Question: What is the least prime number greater than 83 ?

      (A) 85
      (B) 87
      (C) 88
      (D) 89
      (E) 91

Answer: D

Solution and Explanation:

Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with basic mathematics. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Property: There are precisely two different positive factors, 1 and n, for prime numbers (n).
(A) 85 is divisible by five, hence, it is not prime.
(B) 87 is divisible by three (digit sum), hence it is not prime.
(C) 88 is divisible by two, hence, it is not prime.
(D) 89: Prime
(E) 91 = Divided by 13 and 7, thus NOT PRIME.
Correct Answer: D

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Prime numbers are always odd, with the exception of 2.
Hence, Option C was discarded.
Numbers ending in 5 are divisible by 5, and A was eliminated.
B was eliminated when 87 = 8 + 7 = 15 = 1 + 5 = 6 was divisible by 3.
89 is closest to 83 between 91 and 89.
Correct Answer: D

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
The next prime number greater than 83 is either 89 or 91.
We can quickly eliminate 91 as a possibility because it is not a prime number (it is divisible by 7).
Whether or not 89 is prime can be shown by seeing if its square root is divisible by any prime integers smaller than or equal to it (since any composite number must have at least one factor less than or equal to its square root). Since 9.4 is close to the square root of 89, just the primes 2, 3, 5, and 7 need to be checked for divisibility.
It follows that 89 is prime because it cannot be divided by 2, 3, 5, or 7.
Hence, 89 is the largest prime number that is not greater than 83.
Correct Answer: D

“What is the least prime number greater than 83 ?" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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