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OG The estimated number of homeschooled students

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OG The estimated number of homeschooled students

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According to the table shown, the estimated number of home-schooled students in State A is approximately what percent greater than the number in State D?

A. 25%
B. 55%
C. 100%
D. 125%
E. 155%

D

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AbeNeedsAnswers wrote:


According to the table shown, the estimated number of home-schooled students in State A is approximately what percent greater than the number in State D?

A. 25%
B. 55%
C. 100%
D. 125%
E. 155%

D
The estimated number of home-schooled students in State A is greater than the number in State D by 181 - 79 = 102

Thus, the estimated number of home-schooled students in State A is approximately what percent greater than the number in State D by (102/79)*100%

Calculation of (102/79)*100% is challenging without a calculator, however, we can make 102 and 79 smart numbers to ease the calculation. Since the question itself asks for an approximate value, it is expected that we would face ugly numbers.

(102/79)*100% = ~(100/80)*100% = ~125%

Th actual answer would be greater than 125% since we decreased the numerator by 2 and increased the denominator by 1; however, we need not go deep into this as option E (155%) is far greater than ~125%.

The correct answer: D

Hope this helps!

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% greater = 100 * ((new value - old value)/(old value) - 1)

so

100 * ((181 - 79) / 79 - 1) =>

100 * ((102 / 79) - 1) =>

Since 102/79 is pretty close to 4/3, we can say that this is about

100 * (4/3 - 1) or

33%

D is the closest to this, so we're good to go.

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Hi All,

We're told that the estimated number of home-schooled students in State A is approximately what PERCENT GREATER than the number of students in State. While the formal use of the Percent Change Formula will certainly get you the correct answer, the numbers we're dealing with - along with the 'spread' of the Answer choices - provide a nice 'logic shortcut' that you can use to get the correct answer without doing too much math.

To start, it's worth noting that when a positive number is exactly DOUBLE another positive number, that larger number is 100% greater than the smaller number.

In this prompt, the numbers that we're comparing are 181 and 79. If we round those numbers off, we have 180 and 80. Doubling 80 would give us 160. Since 180 is greater than 160, we know that 181 is MORE than 100% greater than 79. 180 is not that much greater than 160 though, so given the two Answers that are greater than 100%, Answer D is almost certainly the correct answer (since 125% fits the logic far better than 155% does).

Final Answer: D

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AbeNeedsAnswers wrote:


According to the table shown, the estimated number of home-schooled students in State A is approximately what percent greater than the number in State D?

A. 25%
B. 55%
C. 100%
D. 125%
E. 155%
We can set up the following expression:

(181,000 - 79,000)/79,000 x 100

Estimating, we have:

(180,000 - 80,000)/80,000 x 100

100,000/80,000 x 100

10/8 x 100 = 5/4 x 100 = 125%

Answer: D

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Hi,

Regarding the solution below, how do we know what is the "new value" and the "old value" in this case that we are not really calculating a percentage change since both values take place in the same time period. Example, what if I was asked: what percent smaller is State D than State A?

Is there a formula that applies specifically to these "percent greater or percent smaller" problems?

Thanks!

Matt@VeritasPrep wrote:
% greater = 100 * ((new value - old value)/(old value) - 1)

so

100 * ((181 - 79) / 79 - 1) =>

100 * ((102 / 79) - 1) =>

Since 102/79 is pretty close to 4/3, we can say that this is about

100 * (4/3 - 1) or

33%

D is the closest to this, so we're good to go.

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estebanmorillo wrote:
Hi,

Regarding the solution below, how do we know what is the "new value" and the "old value" in this case that we are not really calculating a percentage change since both values take place in the same time period. Example, what if I was asked: what percent smaller is State D than State A?

Is there a formula that applies specifically to these "percent greater or percent smaller" problems?

Thanks!

Percent greater or percent increase:
(bigger value - smaller value)/(smaller value) * 100

Percent less or percent decrease:
(bigger value - smaller value)/(bigger value) * 100

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