If \(2^4,3^3 and11^3\) are Factors of the Product of 1,452 and w, Where GMAT Problem Solving

Question: If \(2^4,3^3 and11^3\)are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?

1. 198
2. 288
3. 363
4. 396
5. 484

Answer:
Solution with Explanation:
Approach Solution (1):

1452 = \(2^4*3 * 11^2\)

\(2^4,3^3 and11^3\)are factors of the product of 1,452 and w

So, \(2^4,3^3 and11^3=2^4*3 * 11^2*w\)

Or, w = \(2^2*3^2 * 11=4*9*11=396\)

Correct Option: D

Approach Solution (2):

\(\frac{1452*w}{2^4*3^3*11^3}=integer\)

\(2^2*3*11^2=1452\)

\(\frac{1452*w}{2^4*3^3*11^3}= \frac{2^2*3*11^2}{2^4*3^3*11^3}\)

\(\frac{w}{2^2*3^2*11}= integer\)

The minimum possible positive value of w is when the value of integer is minimum positive value i.e., 1

\(\frac{w}{2^2*3^2*11}= 1\)

\(w=2^2*3*11=4*9*11=396\)

Correct Option: D

“Ifare factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?”- 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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