we know that uh the person Ben will come for Dina. Okay.

[00:09:27]And uh also there are two people who have got 20 candies. One is Dina and another is Diana as well as Emma have got 20 candies. Now if we put this as Dina okay which is not possible because Ben has to come before Diana. Okay, it is given that Ben will come before Dina.

[00:09:50]So this is Emma. And we also know that Emma has got 14 and six right? So that satisfies the even condition also. So 14 + 6 20. Now we are left with Ben and Nina. So this will be Ben and Nina. So number of candies is 21 and 20. Right?

[00:10:07]Now we need to fill the numbers. Okay.

[00:10:10]So the remaining numbers we need to fill. We know the value of X is 8. So that means 8 will come here and 13 will come here. That makes 21. Now we need to fill the remaining four values. Okay.

[00:10:23]Now what are the remaining four values?

[00:10:24]7 6 7 8 8. One value remaining is 9. 10 is remaining. 11 is remaining. 12 is remaining. Okay. They should add to 22.

[00:10:34]So 10 and 12 make 22. And 9 and 11 make 20. Okay, that is fine. Now let us calculate vertically also. This is 21 29. So these two should add to 21 and these should uh this is 14 and uh 27 these two add to 21. Okay. Now here we will get multiple possible cases.

[00:10:58]We know that this is going to be 9 + 11.

[00:11:01]So if we make it 9 + 11 in that case this number is going to be 12 and 10.

[00:11:08]Right? But if we reverse the numbers suppose we take 10 here then this number has to be 11 so that it becomes 50 and this number will be 12 and this number is going to be 9 in that case. So we will get multiple possible scenarios for uh Carlos and Dina. Okay. So this is the complete table that we will get after using all the conditions. Now let us look at the questions. What is the total number of candies distributed? that is 98.

[00:11:40]What is the median number of melodies distributed? Right? Now let us find the median. So first thing is seven is the lowest number. Eight is the second lowest. So if we go by the first scenario, the green one, the numbers are 7 8 9 12 and 14. So in this case the median is going to be 9.

[00:12:02]If we go by the second case, in that case the number is 7 8 10 11 14. So in that case the median number is 10.

[00:12:12]Right? So the number medium number is 9 or 10. Who received the highest number of? Highest number of is 13 which is received by how many melodies did Kala receive? So for Kala we cannot determine the number of melodies. So it could be 10 or 12 cannot be determined.

[00:12:32]If Diana received more melodies than eclares, okay, how many eclairs did the person last in the queue receive? So last in the queue is Diana itself. So if she received more melodies than so. So that means 11 melodies and nine eclairs.

[00:12:46]So it is asking how many the answer is going to be nine. So this was an interesting set. Hope you loved solving the set and loved the explanation of it.

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