N is a four digit number. N = ABCD where A, B, C, D are distinct

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 4 variables: Let the original condition in a DS question contain 4 variables. Now, we know that each condition (1) and (2) would usually give us an equation each, however, since we need 4 equations to match the numbers of variables and equations in the original condition, the unequal number of equations and variables should logically give us an answer E.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find possible values of N exist for any fixed set of four values of A, B, C, D.

=> N = ABCD

Second and the third step of Variable Approach: From the original condition, we have 4 variables (A, B, C, and D).To match the number of variables with the number of equations, we need 4 equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.

Let’s take a look at both conditions combined together.

Condition(1) tells us that A + B + C + D = 10.

Condition(2) tells us that A + B + C - D = 8.

=> A + B + C = 10 - D and A + B + C = 8 + D

=> 10 - D = 8 + D

=> D = 1 and hence A + B + C = 9

For A + B + C = 9: 2 + 3 + 4 = 9 = 4 * 3 * 2 * 1 = 24 four-digit numbers.

For A + B + C = 9: 0 + 3 + 6 = 9 = 3 * 3 * 2 * 1 = 18 four-digit numbers.

Since the answer is not unique, both conditions together are not sufficient by CMT 2.

So, E is the correct answer.

Answer: E

NOTE: When you know that the most likely answer is E, combined both the conditions and solve. Don't solve separate conditions.