coolhabhi wrote:Q) A and B are two numbers such that their G.M is 20% lower than their A.M .Find the ratio between the two numbers.
A)3:2
B)4:1
C)2:1
D)3:1
As I mentioned in my earlier post, we need not know the term "Geometric Mean." However, it is possible that a GMAT test question may first define "Geometric Mean" and then proceed to ask the original question. So, let's solve it.
Arithmetic Mean of A and B = (A+B)/2
Geometric Mean of A and B = √(AB)
Geometric Mean is 20% less than Arithmetic Mean
In other words, Geometric Mean = 80% of Arithmetic Mean
So, √(AB) = (80/100)[(A+B)/2]
Simplify right side: √(AB) = (40/100)(A+B)
Simplify: √(AB) = (2/5)(A+B)
Square both sides: AB = (4/25)(A+B)²
Expand right side: AB = (4/25)(A² + 2AB + B²)
Multiply both sides by 25: 25AB = 4(A² + 2AB + B²)
Expand: 25AB = 4A² + 8AB + 4B²
Set equal to zero: 4A² - 17AB + 4B² = 0
Factor: (4A - B)(A - 4B) = 0
So, (4A - B) = 0, or (A - 4B) = 0
If 4A - B = 0, then B = 4A, so their ratio is [spoiler]4:1[/spoiler]
If A - 4B = 0, then A = 4B, so their ratio is also [spoiler]4:1[/spoiler]
Answer:
B
Cheers,
Brent
