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

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Tom is on a certain diet that requires him to limit the  [#permalink]

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01 Mar 2014, 11:23
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Difficulty:

45% (medium)

Question Stats:

74% (02:29) correct 26% (02:21) wrong based on 343 sessions

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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

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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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03 Mar 2014, 19:57
10
1
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
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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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01 Mar 2014, 11:24
2
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.

[3000s + 2600(10 - s)] ÷ 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.

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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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01 Mar 2014, 11:34
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
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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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22 Feb 2015, 08:22
Anshulmodi wrote:
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

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

thanks
Lucky
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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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22 Feb 2015, 14:17
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.

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** SVP Joined: 06 Nov 2014 Posts: 1877 Re: Tom is on a certain diet that requires him to limit the [#permalink] ### Show Tags 28 Feb 2015, 10:54 Anshulmodi wrote: 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 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: http://www.optimus-prep.com/gmat-on-demand-course
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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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28 Jul 2016, 13:17
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Top Contributor
1
Anshulmodi wrote:
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

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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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28 Jul 2016, 21:11
2
Anshulmodi wrote:
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

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.

For more on scale method, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
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Tom is on a certain diet that requires him to limit the  [#permalink]

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20 Aug 2016, 13:47
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.
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Tom is on a certain diet that requires him to limit the  [#permalink]

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23 Aug 2016, 15:53
Anshulmodi wrote:
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

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
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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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23 Aug 2016, 16:46
Anshulmodi wrote:
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

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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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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24 Mar 2017, 10:13
we can solve it with 2 equations:
x+y=10
(2400+200)*x+(2400+200*3)y=27200
y is 3
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Re: Tom is on a certain diet that requires him to limit the  [#permalink]

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14 Mar 2018, 18:16
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.

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 . This must be the correct answer.

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Re: Tom is on a certain diet that requires him to limit the &nbs [#permalink] 14 Mar 2018, 18:16
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