Is my approach correct?

[aces021]

Tom is on a certain diet that requires him to limit the number of calories he takes in each day. He is allowed to take in 2400 calories each day from three square meals, and 200 calories each day from snacks and dessert combined. On some days, he splurges by taking in three times the recommended number of calories from snacks and dessert. The rest of the days, he follows the calorie guidelines precisely. If his average calorie intake for a 10 day period was 2720, on how many days did he splurge?

A. 3
B. 4
C. 5
D. 6
E. 7


Am I solving this correctly? I haven't seen this approach online.


10(days)*2,720(ave per day)=27,200

2400(10 days)+200X=27,200

24,000+200X=27,200

200X=3200

X=16

16 (total snacks) -10 (total days) = 6 (extra snacks consumed)

6/2(he takes 3 times the recommended calories, I already included 1 time in the above equation, therefore I divide by 2) = 3

[[email protected]]

Hi aces021,

Yes, your math is correct. It's worth noting that there are several ways to "do the math" in this question OR you could TEST THE ANSWERS instead of doing lots of calculations. Here's how:

We're told that the average for 10 days was 2720 calories, so the total number of calories is 2720 x 10 = 27,200

We're told that...
on a normal day, Tom eats 2400+200 calories = 2600 calories
on a splurge day, Tom easts 2400 + 600 calories = 3000 calories

We're asked for the number of splurge days.

Let's TEST THE ANSWERS...

Answer B = 4.
4 splurge days = 4 x 3000 = 12,000
6 normal days = 6 x 2600 = 15,600
Total Calories = 27,600
This is TOO MANY CALORIES (we're supposed to have 27,200), so this answer has TOO MANY splurge days.

The only answer that would give us fewer calories is answer A. This must be the correct answer.

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

[GMATGuruNY]

Tom is on a certain diet that requires him to limit the number of calories he takes in each day. He is allowed to take in 2400 calories each day from three square meals, and 200 calories each day from snacks and dessert combined. On some days, he splurges by taking in three times the recommended number of calories from snacks and dessert. The rest of the days, he follows the calorie guidelines precisely. If his average calorie intake for a 10 day period was 2720, on how many days did he splurge?

A. 3
B. 4
C. 5
D. 6
E. 7

This is a weighted average/mixture question.

Ingredient 1: Average caloric intake on deprived days = meal calories + snack calories = 2400 + 200 = 2600.
Ingredient 2: Average caloric intake on splurge days = meal calories + snack calories = 2400 + 3*200 = 3000.
Mixture: Average caloric intake for the MIXTURE of deprived days and splurge days = 2720.

Let D = the number of deprived days and S = the number of splurge days.
To determine the ratio of D to S in the mixture, use ALLIGATION:

Step 1: Plot the 3 averages on a number line, with the averages for the two ingredients on the ends and the average for the mixture in the middle.
D 2600--------------2720-------------3000 S

Step 2: Calculate the distances between the averages.
D 2600------120----2720-----280-----3000 S

Step 3: Determine the ratio in the mixture.
The required ratio of D to S is the RECIPROCAL of the distances in red.
D:S = 280:120 = 7:3.

Thus, of the 10 days, D=7 and S=3.

The correct answer is A.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

[aces021]

Tom is on a certain diet that requires him to limit the number of calories he takes in each day. He is allowed to take in 2400 calories each day from three square meals, and 200 calories each day from snacks and dessert combined. On some days, he splurges by taking in three times the recommended number of calories from snacks and dessert. The rest of the days, he follows the calorie guidelines precisely. If his average calorie intake for a 10 day period was 2720, on how many days did he splurge?

A. 3
B. 4
C. 5
D. 6
E. 7

This is a weighted average/mixture question.

Ingredient 1: Average caloric intake on deprived days = meal calories + snack calories = 2400 + 200 = 2600.
Ingredient 2: Average caloric intake on splurge days = meal calories + snack calories = 2400 + 3*200 = 3000.
Mixture: Average caloric intake for the MIXTURE of deprived days and splurge days = 2720.

Let D = the number of deprived days and S = the number of splurge days.
To determine the ratio of D to S in the mixture, use ALLIGATION:

Step 1: Plot the 3 averages on a number line, with the averages for the two ingredients on the ends and the average for the mixture in the middle.
D 2600--------------2720-------------3000 S

Step 2: Calculate the distances between the averages.
D 2600------120----2720-----280-----3000 S

Step 3: Determine the ratio in the mixture.
The required ratio of D to S is the RECIPROCAL of the distances in red.
D:S = 280:120 = 7:3.

Thus, of the 10 days, D=7 and S=3.

The correct answer is A.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

That's an interesting approach. Thanks for the problem suggestion.

[Brent@GMATPrepNow]

Tom is on a certain diet that requires him to limit the number of calories he takes in each day. He is allowed to take in 2400 calories each day from three square meals, and 200 calories each day from snacks and dessert combined. On some days, he splurges by taking in three times the recommended number of calories from snacks and dessert. The rest of the days, he follows the calorie guidelines precisely. If his average calorie intake for a 10 day period was 2720, on how many days did he splurge?

A. 3
B. 4
C. 5
D. 6
E. 7

We can also apply the formula for weighted averages:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Given:
Regular days: 2600 calories
Splurge days: 3000 calories

Let R = number of days in which Tom ate the regular amount
Let S = number of days in which Tom splurged

Since there were 10 days altogether, we can write: R + S = 10

Next, from the above formula, we get: 2720 = (R/10)(2600) + (S/10)(3000)
Multiply both sides by 10 to get: 27200 = 2600R + 3000S
Divide both sides by 100 to get: 272 = 26R + 30S
Rewrite as: 26R + 30S = 272

We now have a system of two equations that we must solve for S:
R + S = 10
26R + 30S = 272

Take the top equation and multiply both sides by 26 to get:
26R + 26S = 260
26R + 30S = 272

Subtract the red equation from the blue equation to get: 4S = 12
Solve, S = 3

Answer: A