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Bunuel
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Bunuel
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

Let’s test each answer choice:

A) 500 to 520

(520 - 500)/500 x 100

20/500 x 100

2/50 x 100

Answer A is equivalent.

B) 200 to 208

(208 - 200)/200 x 100

8/200 x 100

2/50 x 100

Answer B is equivalent.

C) 100 to 104

(104 - 100)/100 x 100

4/100 x 100

1/25 x 100

Answer C is equivalent.

D) 25 to 26

(26 - 25)/25 x 100

1/25 x 100

Answer D is equivalent.

E. 10 to 12

(12 - 10)/10 x 100

2/10 x 100

Answer E is NOT equivalent.

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.

Let’s check the answer choices:

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.

Answer: E
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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

So our answer is E
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