In the first quarter of 2008, Harry's Hardware Store sold 30 : Problem Solving (PS)

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BrentGMATPrepNow

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

Updated on: 12 Nov 2019, 17:27

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mustu wrote:

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%

1st quarter: hammers/nails = 300/12,000 = 150/6000
2nd quarter: hammers/nails = 375/18,000 = 125/6000
ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.

So, our ratio went from 150/6000 to 125/6000
Ignoring the denominators, we went from 150 to 125
The percent change = 100(difference in values)/(original value)
= (100)(150 - 125)/150
= (100)(25)/150)
= (100)(1)/(6)
= 100/6
≈ 16.666...

Answer: D

Originally posted by BrentGMATPrepNow on 11 Sep 2016, 15:39.
Last edited by BrentGMATPrepNow on 12 Nov 2019, 17:27, edited 1 time in total.

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Re: Percent and Weighted averages [#permalink]

07 Jul 2011, 09:12

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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%

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Re: Percent and Weighted averages [#permalink]

07 Jul 2011, 09:30

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, 09:45

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 %

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Re: Percent and Weighted averages [#permalink]

07 Jul 2011, 15:27

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%

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Re: Percent and Weighted averages [#permalink]

08 Jul 2011, 17:51

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.

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Re: Percent and Weighted averages [#permalink]

11 Jul 2011, 04:07

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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.

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Re: Percent and Weighted averages [#permalink]

11 Jul 2011, 04:39

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.

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, 10:22

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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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Re: Percent and Weighted averages [#permalink]

29 Dec 2011, 11:33

% 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, 02:49

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, 03:03

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, 03:26

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]

29 Feb 2016, 15:00

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imerial wrote:

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

I dont think 1/8 equals 16.67

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Re: In the first quarter of 2008, Harry's Hardware Store sold 30 [#permalink]

23 Nov 2016, 05:17

GMATPrepNow wrote:

mustu wrote:

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%

1st quarter: hammers/nails = 300/12,000 = 150/6000
2nd quarter: hammers/nails = 375/18,000 = 125/6000
ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.

So, our ratio went from 150/6000 to 125/6000
Ignoring the denominators, we went from 150 to 125
The percent change = 100(difference in values)/(original value)
= (100)(150 - 125)/150
= (100)(25)/150)
= (100)(1)/(6)
= 100/6
≈ 16.666...

Answer: [you-tube]D[/you-tube]

Would you mind explaining how you got those 6000 ie common denominator under 2 minutes? What approach did you take?

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Re: In the first quarter of 2008, Harry's Hardware Store sold 30 [#permalink]

27 Nov 2019, 11:54

Expert Reply

mustu wrote:

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%

The ratio of hammers to nails in the first quarter was 300/12,000 = 3/120 = 1/40. The ratio of hammers to nails in the second quarter was 375/18,000 = 1/48.

We can use the percent change formula: (New - Old)/Old x 100 to create the equation:

(375/18,000 - 300/12,000)/(300/12,000) x 100

(1/48 - 1/40)/(1/40) x 100

(5/240 - 6/240)/(1/40) x 100

-1/240 x 40 x 100 = -1/6 x 100 = -16.67%, which is approximately a 17% decrease.

Answer: D

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Re: In the first quarter of 2008, Harry's Hardware Store sold 30 [#permalink]

27 Sep 2020, 14:00

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Nasahtahir wrote:

GMATPrepNow wrote:

mustu wrote:

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%

1st quarter: hammers/nails = 300/12,000 = 150/6000
2nd quarter: hammers/nails = 375/18,000 = 125/6000
ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.

So, our ratio went from 150/6000 to 125/6000
Ignoring the denominators, we went from 150 to 125
The percent change = 100(difference in values)/(original value)
= (100)(150 - 125)/150
= (100)(25)/150)
= (100)(1)/(6)
= 100/6
≈ 16.666...

Answer: [you-tube]D[/you-tube]

Would you mind explaining how you got those 6000 ie common denominator under 2 minutes? What approach did you take?

We have 300/12,000 and 375/18,000
I recognized that 12,000 and 18,000 are both multiples of 6000
So, if we take 300/12,000 and divide numerator and denominator by 2, we get: 150/6000
Similarly, we can take 375/18,000 and divide numerator and denominator by 3, we get: 125/6000

gmatclubot

Re: In the first quarter of 2008, Harry's Hardware Store sold 30 [#permalink]

27 Sep 2020, 14:00

GMAT Problem Solving (PS) Questions

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