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# If Mary has half as many cents as Nora has dollars, then No

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If Mary has half as many cents as Nora has dollars, then No [#permalink]  02 Jun 2018, 03:36
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Question Stats:

18% (00:00) correct 81% (01:04) wrong based on 11 sessions
If Mary has half as many cents as Nora has dollars, then Nora has what percent more cents than Mary does? (100 cents = 1 dollar)

(A) 100%
(B) 200%
(C) 1,990%
(D) 19,900%
(E) 20,000%
[Reveal] Spoiler: OA

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Re: If Mary has half as many cents as Nora has dollars, then No [#permalink]  06 Jun 2018, 15:20
Expert's post
sandy wrote:
If Mary has half as many cents as Nora has dollars, then Nora has what percent more cents than Mary does? (100 cents = 1 dollar)

(A) 100%
(B) 200%
(C) 1,990%
(D) 19,900%
(E) 20,000%

We can assume that Mary has 10 cents and thus Nora has 20 dollars, or 2000 cents. Using the “percent greater than” formula: (Nora - Mary)/Mary x 100%, we see that Nora has

(2000 - 10)/10 x 100%

1990/10 x 100%

199 x 100%

19,900% more cents than Mary does.

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Re: If Mary has half as many cents as Nora has dollars, then No [#permalink]  11 Jul 2018, 13:29
Expert's post
Explanation

Because no actual amounts of money are stated in the question, use smart numbers to solve this problem. If Mary has half as many cents as Nora has dollars, then, as an example, if Nora had $10, Mary would have 5 cents. Nora’s$10 equals 1,000 cents. To determine what percent more cents Nora has, use the percent change formula:

Percent Change=$$(\frac{Difference}{original} \times 100)$$

Percent Change=$$(\frac{1000-5}{5} \times 100)=19900\%$$

Any example in which “Mary has half as many cents as Nora has dollars” will yield the same result. Note that the percent change formula is required—a percent more (or percent increase) is not the same as a percent of something.

To do the problem algebraically (which is more difficult than using a smart number, as above), use M for Mary’s cents and N for Nora’s cents. Divide N by 100 in order to convert from cents to dollars, $$\frac{N}{100}$$, and set up an equation to reflect that Mary has half as many cents as Nora has dollars:

$$M= \frac{1}{2} (\frac{N}{100})$$

$$M=\frac{N}{200}$$

$$200M=N$$

Therefore, Nora has 200 times as many cents. 200 times as many is 199 times more. To convert 199 times more to a percent, add two zeros to get 19,900%.
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Re: If Mary has half as many cents as Nora has dollars, then No [#permalink]  10 Apr 2019, 07:22
As algebraic approach I would do the following:

"If Mary has half as many cents as Nora has dollars"

M = (1/2)*(N/100) - I divided by 100 because I need to 'equalize' cents Mary with cents Nora
M = N/200
N = 200M

"(...) then Nora has what percent more cents than Mary does? (100 cents = 1 dollar)"

"what percent more than" - is an "alert" that I need use the "percent greater than" formula:
(N - M)/M x 100%

so,
(200M - M)/M x 100% =
199/M x 100% =
19,900%

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Re: If Mary has half as many cents as Nora has dollars, then No   [#permalink] 10 Apr 2019, 07:22
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