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A certain state's milk production was 980 million pounds in 2007 and 2

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Re: A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
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Kudos
Step 1: Understand (Glance Read Jot)

The answers are spread out, which suggests Estimation. Choices (A) and (B) are close to 100, choice (C) is close to 1,000, and (D) and (E) are in the ballpark of 10,000. The answer choices are also clean values, so consider Working Backwards.

The question gives numbers in terms of millions and billions and in terms of pounds and gallons; this question might be testing Translations, namely unit conversions.

The words how many more indicate that you are looking for the difference between two numbers (so, subtraction), which means that working backwards might be a bit more difficult; it is easier to work backwards when the answers are a simple value to plug in, rather than a relationship. The word approximately indicates once again that estimation might be possible.

Jot down the given numbers, conversion rates, and what the question is asking for:

980 million pounds → 2.7 billion pounds

1 billion = 109

1 million = 106

1 gallon = 8.6 pounds

How many more gallons?

Step 2: Plan (Reflect Organize)

The answer choices represent the difference between the 980 million pounds in 2007 and the 2.7 billion pounds in 2014. To work backwards from the answer choices, all values (2007, 2014, and the answer choices) will need to be converted to the same units.

The likeliest mistakes are decimal misplacement (wrong number of zeros) and multiplicative inverse errors (dividing by 8.6 versus multiplying by 8.6). Be careful with units (pounds, gallons) and with powers of 10. When a GMAT problem underlines a word, pay attention: make sure the answer is in millions of gallons.

Among the choices, the easiest numbers to work with are 100 and 200, and it’s generally recommended to work backwards from (B) or (D), so work backwards from (B) first, then evaluate whether to continue working backwards or to estimate.

Because the answer choices are so spread out, consider using estimation throughout to make the computation easier.

Step 3: Solve (Do the Work)

Working Backwards

First find the difference between production in 2007 and 2014. Since 980 million is approximately 1 billion, the difference is approximately 1.7 billion, or 1700 million pounds.

Be careful! Trap answer (C) is 1700, but the answers are in millions of gallons, not millions of pounds. The correct answer will be the one that, when converted to pounds, equals 1700.

To convert gallons to pounds, you would multiply each answer choice by 8.6. However, simplify the computation by benchmarking.

Choice (B):
200 million gallons @ 8 pounds/gallon = 1600 million pounds of milk
200 million gallons @ 9 pounds/gallon = 1800 million pounds of milk

Since the actual weight is 8.6 pounds/gallon, 200 million gallons will be about halfway between 1600 and 1800 million pounds of milk. The target difference is 1700 million pounds; this is the correct answer.

Algebra

See the Official Guide solution for the algebraic method of converting the units and solving.

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A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
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Top Contributor
SOLUTION:

A NEW OG 2021 QUESTION

Its a Conversion Question

Milk production in 2014 = 2.7 billion pounds

= 2.7 x 1000 = 2700 million pounds

Milk production in 2007 = 980 million pounds

Increase in milk production = 2700 -980

= 1720 million pounds

1 gallon = 8.6 pounds

=> 1 pound = 1/8.6 gallons

Thus 1720 million pounds = 1720 x 1/8.6 gallons

Round 8.6 to 10 (given the large difference in options)and you would have 172 million gallons (approx.)

Nearest value to this is 200 million pounds (OPTION B)

Hope this helps

Originally posted by CrackverbalGMAT on 11 Feb 2021, 23:09.
Last edited by CrackverbalGMAT on 22 Jun 2024, 01:16, edited 1 time in total.
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Re: A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
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parkhydel
A certain state's milk production was 980 million pounds in 2007 and 2.7 billion pounds in 2014. Approximately how many more million gallons of milk did the state produce in 2014 than in 2007 ? (1 billion = 10^9 and 1 gallon = 8.6 pounds.)

A. 100
B. 200
C. 1,700
D. 8,200
E. 14,800

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Re: A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
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Kudos
I found this much easier and faster when I approximated this. Wondering if anyone else did the same?

