Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
First, translate the expression 21#42, using the definition given:
21#42 = 21×24×27×30×33×36×39×42
You need the prime factorization of this enormous product.
Since these are consecutive multiples of 3, a good move is to factor out that 3 from each multiple. You have 8 multiples, all multiplied together, so you get 38:
21#42 = 38(7×8×9×10×11×12×13×14)
Now replace each consecutive integer with its prime factorization:
21#42 = 38(7×2×32×(2×5)×11×(22×3)×13×(2×7))
Group up the prime bases:
21#42 = 27×311×5×72×11×13
Don’t forget to put in an understood 1 for the primes lacking explicit exponents:
21#42 = 27×311×51×72×111×131
Finally, add up the exponents:
7 + 11 + 1 + 2 + 1 + 1 = 23
The correct answer is A.