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# In the first quarter of 2008, Harry's Hardware Store sold 30

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In the first quarter of 2008, Harry's Hardware Store sold 30 [#permalink]  07 Jul 2011, 08:00
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Difficulty:

55% (hard)

Question Stats:

65% (03:19) correct 35% (02:21) wrong based on 101 sessions
In the first quarter of 2008, Harry's Hardware Store sold 300 hammers and 12,000 nails. In the second quarter of 2008, the store sold 375 hammers and 18,000 nails. By approximately what percent did the ratio of hammers sold to nails sold decrease from the first quarter to the second quarter.

A. 0.4%
B. 2.1%
C. 2.5%
D. 17%
E. 25%
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Jul 2013, 03:07, edited 1 time in total.
Renamed the topic, edited the question added the answer choices and OA.
Current Student
Joined: 26 May 2005
Posts: 565
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Kudos [?]: 152 [1] , given: 13

Re: Percent and Weighted averages [#permalink]  07 Jul 2011, 08:12
1
KUDOS
mustu wrote:
Hello,

A store sold 300 hammers and 12,000 nails on year 0 and 375 hammers and 18,000 nails on year 1. By approximately what percent did the ratio of hammers sold to nails sold decrease?

I have picked up this question from the MGMAT offical guide.

OA = 16.7%

Can someone please explain me the steps to reach the solution. I am lost in the middle ..

Regards
Mustu

The old ratio was
1:400 (300:12000)
new ratio is
1:480 (375:18000)

change = 1-400/480 = 1-.83333 =16.7%
or
1/400 = .0025
1/480 = .00208
1- .00208/.0025=16.7%
Intern
Joined: 28 Mar 2011
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Re: Percent and Weighted averages [#permalink]  07 Jul 2011, 08:30
sudhir18n wrote:
The old ratio was
1:400 (300:12000)
new ratio is
1:480 (375:18000)

change = 1-400/480 = 1-.83333 =16.7%
or
1/400 = .0025
1/480 = .00208
1- .00208/.0025=16.7%

Hi Sudhir,
Why do u take it as 1-400/480 ?? This is the step that i am not understanding.

Original - change = New

--> We have original as 1/40 and change as 1/48.

So change = Original - New
1/40 - 1/48 right ?

Should we consider original as 100% ( 1 ) and thats the reason?

Regards
Mustu
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Re: Percent and Weighted averages [#permalink]  07 Jul 2011, 08:45
mustu wrote:
sudhir18n wrote:
The old ratio was
1:400 (300:12000)
new ratio is
1:480 (375:18000)

change = 1-400/480 = 1-.83333 =16.7%
or
1/400 = .0025
1/480 = .00208
1- .00208/.0025=16.7%

Hi Sudhir,
Why do u take it as 1-400/480 ?? This is the step that i am not understanding.

Original - change = New

--> We have original as 1/40 and change as 1/48.

So change = Original - New
1/40 - 1/48 right ?

Should we consider original as 100% ( 1 ) and thats the reason?

Regards
Mustu

I should have taken 40 and 48 and not 400 and 480.
your formula is right , but that will give u only the absolute value of change and % change

for percent change
change% = ( original - new)/orginal * 100
=( 1/40 - 1/48)/1/40 * 100
solve this and you will get a negative 16.7 % , which means a decrease of 16.7 %
Director
Joined: 01 Feb 2011
Posts: 759
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Kudos [?]: 75 [0], given: 42

Re: Percent and Weighted averages [#permalink]  07 Jul 2011, 14:27
year 0 -> H/N = 300/12000 = 1/40

year 1 -> H/N = 375/18000 = (1/40)(150/180)

% decrease = (1/40)(1-150/180) *100 / (1/40)

=16.67%
Intern
Joined: 09 Jun 2011
Posts: 24
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Kudos [?]: 7 [1] , given: 2

Re: Percent and Weighted averages [#permalink]  07 Jul 2011, 14:55
1
KUDOS
There's an easier way to do it.
300h + 1200n in year 0
375h + 1800n in year 1
75h+600n is the difference
75/600 = 1/8 or 16.67
Veritas Prep GMAT Instructor
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Re: Percent and Weighted averages [#permalink]  07 Jul 2011, 21:08
6
KUDOS
Expert's post
2
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BOOKMARKED
mustu wrote:
Hello,

A store sold 300 hammers and 12,000 nails on year 0 and 375 hammers and 18,000 nails on year 1. By approximately what percent did the ratio of hammers sold to nails sold decrease?

I have picked up this question from the MGMAT offical guide.

OA = 16.7%

Can someone please explain me the steps to reach the solution. I am lost in the middle ..

