Country ---Amount Recycled---------Amount Disposed of
A------------16,700-------------------- 142,800

B-------------8,800----------------------48,000

C------------13,000----------------------51,400

D-------------3,900----------------------20,300

E-------------3,300----------------------16,200

The table above shows the amount of waste material, in tons, recycled by each of five counties in a single year and the amount of waste material, also in tons, that was disposed of in landfills by the five counties in that year. Which county had the lowest ratio of waste material disposed of to waste material recycled in the year reported in the table?
A. A
B. B
C. C
D. D
E. E

Question asks to determine lowest ratio of amount disposed / amount recycled.

(A) 142,800 / 16,700 = ~ 8 - 9

(B) 48,000 / 8,800 = ~ 6

(C) 51,400 / 13,000 = ~4

(D) 20,300 / 3,900 = ~ 5

(E) 16,200 / 3,300 = ~ 5

Answer: C.

My advice is before doing calculations estimate the numbers and start with the easiest. No need for exact numerical values, so good approximation will work in this case.
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such questions do not ask you to precisely calculate the numbers, thereby asking you to rather estimate.

a) \(\frac{143}{17}\) ~some big number

b) \(\frac{48}{9}\) ~ 5+

c) \(\frac{51}{3}\) ~4

d) \(\frac{20}{4}\) ~5

e) \(\frac{16}{3}\) ~5

C is the lowest and is the correct ans.

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Hello members,

Since the purpose of this question is to practise estimation, I will explain here an interesting way. Start by multiplying denominator by 10 and see if numerator is greater than or less than denominator multiplied by 10. If numerator is less, half the (denominator*10) and see if it less or greater than the new numerator .

[162/33] , here 33x10=330, 330>162, 330/2=165, 165>162 (this means that numerator is around 4 times the denominator)

[203/39], here 39x10=390, 390>203, 390/2=195, 195<203 (this means that numerator is more than 5 times denominator)

[514/130], here 130x10=1300, 1300>514, 1300/2=650, 650 >514 (this means that numerator is less than 5 times and infact a little calculation will show that it is less than 4 times the numerator)

[480/88], here 88x10=880, 880>480, 880/2=440, 440<480 (this means that numerator is more than 5 times the denominator)

[1428/167], here 167x10=1670, 1670>1428, 1670/2=835, 835 < 1428 (this means that numerator is much more than 5 times the denominator)

By finding this strategy, we can see that [514][/130] yields the lowest fraction.

Hi all,

Could someone help me with the phrasing?
The question asks for the lowest ratio ... yet the right aswer is the highest ratio.
I mean for A: there is 9:1 ... 9 waste to 1 recycled
for C: there is 3:1 ... 3 waste to 1 recycled

I would assume that the higher number (9/1=9; 3/1=3) would mean a lower ratio.
If you try to make sense of the ratio than the ratio is high e.g. 1:2 or 1:10 etc... the higher the recycled part the higher the ratio is.

Thanks

Lowest ratio is lowest number.
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Hi,

how did you solve? can you explain the easiest way to calculate such big division.

thanks!

Bunuel when all can we take approximations? Because I have tried using this method but it gives different answer. How much and when to estimate?

Collected several articles on this issue:
How to Do Math on the GMAT Without Actually Doing Math
The Power of Estimation for GMAT Quant
How to Plug in Numbers on GMAT Math Questions
Number Sense for the GMAT
Can You Use a Calculator on the GMAT?
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT

All this is from QUANTITATIVE BOOKS AND STRATEGIES.

Hope it helps.
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Notice that you can turn all the denominators approximately into 16.000

______ Denominator_____Multiplier______New Numerator
A) ->_____16,700____________~x1____________142,800
B) ->_____8,800_____________~x2___________<96,000
C) ->_____13,000____________~x\(\frac{5}{4}\)____________62,500 -> The lowest
D) ->_____3,900_____________~x4____________80,000
E) ->_____3,300_____________~x5____________>80,000

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