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A.P,G.P Question

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A.P,G.P Question

by alexi_laiho » Thu Aug 07, 2008 5:02 am
What are the two positive numbers?
(A) Their geometric mean is equal to their arithmetic mean
(B) Their geometric mean is greater than their arithmetic mean by 1.5


1. statement (A) alone is sufficient but statement (B) alone is not
2. statement (B) alone is sufficient but statement (A) alone is not
3. both (A) and (B) together are sufficient but none of them alone is sufficient
4. both statements are sufficient independently
5. both (A) and (B) together are not sufficient

Please provide your answers with explanations..thanks in advance
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Source: — Data Sufficiency |

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Re: A.P,G.P Question

by Ian Stewart » Thu Aug 07, 2008 6:27 am
alexi_laiho wrote:What are the two positive numbers?
(A) Their geometric mean is equal to their arithmetic mean
(B) Their geometric mean is greater than their arithmetic mean by 1.5
This is definitely not a real GMAT question (what is the source?).

First, you do not need to know what a 'geometric mean' is for the GMAT.
Second, the two statements contradict each other, making it logically impossible to consider the two statements together, which can never happen on the GMAT.

In any case, I'll show that the first statement is insufficient, and the method can be applied to the second. Call the two numbers a and b:

Their arithmetic mean is (a+b)/2
Their geometric mean is sqroot(ab)

We know these are equal:

(a+b)/2 = sqroot(ab)
a - 2sqroot(ab) + b = 0
(sqroot(a) - sqroot(b))^2 = 0

So sqroot(a) = sqroot(b), and a = b. That's all we learn from Statement 1, so it is not sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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