Explanation

A prime number is any number that has no factors other than 1 and itself. It is wise to memorize the first 10 prime numbers before the GRE:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

If a is the smallest prime number greater than 21, it must be 23.

If b is the largest prime number less than 16, it must be 13.

Find ab:

\(23 \times 13 = 299\)

Hence option A is correct.
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The next prime above 21 is 23, since 22 is even. So a is 23.

The greatest prime less than 16 is 13, so b is 13.

Rather than multiply 13 and 23, notice that if you did, the units digit of the number will be 9, since 3x3 is 9. Since A is the only answer ending in 9, the answer must be A.
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The smallest prime number greater than 21 is 23. The largest prime number less than 16 is 13.

Thus, a x b = 23 x 13 = 299.

Answer: A
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