Each of a, b, and c is positive. Does B = root AC ?
STATEMENT 1:
a/b = b/c
STATEMENT 2:
1/b^3 = 1/(ABC)
IMO - E
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Each of a, b, and c is positive. Does ? STATEMENT 1: STATE
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Target question: Does B = sqrt(AC)?varun289 wrote:Each of a, b, and c is positive. Does B = root AC ?
STATEMENT 1: a/b = b/c
STATEMENT 2: 1/b^3 = 1/(ABC)
This is a great candidate for rephrasing the target question.
Take B = sqrt(AC) and square both sides to get: B^2 = AC
Rephrased target question: Does B^2 = AC?
Aside: If anyone is interested, we have a free video on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: A/B = B/C
Cross multiply to get B^2 = AC
Perfect. This means that B^2 definitely equals AC
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: 1/B^3 = 1/(ABC)
Cross multiply to get B^3 = ABC
Divide both sides by B to get B^2 = AC
Perfect. This means that B^2 definitely equals AC
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
NOTE: Our solution was made easier by the fact that A, B and C are positive. For example, if it were possible that B=0, then we wouldn't be able to divide both sides of the equation by B, as we did with statement 2.
Cheers,
Brent
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sonalibhangay
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I thought of Geometric mean on this question:
The question asks, is 'b' the Geomtric mean ? and are these +ve numbers in GP?
S1 - Ratio between two consecutive elements is same = this is a GP ---- > and b is the central value = Geometric Mean
S2- Second is really a deduction. b^2 = AC .
Hope this line of thought is alright!
The question asks, is 'b' the Geomtric mean ? and are these +ve numbers in GP?
S1 - Ratio between two consecutive elements is same = this is a GP ---- > and b is the central value = Geometric Mean
S2- Second is really a deduction. b^2 = AC .
Hope this line of thought is alright!
