During the first 11 months of a recent year, a certain charitable orga

Question

During the first 11 months of a recent year, a certain charitable organization received an average of $20,600 per month in donations. How much did the organization receive in donations during December of that year if the average amount of donations per month for the entire year was $21,000?

A. $21,400
B. $21,600
C. $24,000
D. $25,400
E. $25,800

A. $21,400
B. $21,600
C. $24,000
D. $25,400
E. $25,800

Bunuel · Accepted Answer

The average to rise by $400, from $20,600 to $21,000, December donation should compensate those $400 for each of the first 11 months, so should have 11*400 more than $21,000: 11*400 + 21,000 = $25,400.

Answer: D.

MKS · Answer

Say for December month, It is X

then
 11*(20600) + X = 12 * (21000) 
=> x = 25400 - Option D

bharatS · Answer

Hello There,
Average for 11 months = 20,600
M1 + M2 + ……. + M11
------------------------------- = 20,600
 11

M1 + M2 +……..+ M11 = 20,600 X 11 = 2,26,600

Average for 12 months = 21,000
M1 + M2 + ……. + M11 + M12
----------------------------------------- = 21,000
 12

(M1 + M2 +……..+ M11) + M12 = 21,000 X 12
2,26,600 + M12 = 2,52,000
M12 = 2,52,000 – 2,26,600 = 25,400

KarishmaB · Answer

Your method is correct but it involves quite a bit of calculations. The method used by Bunuel above is much more crisp.

bharatS · Answer

Hello There,
Ya, was just trying to explain the concept. Surely will follow Bunuel. Thanks for your inputs.

pacifist85 · Answer

While I like the response by MKS, I also tried to do it another way and it doesn't work out.
Could you tell me what I am doing wrong?

So, starting by looking for the sum of the earning we have:
20600 = S/11 --> S = 226600

Then if we add the remaining earning for the last month of the year this becomes:
21000 = (226600 + x) / 12 => x = 229400, which is wrong...

EMPOWERgmatRichC · Answer

Hi pacifist85,

Your set-up and logic are fine.

When you get to this point in the "math"....

21000 = (226600 + x) / 12

....What did you do next? (you include a value for X that was incorrect, so I don't know HOW you worked through your math).

Here is a correct series of math "steps":
21,000(12) = 252,000

252,000 = 226,600 + X
25,400 = X

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

pacifist85 · Answer

Hi Rich,

What I did next was to just solve for X:
21000 = (226600 + x) / 12 => x = 229400.

So, my reasoning behind this was to add the missing amount to the S ( 226600 + x ) and divide again by 12, because now we have a new day to account for ( / 12 ). And I know see that I actually get the correct answer. As 21000*12=226600+x --> 252000 = 226600 + x --> 252000 - 226600 = x --> x = 25400.

At the moment I don't know what my problem was.. Perhaps I shouldn't be GMATing for 12 hours evryday...

But, what did you mean with "What did you do next? (you include a value for X that was incorrect, so I don't know HOW you worked through your math)". Why was adding X there incorrect?

Thank you!

EMPOWERgmatRichC · Answer

Hi pacifist85,

I was asking about how you did your calculation because you did not include that information. There was just a number (229,400) and a comment stating "...which is wrong." You got to that number somehow, but you did not explain how.

Just about every Test Taker makes some silly mistakes during practice; to keep those silly mistakes from happening AGAIN, it's important to define WHY they happened in the first place. Maybe you didn't take enough notes, maybe you did math in your head, maybe you used "math rules" incorrectly. Whatever the reason, by defining it....you should be able to fix it.

GMAT assassins aren't born, they're made,
Rich

pacifist85 · Answer

Thank you Rich. It is true that I make such silly mistakes more often than I should. Be it in mistakes is easy calculations or even copying the figures incorrectly... Not sure what is wrong there. I guess I cannot focus as much as needed!

Thank you though, because up until you told me that the solution seems correct (apart from the result of course) I was thinking that I was solving the problem incorrectly. Which was surprising since statistics is one of my strengths!

believer700 · Answer

Hi  Bunuel   VeritasPrepKarishma ,

I was reviewing the GMATPrep mock I gave today, I scored a Q48 with 7 incorrect, with last 17 Q's correct.

This particular question came as Q28( The difficulty level mentioned here is sub 600), and Q27 that came in the mock has a difficulty level of 700+ on GMAT Club, are the GMAT prep test not adaptive? or is the same fluctuation in the difficulty level of the Q can be expected in the Exam?

I am a retaker, have Q46 and Q44 in my previous two attempts, so needed to be sure, whether this is an inflated score or pretty much according to my current ability. 
Exam Pack 1 :
GMAT3 (Q48,V37)
GMAT4(Q48,V39)

TIA

KarishmaB · Answer

GMAT Prep is adaptive. Some sudden variation in difficulty level could be there because the algorithm considers various aspects (other than the difficulty level) such as the topics that still need to be tested, the question format to be given etc while selecting the next question. 
There is no reason for the score to be inflated.

believer700 · Answer

This helps a lot. Many thanks :-D

daviddaviddavid · Answer

well I spent way too much time trying to find a way avoiding the long multiplication

MHMBA2019 · Answer

average for 11 months = 20,600
20,600= x/11
x=226,600

average for the year= 21,000
21,000=x/12
x=252,000

252,000-226,600= 25,400

Basshead · Answer

If the average amount of donations was $21,000, we need to make up $400 for each prior month.

$400 * 11 + 21,000 = $4,400 + 21,000 = 25,400

Answer is D.

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During the first 11 months of a recent year, a certain charitable orga

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