Regards
Mustu

Another approach:
The number of hammers increased by 25%.
Number of nails increased by 50%.
The new ratio is 1.25/1.5 = 5/6 as compared to 1 before. Hence it decreased by 1/6 which is 16.67%
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews BSchool Thread Master Joined: 26 Mar 2007 Posts: 488 GMAT 1: 680 Q44 V38 Followers: 2 Kudos [?]: 50 [0], given: 123 Re: Percent and Weighted averages [#permalink] 08 Jul 2011, 16:51 I made it until .00208/.0025, my answer was .20 The problem said "APPROXIMATELY" so I stopped at .20 (which should have been .208) I mean, 375/18000 is .00208, but my approximate is .0020 (I stopped bec it said APPROXIMATE) 1-.0020/.0025 is 20%, as compared to the answer, 1-.00208/.0025, which is 16.7%. 16% is a huge diff from 20%. I thought when they used the word "APPROXIMATELY", I could estimate like that. How do I avoid this problem again? How do you know when to estimate like that or not? I guess if they show the answer choices, I'll get it. But I want to be sure. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5853 Location: Pune, India Followers: 1479 Kudos [?]: 7939 [1] , given: 190 Re: Percent and Weighted averages [#permalink] 11 Jul 2011, 03:07 1 This post received KUDOS Expert's post gablaze23 wrote: I made it until .00208/.0025, my answer was .20 The problem said "APPROXIMATELY" so I stopped at .20 (which should have been .208) I mean, 375/18000 is .00208, but my approximate is .0020 (I stopped bec it said APPROXIMATE) 1-.0020/.0025 is 20%, as compared to the answer, 1-.00208/.0025, which is 16.7%. 16% is a huge diff from 20%. I thought when they used the word "APPROXIMATELY", I could estimate like that. How do I avoid this problem again? How do you know when to estimate like that or not? I guess if they show the answer choices, I'll get it. But I want to be sure. They use the word 'approximate' because 16.67% is an approximation of 1/6. You cannot approximate .00208 to be .0020 since the denominator is .0025 which is quite close to .00208. If you do want to approximate, you can use .0021 instead. Of course, options will help. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Percent and Weighted averages [#permalink]  11 Jul 2011, 03:39
gablaze23 wrote:

The problem said "APPROXIMATELY" so I stopped at .20 (which should have been .208)

I mean, 375/18000 is .00208, but my approximate is .0020 (I stopped bec it said APPROXIMATE)

1-.0020/.0025 is 20%, as compared to the answer, 1-.00208/.0025, which is 16.7%.

16% is a huge diff from 20%. I thought when they used the word "APPROXIMATELY", I could estimate like that. How do I avoid this problem again? How do you know when to estimate like that or not? I guess if they show the answer choices, I'll get it. But I want to be sure.

Agree. There are no variants in the question. In case if there will be a big gap btw possible answer the one can save some time.
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Re: Percent and Weighted averages [#permalink]  27 Sep 2011, 09:22
Year 0 --> 300/12000= 1/40
year 1 ---> 375/18000 = 1/48

%change = (1/40 -1/48)/1/40 *100 = 16.6666
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Joined: 29 Jan 2011
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Schools: HKUST, ISB
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Re: Percent and Weighted averages [#permalink]  29 Dec 2011, 10:33
% Decrease = 100 - New Ratio/Old Ratio x 100
100 - 375/18*12/300*100
16.67%
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Re: Percent and Weighted averages [#permalink]  04 Jan 2013, 01:49
VeritasPrepKarishma wrote:
mustu wrote:
Hello,

A store sold 300 hammers and 12,000 nails on year 0 and 375 hammers and 18,000 nails on year 1. By approximately what percent did the ratio of hammers sold to nails sold decrease?

I have picked up this question from the MGMAT offical guide.

OA = 16.7%

Can someone please explain me the steps to reach the solution. I am lost in the middle ..

Regards
Mustu

Another approach:
The number of hammers increased by 25%.
Number of nails increased by 50%.
The new ratio is 1.25/1.5 = 5/6 as compared to 1 before. Hence it decreased by 1/6 which is 16.67%

Karishma,
This is a fantastic approach. Would this work even though hammers are increasing and nails are decreasing in % something like
The number of hammers increased by 25%.
Number of nails decreased by 50%.
The new ratio - 1.25/0.5 ?
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Re: Percent and Weighted averages [#permalink]  04 Jan 2013, 02:03
nishtil wrote:
Year 0 --> 300/12000= 1/40
year 1 ---> 375/18000 = 1/48

%change = (1/40 -1/48)/1/40 *100 = 16.6666

Before coming to this post, I was thinking why hasn't anybody solved the problem this way. I solved this way but after looking at other solutions I thought I got answer by fluke
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Re: A store sold 300 hammers and 12,000 nails on year 0 and 375 [#permalink]  03 Jul 2013, 02:26
300/12000 = 1/40
375/18000 = 1/48

1/40 got reduced to (1/40-1/48), so 100 would get reduced to:

{100 x (1/40-1/48)} / (1/40)
= 100 x { (48-40) / 48 x 40 } x 40
= 100 x 8 / 48
= 16.66
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Re: In the first quarter of 2008, Harry's Hardware Store sold 30 [#permalink]  28 Jul 2014, 20:31
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Re: In the first quarter of 2008, Harry's Hardware Store sold 30   [#permalink] 28 Jul 2014, 20:31
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