parcentage

vishal chugh wrote:A project scheduled to be carried out over a single fiscal year has a budget of $12,600, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4580. By how much was the project over its budget?

Solution:

We know that our yearly budget must be divided into 12 EQUAL monthly allocations, so we need to divide $12,600 by 12. This will give us the amount of each monthly allocation. We have:

$12,600/12 = $1,050

Thus, $1,050 should be spent PER MONTH on the project. Therefore, after 4 months, 4 x $1,050 = $4,200 should have been spent on the project.

However, we are told that $4,580 was actually spent, so the project was over budget by:

$4,580 – $4,200 = $380

The answer is A

Here's the original question with the 5 answer choices.

A project scheduled to be carried out over a single fiscal year has a budget of $12,600, divided into12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,580. By how much was the project over its budget?

(A) $380
(B) $540
(C) $1,050
(D) $1,380
(E) $1,430

Given that the first 3 answer choices are quite spread apart, we might get by with some estimation/number sense.
The 12-month budget is $12,600.
So, the PROJECTED budget PER MONTH = $12,600/12 = $1050

After 4 months, the ACTUAL amount spent = $4580 (total)
So, the ACTUAL spend PER MONTH = $4580/4
Here's where some number sense comes in.
If the actual spend per month were $1100, then the total 4-month spend would be $4400 (too low)
If the actual spend per month were $1200, then the total 4-month spend would be $4800 (too high)
Since $4580 is closer to $4400 than to $4800, we can conclude that the spend per month is closer to $1100 than to $1200.
This means that the actual monthly spend is LESS THAN $1150

So, the PROJECTED budget PER MONTH = $1050, and the actual monthly spend is LESS THAN $1150.
The DIFFERENCE is less than $100/month. In other words, the project is over budget by less than $100 each month.

So, over a 4-month period, the project is over budget by less than $400

Only answer choice A works.

Aside: We have a free video on using number sense and estimation at https://www.gmatprepnow.com/module/gener ... es?id=1111

Cheers,
Brent