In the country of Celebria, the \(Q\)-score of a politician is computed from the following formula:

[M7MBA]

In the country of Celebria, the \(Q\)-score of a politician is computed from the following formula:
\(Q=\dfrac{41ab^2c^3}{d^2},\) in which the variables \(a, b, c,\) and \(d\) represent various perceived attributes of the politician, all of which are measured with positive numbers. Mayor Flower’s \(Q\)-score is 150% higher than that of Councilor Plant; moreover, the values of \(a, b,\) and \(c\) are 60% higher, 40% higher, and 20% lower, respectively, for Mayor Flower than for Councilor Plant. By approximately what percent higher or lower than the value of \(d\) for Councilor Plant is the corresponding value for Mayor Flower?

A. 56% higher
B. 25% higher
C. 8% lower
D. 20% lower
E. 36% lower

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT

[Jay@ManhattanReview]

In the country of Celebria, the \(Q\)-score of a politician is computed from the following formula:
\(Q=\dfrac{41ab^2c^3}{d^2},\) in which the variables \(a, b, c,\) and \(d\) represent various perceived attributes of the politician, all of which are measured with positive numbers. Mayor Flower’s \(Q\)-score is 150% higher than that of Councilor Plant; moreover, the values of \(a, b,\) and \(c\) are 60% higher, 40% higher, and 20% lower, respectively, for Mayor Flower than for Councilor Plant. By approximately what percent higher or lower than the value of \(d\) for Councilor Plant is the corresponding value for Mayor Flower?

A. 56% higher
B. 25% higher
C. 8% lower
D. 20% lower
E. 36% lower

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT

Say the variables Qc, a, b, c, and d are for Councilor Plant and Qm, A, B, C, and D are for Mayor Flower.

Thus, we have

Qm = 2.5Qc;
A = 1.6a;
B = 1.4b; and
C = 0.8c

Thus,

\(\dfrac{41AB^2C^3}{D^2} =2.5 \times \dfrac{41ab^2c^3}{d^2}\)

\(\dfrac{41*1.6a*(1.4b)^2*(0.8c)^3}{D^2} =2.5 \times \dfrac{41ab^2c^3}{d^2}\)

Upon solving, we get D/d = 0.8

=> D = 80% of d

The correct answer: D

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

In the country of Celebria, the \(Q\)-score of a politician is computed from the following formula:
\(Q=\dfrac{41ab^2c^3}{d^2},\) in which the variables \(a, b, c,\) and \(d\) represent various perceived attributes of the politician, all of which are measured with positive numbers. Mayor Flower’s \(Q\)-score is 150% higher than that of Councilor Plant; moreover, the values of \(a, b,\) and \(c\) are 60% higher, 40% higher, and 20% lower, respectively, for Mayor Flower than for Councilor Plant. By approximately what percent higher or lower than the value of \(d\) for Councilor Plant is the corresponding value for Mayor Flower?

A. 56% higher
B. 25% higher
C. 8% lower
D. 20% lower
E. 36% lower

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT

We can let each of the values of a, b c and d in Councilor Plant’s Q-score be 10. Thus the values of a, b and c in Mayor Flower’s Q-score are 16, 14, and 8, respectively. We can let the value of d in Mayor Flower’s Q-score be n. Since the Q-score of Mayor Flower is 150% higher than that of Councilor Plant, we can create the equation:

41*16*(14)^2*(8)^3/n^2 = 2.5 * 41*10*10^2*10^3/10^2

16*196*512/n^2 = 2.5 * 10^4

16*196*512/(2.5*10^4) = n^2

n^2 = 64.22528

n ≈ 8

So Mayor Flower’s d-value is approximately 8, and since Councilor Plant’s d-value is 10, Councilor Plant’s d-value is (10 - 8)/8 = 2/8 = 1/4 = 25% higher than Mayor Flower's.

Answer: B