If the product of the three digits of the positive integer k is 14, wh

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 3 variables and 1 Equation: Let the original condition in a DS question contain 3 variables and 1 Equation. Now, 3 variables and 1 Equation would generally require 2 more equations to give us the value of the variables.

We know that each condition would usually give us an equation, and since we need 2 more equations to match the number of variables and equations in the original condition, the equal number of equations and variables should logically lead to answer C.

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.

Let us give variable to each digit: Hundred's digit(a) ; Ten's digit(b) and One's digit(c).

=> k = 100a + 10b + c

=> We have to find the value of 'k'

=> Given that 'a * b * c = 14'.

Second and the third step of Variable Approach: From the original condition, we have 3 variables (a, b and c) and 1 Equation( abc = 14). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Let’s take a look at both condition together.

Condition(1) tells us that 'k' is an odd integer.

Condition(2) tells us that k < 700.

=> 14 can be expressed as a product of 3 numbers as = 1 * 2 * 7

=> Three digits number less than 100 in which product of digits is 14 are: 127, 172, 271, 217.

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


Both conditions (1) and (2) combined are not sufficient.

So, E is the correct answer.

Answer: E

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