X = 2*(P/ Q)^(n+1). Find X if P, Q and n are positive integers.

Question

X = 2*(\frac{P}{Q})^{n+1} . Find X if P, Q and n are positive integers.

(1) Both P and Q have only 3 factors

(2)  \frac{P^{n-1}}{Q^{2n-1}}= \frac{49}{64}

gmatophobia · Answer

Statement 1

P & Q are squares of an integer. However, we do not know the individual value of P, Q and n. Hence this statement is not sufficient.

Statement 2

\frac{P^{n-1}}{Q^{2n-1}}= \frac{49}{64}

49 can be represented as -  49^1  or  7^2

Case 1   : If the numerator is in the form  x^1

Denominator is in the form  y ^ 3

P = 49
Q = 4
n = 2

However, we can also have some factor that was present in P and Q and that got cancelled out when  P^1  was divided by  Q^3

Ex: 
 P^1 = (49 * 11^3)^1
Q^3 = (4*11)^3
n = 2

In this case we will get a different result for the question. At this stage itself we can conclude that statement 2 is not sufficient. However, let's also check if there are any other power of the numerator that can work.

Case 2   : If the numerator is in the form  x^2

Denominator is in the form  y ^ 5

In this case, n = 3.

However 64 cannot be expressed in the form any integer to the power of 5. Hence we have to discard this case.

Combined

The statements combined we know that P & Q must be perfect squares. Hence P = 49, Q = 4 and n = 2.

Statements combined is sufficient.

Option C

X = 2*(P/ Q)^(n+1). Find X if P, Q and n are positive integers.

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GMAT Data Sufficiency (DS) Questions

X = 2*(P/ Q)^(n+1). Find X if P, Q and n are positive integers.

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