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Is the sum of all the numbers between

Q) Is the sum of all the numbers between prime numbers x and y an even or an odd number?

1)    x = 3  y = 31
2)    y is the largest two digit number, x is even

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

To answer data sufficiency questions you don’t have to solve the problem. You just have to find the sufficient condition to prove the answer choice.

Question:  sum(x+1, x+2….y-1) = Odd or Even

Condition 1: x = 3  y = 31


Sum (4, 5,….30) = odd or Even

You don’t have to solve this but since you are aware of the sequence of numbers between x and y, the answer can be found.

Condition 1 is enough to answer the question

Condition 2: y is the largest two-digit number, x is even

The question mentions that x and y are prime numbers. Condition 2 provides two more additional information about the prime numbers.

Y is the largest two-digit number

Largest two-digit number is 99 but since question specifies that y is a prime number, y should be largest two digit prime number.

The only even prime number is 2. So x =2

Therefore we have to find the sum of all the numbers between  x = 2 and y= largest two digit prime number

Note: One mistake that test takers make is to spend time to find y, which is not necessary.
Once we get x and y, the sum can be calculated based on Arithmetic Progression.

Correct Answer: D

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