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Source: — Data Sufficiency |
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by Patrick_GMATFix » Sat Mar 08, 2014 10:22 am
Percentage difference is a function of the ratio a/b. For instance if that ratio is 1.5/1, then a would be 50% greater than b.

Rephrase the Q: What is a/b?

(1) 4a = 5b means that a/b = 5/4. SUFFICIENT

(2) Knowing the absolute difference between values does not tell us the ratio. if b=1 and a=2001, the ratio is about 2001/1. On the other hand if b=1 trillion and a=1 trillion + 2000, the ratio ratio is about 1/1 (as the numbers get very big, the 2000 difference becomes almost insignificant). NOT SUFFICIENT

The answer is A

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by Matt@VeritasPrep » Sat Mar 08, 2014 10:39 am
candygal79 wrote:If a and b greater than zero, a is what percentage greater than b ?

1) 4a =5b 2) a=b+2000
To find "a is what % greater than b", we can use the percent change formula:

New - Old
---------
Old

or (a - b)/b

Using Statement 1, we have
4a = 5b
Or a = (5/4)b

Plugging that into our formula, we get

((5/4)b - b)/b, or (1/4b)/b, or 1/4, or 25%. Sufficient!

Using Statement 2, we have
a = b + 2000

Plugging that into our formula, we get

((b+2000) - b)/b, or 2000/b. Since we still have a variable in our equation, we can't solve for the percent difference. Insufficient.

Good q!
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by [email protected] » Sat Mar 08, 2014 7:45 pm
Hi candygal79,

This DS question can also be solved by TESTing Values.

We're told that A and B are greater than 0. We're asked for the value of A/B...

Fact 1: 4A = 5B

Let's TEST Values.

If....
A=5
B=4
A/B = 1.25

If A=10
B=8
A/B = 1.25

Etc.
Every possible set of values that you could test leads to the same answer.
Fact 1 is SUFFICIENT

Fact 2: A = B+2000

If...
B=1
A=2001
A/B = 2001/1 = 2001

B=2
A=2002
A/B = 2002/2 = 1001
Fact 2 is INSUFFICIENT

Final Answer: A

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