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Last Updated on May 5, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This is called a “defined function” problem. The parallel lines mean intrinsically nothing, except to establish a relationship between a^k and b. We are given that a^k || b means:
1) b/a^k = integer
2) b/a^(k+1) ≠ integer
Next we are given specific numbers 2^k || 72, and we must use the pattern to determine k, using a = 2 and b = 72; thus, we know:
72/2^k = integer AND 72/2^(k+1) ≠ integer
In order for 72/2^k = integer AND 72/2^(k+1) ≠ integer to be true, k must equal 3. If have trouble seeing how this works, we can plug 3 back in to prove it.
When k = 3, we know:
1) 72/2^3 = 72/8 = 9, which IS an integer.
AND
2) 72/2^(3+1) = 72/2^4 = 72/16 = 4 1/2, which is NOT an integer.
Answer: B
