Tuesday, December 13, 2011

this week's MGRE Math Beast Challenge problem

From here:

"Walter's Exercise"

Every day, Walter burns 500 calories from cardio exercise. On some days, he also burns an additional 600 calories from weight training. If, over a 240-day period, Walter burns an average of 850 calories per day from cardio exercise and weight training combined, then on how many more days did Walter engage in both cardio exercise and weight training than in cardio exercise only?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 140

My answer will appear in the comments.

_

1 comment:

Kevin Kim said...

For our purposes, we need only establish a pair of equations and use the strategy of substitution.

Let x = # 500-calorie days.

Let y = # 1100-calorie days.

First equation:

x + y = 240

Simple. The number of days will need to add up.

Our second equation arises from the fact that we're looking at an average. An average involves adding up a bunch of terms, then dividing by the number of terms added up. (If I'm averaging 10, 20, and 30 together, I divide the sum of those numbers by 3.)

So let's create an equation expressing the average, based on what we know about average calorie burn over 240 days.

[500x + 1100y]/240 = 850

In English, the above would read: "X number of 500-calorie days plus Y number of 1100-calorie days, all divided by 240, equals an average of 850 calories burned daily."

Let's simplify the above a bit, shall we? First, we multiply by 240 on both sides:

500x + 1100y = 850*240

Drop some zeroes to make this easier:

5x + 11y = 85*24
(dividing by 100 on both sides)

Finally,

5x + 11y = 2040

Which means our pair of equations is:

5x + 11y = 2040
x + y = 240

We can use the second equation for the substitution strategy by solving for either x or y. Let's solve for x.

x = 240 - y

So we plug that result into the first equation:

5(240 - y) + 11y = 2040

Which becomes:

1200 - 5y + 11y = 2040

Which in turn becomes:

6y + 1200 = 2040

Which gives us:

6y = 2040 - 1200 = 840

Divide by 6 on both sides:

y = 140

So we now know that, over a period of 240 days, Walter used 140 of them for his 1100-calorie workout. Since we know that

x + y = 240,

we now also know that

x = 100.

Are we done? NO! The problem is asking for how many MORE days Walter engaged in cardio + weights. So we subtract:

140 - 100 = 40.

The answer is (A). And this time, I bet I'm on the money.

Note that (E) is 140. A hasty test-taker might stop at the wrong point in the problem and assume that (E) was the correct answer. That's a fatal mistake on the GRE.

We good? Good.