Tom is on a certain diet that requires him to limit the

Question

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

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

PareshGmat · Accepted Answer

Total Calories taken in 10 days = 27200

Total Calories he should ideally be taking as per diet for 10 days = 26000

Extra Calories taken = 27200 - 26000 = 1200

On some days, he splurges by taking in three times the recommended number of calories from snacks and dessert.

600 - 200 = 400 calories he takes extra

1200/400 = 3 days = Answer = A

BrentGMATPrepNow · Answer

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

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Anshulmodi · Answer

On some days Tom takes in 2400 + 3(200) = 3000 calories, and on other days he takes in 2400 + 200 = 2600 calories.

Let s represent the number of days he splurges, and let n (for normal) represent the number of days he does not splurge.

We know that s + n = 10, and since we are solving for s, we can say that n = 10 – s.

The total number of calories is (3000s + 2600n). Substuting (10 - s) for g we can rewrite the total number of calories as 3000s + 2600(10 - s).

Total number of calories ÷ Total number of days = Average number of calories per day.

÷ 10 = 2720
3000s + 2600(10 - s) = 27,200 (multiply both sides by 10)
26000 + 3000s – 2600s = 27,200
400s = 1200
s = 3

Alternatively, we could have plugged in the answer choices to solve the problem. If Tom had 7 days of consuming 2600 calories, then he must have had 3 days in which he consumed 3000 calories. He would have consumed a total of 7(2600) + 3(3000) = 27,200 calories. 27,200/10 = 2720.

The correct answer is A.

Anshulmodi · Answer

A faster method would be

If tom had followed guidelines precisely on each day than the average would had been 2600 calories (2400 + 200) for 10 day period.

But the average was 2720 i.e 120 more per day over the 10 day period that comes up to 1200 (120 * 10) more for a 10 day period.

The splurge was 200 to 600 (3 times) on x days (to be determined) i.e. 400 (600 - 200) more per day.

So  x = \frac{1200}{400} = 3

Ans A

Lucky2783 · Answer

Is it a 700 Level question on GMAT ? 
Doesnt look like the one.

thanks
Lucky

EMPOWERgmatRichC · Answer

Hi Lucky2783,

Test Takers tend to put a lot of importance on the perceived "level" of a question, when that's actually something of a waste of time. Instead, you should evaluate whether the question is "gettable" or not. To that end, regardless of the difficulty level, if you make a silly/little mistake on a "gettable" question and get it wrong, then THAT is the issue that you need to focus on (and fix). Most questions on the Official GMAT are actually pretty straight-forward. Some of them are 'wordy' and in some cases the information given is not provided in the most useful "order", but if you want that high score, then you have to minimize (or ultimately eliminate) the little mistakes. The real "tough" part is that you have to perform at this level for 4 hours, which is something that most Test Takers have trouble with.

This prompt is wordy, but it's based on simple arithmetic and the Average Formula. As such, it probably doesn't feel that "hard" to you - if that's true, then great - don't worry about what "level" it is. Just get it correct in the most efficient way possible.

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

OptimusPrepJanielle · Answer

On normal days, Tom takes 2400 + 200 = 2600 calories. When he splurges, Tom takes 2400 + 200(3) = 3000 calories. Instead of forming equations, let us go by options. Option A: If he splurges on 3 days then his calorie intake for 10 day period = 3000(3) + 2600(7) = 27200 Hence average = 2720. Hence option A is correct. -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

KarishmaB · Answer

Use the scale method: The number of calories taken on a normal day = 2400 + 200 = AN. Number of calories taken on a splurge day = 2400 + 3*200 = 3000 = AS wN/wS = (AS - Aavg)/(Aavg - AN) = (3000 - 2720)/(2720 - 2600) = 280/120 = 7/3 So on 7 days, he consumed normal calories and he splurged on 3 days. Answer (A) For more on scale method, check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/

gary391 · Answer

For Regular day Average calories = 2400+200 = 2600
For a Splurge day Average calories = 2400+600 = 3000

Average of calories for a mix of a number of Regular days and a number of Splurge days for a period of 10 days = 2720.

- If we have equal number of Regular days (5 days) + Splurge days (5 days) resulting average calories will be = 2800

Since the combined average calories is 2720 we can conclude that we have more Regular days than Splurge days, thus eliminating options c, d and e. Picking option (B) the combined average calories is 2760.

2600*(6/10) +3000(4/10) = 2760

Thus, Eliminating option B the answer is A.

lwulfe · Answer

i feel like an idiot. Did anyone else perceive "three times" the recommended as 3 times 2600. In other words three times the whole days worth. I just thought they meant that the extra calories were coming from desserts and snacks. not that it was only the desserts and snacks that were tripled. UUUUUGghhh

Primate411 · Answer

Total calories taken in 10 days; 2720*10 = 27200

Prescribed calories in 10 days; (2400+200)*10 = 26000

Excess calories taken; 27200-26000 = 1200

Number of splurge days; 1200/200 = 6..... (B)

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SeregaP · Answer

we can solve it with 2 equations:
x+y=10
(2400+200)*x+(2400+200*3)y=27200
y is 3
answer is A

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing 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

ScottTargetTestPrep · Answer

We can let n = the number of days he splurges. Notice that on each of these n days, the total calorie intake 2400 + 3 x 200 = 3000. For each of the 10 - n days he doesn’t splurge, the total calorie intake is 2400 + 200 = 2600. Therefore, we can create the equation:

3000n + 2600(10 - n) = 2720 x 10

30n + 26(10 - n) = 272

30n + 260 - 26n = 272

4n = 12

n = 3

Answer: A

GMATinsight · Answer

Snacks and Dessert - 200 cal

Sometime cal from Snacks and Desserts = 3*200 = 600 cal
Extra intake in those days = 600-200 = 400 calorie

10 days average calorie intake = 2720

10 days extra calorie intake = (2720-2400)*10 = 1200

Extra calories = 1200

i.e. extra splurge days = 1200/400 = 3

Answer: Option A

adityaprateek15 · Answer

Calories he is allowed to take = 2400+200 = 2600
Calories he consumes on days he splurge = 2400 + 200*3 = 3000

Avg. calorie intake for 10 days = 2720

Use alligation:

Days with no extra calorie(C)......Avg. calorie for 10d........Days he consumes extra(EC)
 2600...........................2720...................3000

C: 3000-2720 = 280
EC: = 2720-2600 = 120

C:EC = 7:3

Therefore, days he consumes extra 3/10 = 3 days

luisdicampo · Answer

Deconstructing the Question

Normal daily calories:
  2400 + 200 = 2600

On splurge days, snacks are triple:
  2400 + 600 = 3000

Use extra-calories method.

Step-by-step

Normal total for 10 days:
 2600 	imes 10 = 26000

Actual total:
 2720 	imes 10 = 27200

Extra calories:
 27200 - 26000 = 1200

Extra per splurge day:
 3000 - 2600 = 400

Number of splurge days:
 1200/400 = 3

Answer: A (3)

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