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Percents - Double Matrix : lighting store fixtures

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Percents - Double Matrix : lighting store fixtures

by snigdha1605 » Sun Aug 04, 2013 2:25 am
Hi,

Two questions -
1) Does the gmat have problems of this difficulty level?
2) Can anyone explain how this can be solved by double matrix

A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number of imported lamps stocked at the store?

A. 3
B. 10
C. 13
D. 20
E. 23

OA - E

Thanks in advance!
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by GMATGuruNY » Sun Aug 04, 2013 4:14 am
snigdha1605 wrote:Hi,

Two questions -
1) Does the gmat have problems of this difficulty level?
2) Can anyone explain how this can be solved by double matrix

A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number of imported lamps stocked at the store?

A. 3
B. 10
C. 13
D. 20
E. 23

OA - E

Let F = the number of floor lamps and T = the number of table lamps.

5% of the floor lamps are imported.
Imported table lamps = (1/20)F.

30% of the table lamps are imported.
Imported table lamps = (3/10)T.

Thus:
Total imported = (1/20)F + (3/10)T.

A higher fraction of the table lamps are imported.
To MINIMIZE the number of imported lamps, we must MINIMIZE the number of table lamps.
In the resulting equation above, the least possible value of T=10.
If T=10, then F=400, since T+F = 410.

Plugging F=400 and T=20 into (1/20)F + (3/10)T, we get:
Least possible imported = (1/20 * 400) + (3/10 * 10) = 23.

The correct answer is E.
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by Brent@GMATPrepNow » Sun Aug 04, 2013 4:43 am
snigdha1605 wrote: A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number of imported lamps stocked at the store?

A. 3
B. 10
C. 13
D. 20
E. 23
Notice that a greater proportion (30%) of the table lamps are imported as compared to only 5% of the floor lamps being imported.
So, to MINIMIZE the number of imported lamps, we must MINIMIZE the number of table lamps.

If 30% of the table lamps are imported, then the number of table lamps must be a multiple of 10 (since 30% = 3/10). In other words, 3 out of every 10 table lamps is imported.
For example, there cannot be 8 table lamps since 30% of 8 is not a whole number.

Likewise, the number of floor lamps must be a multiple of 20 (since 5% = 1/20).

Now that we know the number of table lamps must be a multiple of 10, and the number of floor lamps must be a multiple of 20, let's try to MINIMIZE the number of table lamps.

The smallest possible number table lamps is 10, in which case there are 400 floor lamps.
- Of the 10 table lamps, 30% are imported (3 imported)
- Of the 400 table lamps, 5% are imported (20 imported)

Total number of imported lamps = [spoiler]3 + 20 = 23 = E[/spoiler]

Cheers,
Brent
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by snigdha1605 » Sun Aug 04, 2013 4:47 am
Thank you Mitch and Brent!
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by Brent@GMATPrepNow » Sun Aug 04, 2013 4:50 am
snigdha1605 wrote: Two questions -
1) Does the gmat have problems of this difficulty level?
2) Can anyone explain how this can be solved by double matrix
1. Yes, this question is GMAT-worthy. But I'd say it's a 700+ level question.

2. We could use a double matrix to set it up (label the columns "Imported" and "Not Imported," and label the rows "Table Lamps" and "Floor Lamps.") However, at that point, you'd need to recognize that you need to maximize the number of table lamps, and you must recognize that the number of table lamps is a multiple of 10, and the number of floor lamps is a multiple of 20.

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