Statistics and set problems

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Statistics and set problems

by BTGmoderatorRO » Sun Oct 08, 2017 11:33 am

Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5
QA is b.
Is there an easy approach to get the answer here

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Source: Beat The GMAT — Problem Solving | Sun Oct 08, 2017 11:33 am

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by [email protected] » Sun Oct 08, 2017 11:40 am

Hi Roland2rule,

We're told that that sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. We're asked what fraction the sales total for December was relative to the sales total for the YEAR. This question can be solved by TESTing VALUES.

Let's say that for each month, January through November, the store had a sales total of 2. So, the average for those 11 months = 2. This would make the sales total for December = 4(2) = 8

The question asks for the ratio of December sales to sales for the year:

December = 8
Total for the year = 8 + 11(2) = 30
8/30 = 4/15

Final answer: B

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

Contact Rich at [email protected]

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Mon Oct 09, 2017 3:09 pm

Roland2rule wrote:Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5
QA is b.
Is there an easy approach to get the answer here

Hi Roland2rule,
Let take a look at your question. It seems a tricky one.

Let,
The average of the monthly sales totals for January through November = x
Total sales of 11 months from January through November = 11x
Total sales for December = 4 times the average of the monthly sales totals for January through November = 4x

The sales total for December was what fraction of the sales total for the year?
To find the fraction, we need to calculate the total sales for 12 months.

Total sales for 12 months January through December = 11x + 4x = 15x
Total sales for December = 4x
Fraction = 4x/15x = 4/15

Therefore, Option B is correct.

I am available if you'd like any follow up.

GMAT Prep From The Economist
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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Mon Dec 18, 2017 11:54 am

Roland2rule wrote:Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5

We can let n = the average sales for months January through November, inclusive, and thus December = 4n.

Thus, the sum of sales for the year is 11n + 4n = 15n, so December was 4n/15n = 4/15 of the sales for the year.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]