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# What is the ratio of the percent decrease from 4 to 1 to the percent

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Math Expert
Joined: 02 Sep 2009
Posts: 47920
What is the ratio of the percent decrease from 4 to 1 to the percent  [#permalink]

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27 Dec 2017, 01:18
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Difficulty:

25% (medium)

Question Stats:

90% (00:55) correct 10% (01:09) wrong based on 21 sessions

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What is the ratio of the percent decrease from 4 to 1 to the percent decrease from 10 to 7?

A. 1 : 1
B. 5 : 2
C. 4 : 3
D. 15 : 7
E. 25 : 1

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Posts: 553
Re: What is the ratio of the percent decrease from 4 to 1 to the percent  [#permalink]

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27 Dec 2017, 02:19
Bunuel wrote:
What is the ratio of the percent decrease from 4 to 1 to the percent decrease from 10 to 7?

A. 1 : 1
B. 5 : 2
C. 4 : 3
D. 15 : 7
E. 25 : 1

We'll take a shortcut to calculation based on properties of ratios.
This is a Logical approach.

Ratios can be multiplied by a number without changing their value.
For example, a ratio of 4:1 is the same as 8:2 and 12:3.
To find the percent decrease from 4 to 1, we'll multiply by 25 to get 100 to 25.
We can SEE that this is a 75% decrease.
Similarly, multiplying 10 to 7 by 10 gives 100 to 70, a 30% decrease.
Therefore our answer is 75:30 = 15:6 = 5:2

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What is the ratio of the percent decrease from 4 to 1 to the percent  [#permalink]

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27 Dec 2017, 18:17
Bunuel wrote:
What is the ratio of the percent decrease from 4 to 1 to the percent decrease from 10 to 7?

A. 1 : 1
B. 5 : 2
C. 4 : 3
D. 15 : 7
E. 25 : 1

Percentage decrease: $$1-\frac{After}{Before}$$, so $$1-\frac{1}{4}=\frac{3}{4}=75$$% and $$1-\frac{7}{10}=\frac{3}{10}=30$$%

Ratio: $$\frac{3}{4}*\frac{10}{3}=\frac{10}{4}=\frac{5}{2}$$

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What is the ratio of the percent decrease from 4 to 1 to the percent  [#permalink]

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27 Dec 2017, 19:18
Bunuel wrote:
What is the ratio of the percent decrease from 4 to 1 to the percent decrease from 10 to 7?

A. 1 : 1
B. 5 : 2
C. 4 : 3
D. 15 : 7
E. 25 : 1

Percent change (decrease or increase):

$$\frac{Old-New}{Old} * 100$$

From 4 to 1:
$$\frac{4-1}{4}=\frac{3}{4}= .75 * 100 = 75$$ percent

From 10 to 7:
$$\frac{10-7}{10}=\frac{3}{10}=.30 * 100 = 30$$ percent

Ratio of first percent decrease to second percent decrease?
$$\frac{75}{30}=\frac{15}{6} =\frac{5}{2}$$

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What is the ratio of the percent decrease from 4 to 1 to the percent &nbs [#permalink] 27 Dec 2017, 19:18
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