If a and b greater than zero, a is what percentage greater than b ?
1) 4a =5b 2) a=b+2000
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candygal79
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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
-Patrick
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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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To find "a is what % greater than b", we can use the percent change formula:candygal79 wrote:If a and b greater than zero, a is what percentage greater than b ?
1) 4a =5b 2) a=b+2000
New - Old
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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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
