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?
- 198
- 288
- 363
- 396
- 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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