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

Expert replies

Previous Topic Next Topic

AAPL: Moderator; Posts: 2710; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Sat Apr 28, 2018 6:20 am

Timer

00:00

Answers

Stats

Difficulty—

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?

Like this post

Source: Beat The GMAT — Problem Solving | Sat Apr 28, 2018 6:20 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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.

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

swerve: Legendary Member; Posts: 2579; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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.

Regards!

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

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

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review