Multiple choice general knowledge

.Four prime numbers are arranged in ascending order. The product of first three is 385 and that of last three is 1001. The largest prime number is:

  1. 7

  2. 11

  3. 13

  4. 17
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C Correct answer
Explanation

Let the four primes in ascending order be p1, p2, p3, p4. Since p1×p2×p3 = 385 and p2×p3×p4 = 1001, we factor 385 = 5×7×11 and 1001 = 7×11×13. The middle two primes 7 and 11 overlap, so p2 = 7, p3 = 11, and thus p4 = 13, which is the largest prime.

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