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A lighting store is stocked with 410 fixtures. Some of the

by AAPL » Sat Apr 28, 2018 6:20 am

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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

The OA is E.

I tried to solve this PS question as follows,

x = floor lamps
410 - x = table lamps

we want to minimize:

x(5/100) + (410 - x)*(30/100) ==> 123 - x/4

4 is the minimum value for x to be an integer. So the answer would be 123 - 4/4 = 123 - 1 = 122.

Where am I going wrong?
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by GMATGuruNY » Sat Apr 28, 2018 6:57 am
AAPL 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
5% of the floor lamps are imported.
5% = 5/100 = 1/20.
Since 1/20 of the floor lamps are imported, the total number of floor lamps must be a MULTIPLE OF 20.

30% of the table lamps are imported.
30% = 30/100 = 3/10.
Since 3/10 of the table lamps are imported, the total number of table lamps must be a MULTIPLE OF 10.

A smaller fraction of the floor lamps are imported.
Implication:
To MINIMIZE the total number of imported lamps, we must MAXIMIZE the number of floor lamps, as follows:
400 floor lamps and 10 table lamps, for a total of 410 lamps.
Since 1/20 of the floor lamps and 3/10 of the table lamps are imported, we get:
(1/20)(400) + (3/10)(10) = 20 + 3 = 23 imported lamps.

The correct answer is E.
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by GMATGuruNY » Sat Apr 28, 2018 7:32 am
AAPL wrote:x = floor lamps
410 - x = table lamps

we want to minimize:

x(5/100) + (410 - x)*(30/100) ==> 123 - x/4

4 is the minimum value for x to be an integer. So the answer would be 123 - 4/4 = 123 - 1 = 122.

Where am I going wrong?
The expression in blue represents the total number of imported lamps.
Since x/4 is being SUBTRACTED, the expression will be minimized if x/4 is AS GREAT AS POSSIBLE.
Since x must be less than or equal to the total number of fixtures -- 410 -- the greatest possible integer value for x/4 will be yielded if x=400:
123 - 400/4 = 23.
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by Jeff@TargetTestPrep » Wed May 02, 2018 9:32 am
AAPL 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
Since the percentage of table lamps that are imported is much higher than that of the floor lamps (30% vs. 5%), we want to minimize the number of table lamps. We note that 30% = 3/10 of the table lamps are imported. Since the number of imported lamps must be a positive integer, we are looking for an integer value such that 3/10 times that value is also an integer. The smallest such integer is 10. Thus, to minimize the number of imported table lamps, we should take the total number of table lamps to be 10 and thus the number of imported table lamps will be 10 x (3/10) = 3.

Since there are 10 table lamps, this leaves us with 410 - 10 = 400 floor lamps. Since 5% of the floor lamps are imported, there are 400 x (5/100) = 20 imported floor lamps. In total, there are at least 20 + 3 = 23 imported lamps.

Answer: E

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by swerve » Wed May 02, 2018 10:46 am
F + T = 410
Now, the expression for the no. of imported items = 0.05F+0.3T
=> 0.05F+0.3(410-F)=123-0.25F
=>F has to be a multiple of 4
to minimize the expression, we have to maximize F
Max value of F can only be 400, as anything beyond this (404 or 408) will give a fractional value of the no. of imported Ts
Hence, minimum no. of imported stuff = 123-400/4 = 23.

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by [email protected] » Wed May 02, 2018 10:52 am
Hi swerve,

We're told that a lighting store is stocked with 410 fixtures - some of the fixtures are floor lamps and the rest are table lamps and 5% of the floor lamps and 30% of the table lamps are imported. We're asked for the SMALLEST possible number of imported lamps stocked at the store. Sometimes the answer choices to a Quant question are written in such a way that you can actually avoid doing lots of math (in that way the Exam will 'reward' you for being a strong critical thinker by giving you a way to the correct answer that is faster - and less work-intensive - than a traditional 'math' approach).

Here, since we know that 5% of the floor lamps are imported, if ALL 410 fixtures were for floor lamps, then we would have (.05)(410) = 20.5 lamps stocked at the store (at the MINIMUM). Since not all of the fixtures are from floor lamps, we know that the total must actually be HIGHER than that. There's only one answer that matches...

Final Answer: E

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