Consider this set of 5 Integers. {7, C, A, T, 23} What is the Sum of

Wrong OA imo

Statement 1-

2 of the Possible sets

1. {7, 10, 15, 17, 23}; sum= 72
2. {7, 11, 15, 19, 23}; sum=75

Insufficient

Statement 2-

2 of the Possible sets

1. {7, 8, 13, 14, 23}; sum=65
2. {7, 11, 15, 19, 23}; sum= 75

Insufficient

Combining 2 statements

sum= 5*15=75

Sufficient

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 3 variables (C, A and T) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since (7+C+A+T+23)/5 = Mean = Median = 15, we have 7+C+A+T+23 = 75.
Since both conditions together yield a unique solution, they are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If C=8, A=15, T=16, then 7+C+A+T+23 = 7+8+15+16+23=69.
If C=8, A=15, T=17, then 7+C+A+T+23 = 7+8+15+17+23=70.

Since condition 1) does not yield a unique solution, it is not sufficient

Condition 2)

If C=8, A=15, T=22, then 7+C+A+T+23 = 7+8+15+22+23=75.
If C=13, A=16, T=21, then 7+C+A+T+23 = 7+13+16+21+23=80.
Since condition 2) does not yield a unique solution, it is not sufficient

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

(1) Among the remaining 3 integers, now we know the value of one, which is the median of the set. Not sufficient.

(2) The mean and median are same, so the sum will be 5* Mean or 5* Median. We need the value of the mean or median. Not sufficient.

Together we can deduce the sum of this set. Sufficient.

Both statements combined are correct
A Tells median = 15 . Not useful alone
B tells median = mean again not sufficient
Combine
tells Mean = median = 15
now sum is always equal to mean * number of elements
given number of elements = 5
hence sum = 15 *5 = 75

Thus C