The average (arithmetic mean) cost per book for the 12 books on a cert

Question

The average (arithmetic mean) cost per book for the 12 books on a certain table is k dollars. If a book that costs 18 dollars is removed from the table and replaced by a book that costs 42 dollars, then in terms of k, what will be the average cost per book, in dollars, for the books in the table?

A) k+2

B) k - 2

C) 12+ 24/k

D) 12- 24/k

E) 12k-6

A) k+2

B) k - 2

C) 12+ 24/k

D) 12- 24/k

E) 12k-6

rudra316 · Accepted Answer

Average = \frac{Total Cost}{number of books} 
Let S be the sum of costs of all the books.
 K = \frac{S}{12}

One book costing 18 is replaced with one costing 42.
Sum of costs = (S-18) + 42 = S+24

Average =  \frac{(S+24)}{12} 
=  \frac{S}{12}  +2
=  K+2

law258 · Answer

Logically, if we replace a book that was $18 with a book that was $42 --> the difference between the two is 24; this number is "absorbed" by the total number of books (i.e. 12), so each book's average goes up by 2

Abhishek009 · Answer

Total cost of 12 books = 12k

Total cost of books now = 12k - 18 + 42 Or, 12k +24

Average cost will be  \frac{(12k + 24 )}{24}  = k + 2
 
Hence answer will be (A) k + 2

stonecold · Answer

Great Official Question.
Here is my solution to this one=>
Mean (12)=k

Mean = \frac{Sum}{#}

Hence Sum(12)=12k

Now new Sum(12)=12k-18+42=12k+24

New mean = \frac{12k+24}{12}=k+2

Hence A

KrishnakumarKA1 · Answer

Total cost = 12k
After replacement the total cost will be 12k -18 +42 = 12k +24
Average cost is (12k +24)/12 = k+2. Option A

nks2611 · Answer

we can see the book that has replaced cost more (42) and so we can calculate the diff which ultimately increased the avg cost of the books.
so 42-18=24 can be equally divided among 12 books that would be +2 and now as we know the previous avg that k so new avg=old avg(k)+(2)addition in each books cost =k+2

am12k · Answer

Hope this is a correct way to solve it as well:

The difference in sum:  42-18=24

k+\frac{24}{12}=k+2

Answer: A

GloryBoy92 · Answer

Hi Guys I'm trying to figure out how you got from here

=  \frac{S}{12}  +2

to here

=  K+2

PrafulLata · Answer

The average (arithmetic mean) cost per book for the 12 books on a certain table is k dollars. If a book that costs 18 dollars is removed from the table and replaced by a book that costs 42 dollars, then in terms of k, what will be the average cost per book, in dollars, for the books in the table?

A) k+2

B) k - 2

C) 12+ 24/k

D) 12- 24/k

E) 12k-6

So we have given:

Since the average cost of 12 books is K 
which means Cost of 12 books can be written as 12K

Then we have given that one book that cost 18 dollars is removed and replaced with book that cost 42 dollars, so final cost would be

12K - 18 + 42 = 12K +24

So new average would ne (12K + 24)/12

K + 2

Therefore option A is correct.

pulkitt · Answer

Question using Mean deviation 
Assume that the average of all the numbers given here is 18 instead of k. So there are 12 numbers which are all 18 making the average to 18.
 So, it looks something like this 18, 18, 18, 18 ....... (12 times) 
Hence, right now there is no mean deviation,  i.e 0,0,0,0....... (12 times) 
In the next step, the question says k ( which we assumed to be 18) is replaced by 42. Hence the new mean deviation becomes,
 0 - 18 + 42, 0 , 0 , 0 , 0 ...... (12 times) 
 +24, 0, 0, 0, 0, 0 ....... (12 times) 
 This 24 has to be allocated to all the numbers,
So 24/12 = +2

Hence all the numbers will be increased by  + 2,  i.e new mean is now 18+2 = 20.
Answer A,

Hope I was of some help ((:

The average (arithmetic mean) cost per book for the 12 books on a cert

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The average (arithmetic mean) cost per book for the 12 books on a cert

Prep Toolkit

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