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Percentage Question

by karishma315 » Sun Sep 11, 2016 10:48 am
Hi

Please help me with the below question:

In the first quarter of 2008, Harry's Hardware sold 300 hammers and 12000 nails.In the second quarter of 2008,the store sold 375 hammers and 18000 nails .By approximately what percent did the ratio of hammers sold to nails sold decrease from the first quarter to the second quarter?

I am unable to understand the language as well as what will be in the denominator
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by MartyMurray » Sun Sep 11, 2016 1:23 pm
Here's one way to get the answer to this question.

Ratio Of Hammers To Nails First Quarter: 300/12,000

Ratio Of Hammers To Nails Second Quarter: 375/18,000

18,000 = 1.5 x 12,000

So you can make the ratios easily comparable by multiplying both sides of the first by 1.5.

Ratio Of Hammers To Nails First Quarter: 300/12,000 or 450/18,000

So the decrease from the first quarter to the second is 450/18,000 - 375/18,000 = 75/18,000

The percentage decrease is (75/18,000)/(450/18,000) = 75/450 = 1/6 ≈ 16.66 percent.
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by Brent@GMATPrepNow » Sun Sep 11, 2016 2:37 pm
Here's the entire question with answer choices:
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
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by Matt@VeritasPrep » Thu Sep 15, 2016 7:25 pm
First quarter:

Hammers = 300
Nails = 12,000
Hammers/Nails = 300/12000 = 1/40

Second quarter:

Hammers = 375
Nails = 18,000
Hammers/Nails = 375/18000 = 1/48

Our ratio dropped from 1/40 to 1/48, and from there we use our percent change formula:

(1/48 - 1/40)/(1/40)

and we're done!
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hi

by Scott@TargetTestPrep » Fri Nov 22, 2019 11:17 am
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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