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The Quest for 700: Weekly GMAT Challenge

Each week Manhattan GMAT posts a GMAT question on our blog and follows up with the answer the next day. Are you up for the challenge?

The function p(n) on non-negative integer n is defined in the following way: the units digit of n is the exponent of 2 in the prime factorization of p(n), the tens digit is the exponent of 3, and in general, for positive integer k, the digit in the 10k–1th place of n is the exponent on the kth smallest prime (compared to the set of all primes) in the prime factorization of p(n). For instance, p(102) = 20, since 20 = 513022. What is the smallest positive integer that is not equal to p(n) for any permissible n?
(A) 1
(B) 29
(C) 31
(D) 1,024
(E) 2,310


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