The Sum of Prime Numbers that are Greater than 60 but Less than 70 GMAT Problem Solving

Question: The sum of prime numbers that are greater than 60 but less than 70 is

(A) 67
(B) 128
(C) 191
(D) 197
(E) 260

Correct Answer: B
Solution and Explanation:

Approach Solution 1:
Given :

The prime numbers that are greater than 60 , but less than 70

Since prime numbers are natural numbers that are divisible by only 1 and the number itself.
So the prime numbers that are greater than 60, but less than 70 are 61 and 67

Since the prime numbers that are greater than 60 , but less than 70 are 61 and 67
Hence the required sum of prime numbers that are greater than 60 , but less than 70
= 61 + 67
= 128

Approach Solution 2:
Prime number: Nos which has exactly two factors(1 and number of itself)
Prime Nos greater than 60 and less than 70 are 61 and 67
Hence, sum of prime Nos= 61+67= 128

Approach Solution 3:
A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.

Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69

Immediately even numbers can be eliminated because they are divisible by 2 and thus are not prime.

We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.

To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.

We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.

Thus, we can eliminate 63 and 69 from the list because they are not prime.

Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime.
Thus, the sum of 61 and 67 is 128.

“The sum of prime numbers that are greater than 60 but less”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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