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

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07 Jul 2011, 09:00

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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 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)

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 %

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%
_________________

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.

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.
_________________

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.

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 ?

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

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

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28 Jul 2014, 21:31

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

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11 Sep 2016, 15:39

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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...

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

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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?

gmatclubot

Re: In the first quarter of 2008, Harry's Hardware Store sold 30
[#permalink]
23 Nov 2016, 05:17

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