\(42^{9}\) is divisible by each of the following except? GMAT Problem Solving

Question: 42⁹ is divisible by each of the following except?

   A. 16
   B. 36
   C. 49
   D. 84
   E. 132

Answer: E

Approach Solution (1):
Scan the answer choices
E = 132
132 = (2) (2) (3) (11)
Since there are no 11’s in the prime factorization of 42⁹, we can conclude that 42⁹ is not divisible by 132
Correct option: E

Approach Solution (2):
A. 16 = 42⁹ = 2⁹ * 3⁹ * 7⁹ , 16 = 2⁴ , so 42⁹ is divisible by 16
B. 36 = 42⁹ = 2⁹ * 3⁹ * 7⁹ , 36 = 2² * 3² , so 42⁹ is divisible by 36
C. 49 = 42⁹ = 2⁹ * 3⁹ * 7⁹ , 49 = 7² , so 42⁹ is divisible by 49
D. 84 = 42⁹ = 2⁹ * 3⁹ * 7⁹ , 84 = 2² * 3⁷ , so 42⁹ is divisible by 84
E. 132 = 42⁹ = 2⁹ * 3⁹ * 7⁹ , 132 = 2² * 3 * 11 , so 42⁹ is not divisible by 132
Correct option: E

Approach Solution (3):
42 = 2 * 3 * 7
Search for a option which has some prime number apart from these
Option E
132 = 2 * 2 * 3 * 11
Since 42⁹ does not have 11 in it so it won’t be divisible by 132
Correct option: E

“ 42⁹ is divisible by each of the following except?”- 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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