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# The percent change from 50 to 52 is NOT equivalent to the percent chan

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Joined: 02 Sep 2009
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The percent change from 50 to 52 is NOT equivalent to the percent chan  [#permalink]

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28 Sep 2017, 01:44
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25% (medium)

Question Stats:

88% (00:38) correct 12% (00:21) wrong based on 34 sessions

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The percent change from 50 to 52 is NOT equivalent to the percent change from

A. 500 to 520
B. 200 to 208
C. 100 to 104
D. 25 to 26
E. 10 to 12

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The percent change from 50 to 52 is NOT equivalent to the percent chan  [#permalink]

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28 Sep 2017, 01:55
The percent change from 50 to 52 is NOT equivalent to the percent change from ?

% change from 50 to 52 = (52-50)/50 * 100 = 4% increase

A. 500 to 520 => 20/500 * 100 = 4%
B. 200 to 208 => 8/200* 100 = 4
C. 100 to 104 => 4/100* 100 = 4
D. 25 to 26 => 1/25* 100 = 4
E. 10 to 12 => 2/10 * 100 = 20

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The percent change from 50 to 52 is NOT equivalent to the percent chan  [#permalink]

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28 Sep 2017, 10:38
Bunuel wrote:
The percent change from 50 to 52 is NOT equivalent to the percent change from

A. 500 to 520
B. 200 to 208
C. 100 to 104
D. 25 to 26
E. 10 to 12

30-second way, no long division, no calculating percent change: Use a multiplier or compare fractions. These answers' numbers are easy.

This question is about equivalent ratios, too. For percent change to be equivalent, the ratio of (A:B) in the answers must be identical to ratio of 50:52.

Choose the easiest: multipliers, divisors, or fraction comparison ($$\frac{50}{52}$$ compared to $$\frac{A}{B}$$)

A) 500 to 520:
50 * 10 = 500
52 * 10 = 520
Same multiplier. Ratio holds. Equivalent percent change. EQUIVALENT

B. 200 to 208:
50 * 4 = 200. 52 * 4? 208. EQUIVALENT

C. 100 to 104
50 * 2 = 100. 52 * 2? 104. EQUIVALENT

D. 25 to 26
$$\frac{50}{2}$$ = 25. $$\frac{52}{2}$$? 26. EQUIVALENT

E. 10 to 12:
By POE this is the answer.
10 * 5 = 50. 12 * 5?
12 * 5 = 60, and $$60\neq{52}$$.
Ratios are not equivalent. Hence percent change is NOT EQUIVALENT.*

*If in doubt, do the math for just this answer.
Percent change from 50 to 52?
$$\frac{52-50}{50} = \frac{2}{50}$$ = .04 * 100 = 4%

Percent change from 10 to 12?
$$\frac{2}{10}$$ = .20 * 100 = 20%

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Re: The percent change from 50 to 52 is NOT equivalent to the percent chan  [#permalink]

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03 Oct 2017, 10:04
Bunuel wrote:
The percent change from 50 to 52 is NOT equivalent to the percent change from

A. 500 to 520
B. 200 to 208
C. 100 to 104
D. 25 to 26
E. 10 to 12

To solve, we’ll use the percent change formula: (new - old)/old x 100.

The percentage change from 50 to 52 is:

(52 - 50)/50 x 100 = (2/50 x 100) = (1/25) x 100

A) 500 to 520

(520 - 500)/500 x 100

20/500 x 100

2/50 x 100

B) 200 to 208

(208 - 200)/200 x 100

8/200 x 100

2/50 x 100

C) 100 to 104

(104 - 100)/100 x 100

4/100 x 100

1/25 x 100

D) 25 to 26

(26 - 25)/25 x 100

1/25 x 100

E. 10 to 12

(12 - 10)/10 x 100

2/10 x 100

Alternate solution:

If the numbers have the same percentage change as that from 50 to 52, they must have the same ratio as 50 to 52.

We see that the ratio of 50 : 52 = 25 : 26 after simplifying.

A) 500 to 520 = 50 : 52 = 25 : 26

B) 200 to 208 = 50 : 52 = 25 : 26

C) 100 to 104 = 50 : 52 = 25 : 26

D) 25 to 26 = 25 : 26

E) 10 to 12 = 5 : 6 ≠ 25 : 26

Since 10 to 12 does not have the same ratio as 50 to 52, its percentage change is NOT equivalent to that of 50 to 52.

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Re: The percent change from 50 to 52 is NOT equivalent to the percent chan  [#permalink]

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03 Oct 2017, 11:18
Simplest way is to look at ratios. If ratio to A:B is same as ratio of C:D, then the percentage difference of B from A is going to be exactly the same as percentage difference of D from C - and vice versa. Given quantities ratio = 52/50 = 26/25

Lets go through our options

A. 520/500 = 26/25 same
B. 208/200 = 26/25 same
C. 104/100 = 26/25 same
D. 26/25 same
E. 12/10 = 6/5 Not Same

Re: The percent change from 50 to 52 is NOT equivalent to the percent chan &nbs [#permalink] 03 Oct 2017, 11:18
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