2007 = 980 million pounds ~ 1 billion pounds
2014 = 2.7 billion pounds ~ 3 billion pounds
1 gallon = 8.6 lbs ~ 10lbs
--> Therefore difference ~ 2 billion pounds

When I did it this way it's very easy to calculate the pounds into gallons and I got 200 (B) on the dot.
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Re: A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
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uazo
I found this much easier and faster when I approximated this. Wondering if anyone else did the same?

2007 = 980 million pounds ~ 1 billion pounds
2014 = 2.7 billion pounds ~ 3 billion pounds
1 gallon = 8.6 lbs ~ 10lbs
--> Therefore difference ~ 2 billion pounds

When I did it this way it's very easy to calculate the pounds into gallons and I got 200 (B) on the dot.

Yes, excellent solution!

There are 2 main signals to approximate:
1) the question specifically says "appoximately" or "closest"

Here are several other good official questions you can practice this on:

Question: https://gmatclub.com/forum/last-year-me ... l#p2105366
Solution: https://gmatclub.com/forum/last-year-me ... l#p3095151

Question: https://gmatclub.com/forum/a-corporatio ... l#p1333975
Solution: https://gmatclub.com/forum/a-corporatio ... l#p3094235

Question: https://gmatclub.com/forum/a-certain-ma ... l#p1704897
Solution: https://gmatclub.com/forum/a-certain-ma ... l#p3095635

Question: https://gmatclub.com/forum/a-certain-to ... l#p2103837
Solution: https://gmatclub.com/forum/a-certain-to ... l#p3097219

Question: https://gmatclub.com/forum/last-year-sh ... l#p2506524
Solution: https://gmatclub.com/forum/last-year-sh ... l#p3098048
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A certain state's milk production was 980 million pounds in 2007.png [ 194.37 KiB | Viewed 11571 times ]

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Re: A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
Let's solve the given problem. We want to determine approximately how many more million gallons of milk the state produced in 2014 compared to 2007.

Given information:
Milk production in 2007: 980 million pounds.
Milk production in 2014: 2.7 billion pounds.

To find the difference in milk production between the two years, we need to calculate the change in pounds and then convert it to gallons. We'll follow these steps:

Calculate the difference in milk production in pounds:
Difference = Milk production in 2014 - Milk production in 2007
Difference = 2.7 billion pounds - 980 million pounds
To simplify the calculation, we need to convert both values to the same unit. Given that 1 billion is equal to 10^9, we can convert 2.7 billion pounds to 2.7 * 10^9 pounds.

Difference = 2.7 * 10^9 pounds - 980 million pounds

Convert the difference from pounds to gallons:
To convert pounds to gallons, we are given that 1 gallon is equal to 8.6 pounds. Therefore, we divide the difference in pounds by 8.6 to get the difference in gallons:
Difference in gallons = Difference / 8.6

Now, let's calculate the approximate value for the difference:

Difference in gallons ≈ (2.7 * 10^9 pounds - 980 million pounds) / 8.6

Calculating the above expression:

Difference in gallons ≈ (2.7 * 10^9 - 980 * 10^6) / 8.6 ≈ (2.7 * 10^9 - 0.98 * 10^9) / 8.6 ≈ 1.72 * 10^9 / 8.6 ≈ 200 million gallons

The approximate difference in milk production between 2014 and 2007 is (B) 200 million gallons.
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Re: A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
2700 - 980 = 1720 m.pounds

1 gallon = 8.6

1720/8.6 = 200 m.gallons

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A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
2
Kudos
Short video solution here:

The question asks for "how many more million gallons", so our steps are:

1) Round to 1,000 million and 3,000 million pounds. (A billion is 1,000 million)

2) Find the difference: 2,000 million pounds

3) Convert from gallons to pounds. Round the 8.6 pounds per gallon to 10:

2000 / 10 = 200

Attachments

2023-12-22 21_09_20-Round when it says _approximately_! _A certain state's milk production was 980 m.png [ 3.26 MiB | Viewed 4372 times ]

A certain state's milk production was 980 million pounds in 2007 and 2 [#permalink]
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