If 2p + 1/p = 4, Then what is the Value of p^3 + 1/8p^3 ? GMAT Problem Solving

Question: If \(2p+\frac{1}{p}=4\), then what is the value of \(p^3+\frac{1}{8p^3}\) ?

1. 4
2. 5
3. 8
4. 15
5. 16

Answer: B

Approach Solution (1):

\(2p+\frac{1}{p}=4\)

Let's divide by 2 in LHS & RHS
=> p + \(\frac{1}{2p}\)= 2...(1)
Let's square the expression
=> \(p^2+ 1/4 p^2 + 1= 4\)
=> \(p^2+ 1/4p^2 = 3...(2)\)
Now we have to get the value of p^3 + 1/8p^3
This expression can be re-written as

\((p + 1/2p)( p^2+ 1/4p^2 -\frac{1}{2} )\)

Plugging the value from equations (1) & (2) above

\((p +\frac{1}{2p})( \frac{1}{p}+ 1/4p^2 -\frac{1}{p}) = 2*(3 -\frac{1}{2} ) = 5\)

Correct Option: B

“If \(2p+\frac{1}{p}=4\) , then what is the value of \(p^3+\frac{1}{8p^3}\) ?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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