When a user conducts a search of a certain library database, the database returns the results as a list of items (books, magazines, etc.) that match the search criteria. The user can select from two settings to establish a maximum number of items –either 12 or 24–to be displayed at a time. If the list contains more items than the established maximum, the list will be displayed on multiple pages, with each page (with the possible exception of the last page) containing the established maximum number of items, and with each item in the list appearing on exactly one of the pages. The maximum established by the user does not affect the total number of items listed. For the list of n items returned by a particular search of the database, the number of items, X , displayed on the last page when the established maximum is 12 is different from the number of items, Y , displayed on the last page when the established maximum is 24. Select for X and for Y values that are jointly consistent with the information provided. Make only two selections, one in each column. ID: 700353

It's an elegant remainder question as highlighted by you. When N/12 it leaves a remainder of X, and when N/24, it leaves a remainder Y. The Key is they have provided that X and Y are different, that is only possible if N>12 and N 24, (since 24 = 2*12) will produce X and Y same. Now, plugging in values is the best way forward forward. For X=1, N becomes 13 and so does Y becomes 13 when N/24. But that's not in option. Ans for X =5, N becomes 17, And Y also becomes 17 when N/24. Bingo, that's the answer.

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When a user conducts a search of a certain library database, the data

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rishavbatra

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It's an elegant remainder question as highlighted by you.

When N/12 it leaves a remainder of X, and when N/24, it leaves a remainder Y. The Key is they have provided that X and Y are different, that is only possible if N>12 and N<24. Because, N<12 will be produce X and Y to be same. Similarly, N>24, (since 24 = 2*12) will produce X and Y same.

Now, plugging in values is the best way forward forward. For X=1, N becomes 13 and so does Y becomes 13 when N/24. But that's not in option.
Ans for X =5, N becomes 17, And Y also becomes 17 when N/24. Bingo, that's the answer.

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Firstly X and Y have to be different.

If n>24 or n <12, division by both 12 & 24 will leave same remainder hence it has to be between 12 & 24.

Start with checking for division by 12: the remainder when divided by 12 has to be by logic less than 12.
in case of remainder=1 => n = 13. 13 divided by 24 leaves remainder of 13 which is not in options. incorrect
in case of remainder=5 => n = 17. 17 divided by 24 leaves remainder of 17 which is in options. correct.
in case of remainder=7 => n = 19. 19 divided by 24 leaves remainder of 19 which is not in options. incorrect

Correct ans: X=5, Y=17