Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
A lighting store is stocked with 410 fixtures. Some of the [#permalink]
11 Mar 2013, 22:42
5
This post received KUDOS
3
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
75% (hard)
Question Stats:
62% (03:11) correct
38% (02:18) wrong based on 232 sessions
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?
Re: A lighting store is stocked with 410 fixtures. Some of the f [#permalink]
12 Mar 2013, 00:12
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
emmak 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? 3
10
13
20
23
Let the no. of floor lamps = x and table lamps = y. Thus, x+y = 410.
Also, we have to minimize the expression\(\frac{5}{100}*x+\frac{30}{100}*y\). This is equal to\(\frac{5}{100}(x+y)+\frac{y}{4}\).
or \(\frac{5}{100}*410+\frac{y}{4}\).
or 20.5 +\(\frac{y}{4}\)is the final expression. Now this value is equal to one of the given options. As all the first 4 options give a negative value for y, thus the only correct option is 23.
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
12 Mar 2013, 05:17
1
This post received KUDOS
Expert's post
emmak 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?
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
26 Jun 2013, 10:44
1
This post received KUDOS
Expert's post
emailmkarthik wrote:
x= floor lamps 410-x= table lamps
we want to minimize:
\(x*\frac{5}{100} + (410-x)*\frac{30}{100}\)
-> \(123-\frac{x}{4}\)
4 is minimum value for x to be integer. So answer would be \(123- \frac{4}{4}\)
\(= 123-1 = 122\)
Where am I going wrong?
We want to minimize not maximize the expression,.
x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
26 Jun 2013, 11:10
Bunuel wrote:
emailmkarthik wrote:
x= floor lamps 410-x= table lamps
we want to minimize:
\(x*\frac{5}{100} + (410-x)*\frac{30}{100}\)
-> \(123-\frac{x}{4}\)
4 is minimum value for x to be integer. So answer would be \(123- \frac{4}{4}\)
\(= 123-1 = 122\)
Where am I going wrong?
We want to minimize not maximize the expression,.
x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.
Hope it's clear.
Cool. Thanks for the response.
But i'm guessing 123-5x/20 can be written as 123- x/4
if x has to be the greatest multiple of 4 less then 410, then it would be 408.
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
26 Jun 2013, 11:13
1
This post received KUDOS
Expert's post
emailmkarthik wrote:
Bunuel wrote:
emailmkarthik wrote:
x= floor lamps 410-x= table lamps
we want to minimize:
\(x*\frac{5}{100} + (410-x)*\frac{30}{100}\)
-> \(123-\frac{x}{4}\)
4 is minimum value for x to be integer. So answer would be \(123- \frac{4}{4}\)
\(= 123-1 = 122\)
Where am I going wrong?
We want to minimize not maximize the expression,.
x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.
Hope it's clear.
Cool. Thanks for the response.
But i'm guessing 123-5x/20 can be written as 123- x/4
if x has to be the greatest multiple of 4 less then 410, then it would be 408.
Hence 123-408/4 --> 123-102 -->21
Any mistake here?
Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers. _________________
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
01 Sep 2013, 02:54
F + T = 410 Now, 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
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
06 Sep 2013, 04:18
Superb question. The first thing that got me going was the 410 number. Nothing special in it. But when I was thinking about the min number which has .3 of it as an integer, it sort of clicked ( 400 + 10 ) . Thanks for a nice question
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
07 Sep 2013, 05:27
E, You have to maximize the lower percentage and minimize the bigger percentage.
All we need is 30/100*x (must be an integer), therefore x must be a multiple of 10. therefore x=10 which gives number of table lamps=3 => number of floor lamps=5/100*400=20
Total lamps (minimum case)=table+floor lamps=3+20=23 _________________
--It's one thing to get defeated, but another to accept it.
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
16 Sep 2013, 00:37
Is it wrong just to say that 5% of 410 is 20.5, and you can not have half a lamp use logic and say that there has to be at least more than 21 lamps that were imported.
Since 23 is an actual integer would that make sense as a logical answer without going through the algebra? _________________
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
20 Oct 2014, 21:29
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: A lighting store is stocked with 410 fixtures. Some of the [#permalink]
12 Nov 2014, 01:11
How I broke this down was:
The number of imported lamps would be minimum if all 410 were floor lamps (as floor lamps have a lower weight of imported ones). i.e. 5%*410 = 20.5 imported floor lamps. However since fractional lamps are not possible (and also the question states that some of the table lamps are also imported) only 20 of these imported lamps must be floor lamps. This implies that the total number of floor lamps = 20/.05= 400. Hence the remaining 10 are table lamps, 10*30%= 3 out of which are imported. So 20+3 = 23.
Hope this helps!
gmatclubot
Re: A lighting store is stocked with 410 fixtures. Some of the
[#permalink]
12 Nov 2014, 01:11
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...