Data Sufficiency

In a library, N books are placed on seven shelves averagely, and one is remained on the desk. what is N ?
1). If they are place on nine shelves averagely, seven books will be remained.
2). If they are place on four shelves averagely, three books will be remained.

I got a number i.e. 43 that satisfies both the statements but please tell me is there any other number that satisfies the above statements and how to get all those numbers in 2mins.. coz the final answer depends on the numbers if there are any except 43.. Please lemme know the easier method to do it..

IMO E
N books are placed on seven shelves averagely, and one is remained on the desk
so numbers can be 8,15,22,29 and so on
If they are place on nine shelves averagely, seven books will be remained
numbers can be 16,25...and so on

If they are place on four shelves averagely, three books will be remained.
numbers are 7,11..and so on
combining all
8+7n1=16+9n2=7+4n3
can't find the values of n1,n2 and n3

tohellandback wrote:IMO E
N books are placed on seven shelves averagely, and one is remained on the desk
so numbers can be 8,15,22,29 and so on
If they are place on nine shelves averagely, seven books will be remained
numbers can be 16,25...and so on

If they are place on four shelves averagely, three books will be remained.
numbers are 7,11..and so on
combining all
8+7n1=16+9n2=7+4n3
can't find the values of n1,n2 and n3

hmm..I actually don't understand your logic. Can you please elaborate?

Thanks,
kanha81

ketkoag wrote:In a library, N books are placed on seven shelves averagely, and one is remained on the desk. what is N ?
1). If they are place on nine shelves averagely, seven books will be remained.
2). If they are place on four shelves averagely, three books will be remained.

First, let me say that this is a horribly worded question - where's it from? "Averagely" isn't even a word and the grammar is horrible.

So, either you should never trust questions from this source or you should do a better job transcribing the questions that you post.

However, we can use our decoder ring to figure out how the question should have read:

N books are equally distributed among 7 shelves in a library. If 1 book remains on the desk, what's the value of N?

Step 1 of the Kaplan method for DS: focus on the question stem.

We want to know exacly how many books we started with. We're told that N/7 has a remainder of 1. So, we know that N=1, 8, 15, 22, ...

Step 2 of the Kaplan method for DS: consider each statement alone, in conjuction with the stem.

(1) N/9 has a remainder of 7. So, N=7, 16, 25, ...

Is this sufficient to determine the value of N? No - since we have no maximum value, there will be an infinite number of points of intersection between the two sets we have for N.

For example, N could be 43. However, N could also be 106, 169, ... (since 7*9=63, you can just add 63 to each number to find the next possible solution).

We can get more than one value for N: insufficient.

(2) N/4 has a remainder of 3.

Using the exact same logic as above, there will be an inifinite number of possible values for N: insufficient.

Step 3 of the Kaplan method for DS: if necessary, combine the statements.

Now we have 3 facts about N:

N/7 has remainder 1, N/9 has remainder 7, N/4 has remainder 3.

However, using the exact same logic as we did in (1) above, there will be an infinite number of possible values for N that satisfy these conditions: insufficient, choose (E).

ketkoag wrote:I got a number i.e. 43 that satisfies both the statements but please tell me is there any other number that satisfies the above statements and how to get all those numbers in 2mins.. coz the final answer depends on the numbers if there are any except 43.. Please lemme know the easier method to do it.

Here's what you should have been thinking: I got a number that works. Out of all the numbers in the universe, is there reason for me to believe that no other numbers will also work?

Knowing that factors/multiples/remainders recur in infinite patterns, the answer to that question should have been "no, there isn't - lots of numbers will work". Once you figure that out, there's no need to actually go looking for another number - just knowing that many exist is enough reason to choose (E).

Remember - our goal in DS is to do as little work as possible. On value questions, we don't need to actually calculate the value(s), we just need to recognize if there's exactly one value or multiple values.

thanks for the great explanation..
sure, i'll not use this source in future.
i got this question from the internet and posted it as it is..
i'll definitely transcribe any weird structure before posting it in future.
thanks again..