Solution:
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.
Now we will solve this DS question using the Variable Approach.
Let’s apply the 3 steps suggested previously.
Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.
Let N = 11a + 10b + c. Then we have to find the maximum possible value of N.
Since N is a three-digit integer, we need the value of a to be the maximum possible value, and b > c.
Follow the second and the third step: From the original condition. We have 4 variables (N, a, b, and c) and 1 equation (N = 100a + 10b + c). To match the number of variables with the number of equations, we need 3 more equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.
Recall 3 Principles and choose E as the most likely answer. Let’s look at both conditions (1) and (2) together. They tell us that b > 2a + c and c > 0.
The maximum value b can take is 9. For 9 > 2a + c, let’s find values for a and c.
=> c > 0 means the values c can have start at 1.
=> 9 > 2a + 1 – In this case a = 3.
=> 9 > 2a + 2 – In this case a = 3
=> 9 > 2a + 3 – In this case a = 2.
The largest possible value of a is 3, and the maximum value of c is then 2.
Then, N = 100*3+ 10*9 + 2 = 392. The answer is unique, and both conditions (1) and (2) combined are sufficient, according to CMT 2, which states that the number of answers must be only one. So, C seems to be the answer.
Since this question is an integer question, which is also one of the key questions, we should apply CMT 4(A), which states that if an answer C is found too easily, either A or B should be considered as the answer.
Let’s look at each condition separately.
Condition (1) tells us that b > 2a + c, from which we get that for b to be greater than (2a + c), its value depends on a and c. We have digits from 0 to 9, so b cannot be greater than 9. Suppose b = 9. That means a can be 3, and c can be 2. Then we get 2a + c = 2*3 + 2 = 8 since 9 is greater than 8.
However, if a = 0, then b > c and c can have any value from 0 to 8.
Similarly, if c is 0, then b > 2a and a can have values from 0 to 4.
The answer is not unique, and the condition is not sufficient, according to CMT 2, which states that the number of answers must be only one.
Condition (2) tells us that c > 0, from which we cannot determine anything about the value of a.
The answer is not unique, and the condition is not sufficient, according to CMT 2, which states that the number of answers must be only one.
So, really, both conditions (1) and (2) combined are sufficient.
Both conditions (1) and (2) together are sufficient.
Therefore, C is the correct answer.
Answer: C
