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

Question

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

nisen20 · Accepted Answer

n=12a+x=24b+y

y-x=12(a-2b)

the difference between x and y is a multiple of 12.

zlishz · Answer

Let us categorize both searches as Search 1 and Search 2

In search 1: total items = n,
maximum # of items displayed on one page = 12 and # of items on the last page = X
Thus, it can be written as
n= 12 p + X (here, p = number of pages with the max. # of items displayed is 12)
This equation seems familiar as a remainder equation, where the question would have been : when n is divided by 12, the remainder is X and the quotient is p.
thus, we know that in remainder<divisor always, hence, here, X<12
That leaves us with option 1, 5 and 7 for X

n= 12p+1 => n = 13, 25, 37, 49, 61...
n= 12p+5 => n= 17, 29, 41, 53, 65...
n= 12p+7 => n= 19, 31, 43, 55, 67...

In search 2: total items = n,
maximum # of items displayed on one page = 24 and # of items on the last page = Y
Thus, it can be written as
n= 24q + Y (here, q = number of pages with the max. # of items displayed is 24)
In line with the reasoning above, we have Y<24
let's check for Y = 17 or 12
n= 24q+12 => 36, 60,...
n= 24q+17 => 41, 65,...

Thus, X= 5 and Y= 17.

nguyenpham1309 · Answer

1. In case the total number of items (n) > 24, the remainder of items on the last page will be the same for both the 12-item setting and the 24-item setting.
For example: n = 30,
- 12-item setting pages contain 12-12-6 items on each page
- 24-item setting pages contain 24-6 items. The number of items on the last page is the same (6).
"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." -> X and Y must be different.

2. In case the total number of items (n) <= 12, the remainder of items on the last (also the only) page will be the same and equal to n

3. Thus, the n range must be between 12 and 24, 12 < n <= 24.
-> Test the number for X to see where we can find 12 + X = Y, which also satisfies another given value
- 12 + 1 = 13 (don't have 13)
- 12 + 7 = 19 (don't have 19)
- 12 + 12 = 24 (don't have 24)
- 12 + 17 = 29 (fall into scenario 1)
- 12 + 5 = 17 => X = 5 and Y = 17

akshatv45 · Answer

Think about it, a number that is larger than 12 and smaller than 24 will give 2 extra pages in case of 12 and 1 extra page in case of 24. Only such number in the list is 17. So in case of 24 pages config, answer will be 17. But this number is just 5 more than 12. So answer in case of 12 page config will be 5.

Bismuth83 · Answer

1. Let's draw a diagram based on the problem.

2. We are asked to find what X and Y could be. Notice that 0 \( \leq \) X \( \leq \) 12 and 0 \( \leq \) Y \( \leq \) 24.

3. Both possible variants have n items in the list. This can be represented as 2 equations:

12(a - 1) + X = n and 24(b - 1) + Y = n

4. There is too little information to directly solve for X and Y, so we have to look at divisibility by 12. Notice that X will have the same remainder as n when divided by 12. The same can be said about Y. Therefore, X and Y have the same remainder.

5. Let's look at our answer options: 1, 5, 7, 12, 17. Their remainders, when dividing by 12, will be: 1, 5, 7, 0, 5. That means X and Y can only be 5 or 17. In addition, note that X doesn't equal Y and X \( \leq \) 12.

6. That means our answer will be X = 5 and Y = 17.

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saurvan · Answer

I understood the concept but why is my reasoning wrong? 
 
Lets say 29 Total results are there. If divided by 12 or 24 the remainder is 5. Hence I chose x=y=5

Ilanchezhiyan · Answer

i made the same mistake. it is mentioned that x and y can not be same.

kirallight · Answer

My approach is this. Any number divisible by 24 is divisible by 12.
Any number Y that is on last page (which means that it is the remainder when divided by 24) which is less than 12 will be the same as X (since 12 divides 24) and it is stated that X and Y are not equal. That leaves us with 2 options for 24 -> 12 and 17.

Let's take 12 for Y, that means that the same n when divided by 12 should leave 0 for X (that options is not present), so obvious answer is 17 for Y and 17-12 = 5 = X.
Let us check. When 17a is divided by 24 , that leaves remainder of 17 (unless a is 24 or multiple of 24 which is not the case).
Not 17a when divided by 12 gives us 5 = X

So, X=5 and Y=17

Nairobisha · Answer

I understood that differece of x and y is a multiple of 12. But among x and y, which is the maximum? How do we know if x=5 and y=17 or x=17 and y=5? Can someone please help? Thanks

Bunuel · Answer

Ask yourself, can x be 17?

bb · Answer

X appears on the page with 12 items. Would be hard to fit 17 into a 12-item list. This is the condition written in the question.

Armaan209 · Answer

Let a be the number of full pages in 12 setting 
a/2 would be the number of full pages in 24 setting
 hence, 12(A) + X = 24(A/2) + y 
> y-x = 6(a)

So y-x will be either 6, 12 , 18, ......
with y=17 and x =5 this satisifes

Can,Will · Answer

i am not able to understand what is being asked in the question.
got confuse "select for  X  and for  Y  values that are jointly consistent with the information provided. Make only two selections, one in each column"
what does mean by "jointly consistent" since x and y are different (given)

Armaan209 · Answer

It is a remainders concept question

D3N0 · Answer

you can never have a remainder greater than the divisor.
that's why you can't have 17 as a remainder in search of 12 results per page (divisor is 12) so it has to be with the 24
 
 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.

D3N0 · Answer

Ans: X = 5 and Y = 17

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 .

We have two divisors 12 and 24 of n and we know that the X is different than Y. We need to find the X and Y combo
we can take the options as value of X and find the corresponding Y: (easiest way in my opinion)

if X = 1 --> n = 13 --> Y = 13 (not in options)
if X = 5 --> n = 17 --> Y = 17 (In option- Right combo)  Answer

We can solve the other options too (for fun only)
if X = 7 --> n = 19 --> Y = 19 (not in options)
If X = 12 --> n = 0 --> Y = 24 (not in options)
X = 17 is not possible. (Reminder will always be <12 for X)

D3N0 · Answer

This is a good way of thinking, and I think it allows me to think more logically.

Sijojohnn · Answer

because the number is the same n the 
 12k + x equal 24 + y

then we get k- 2m = y-x divided by 12 
so x or y could be either 17 or 12 
because more than 12 is divided x cannot be 17 and its 5 and y =17

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