If a + b + c = 50, what is the value of a ?

1. c = 4a-6 , this does not give any information about exact numbers. Insufficient.

2. Average of b+c = 2a , which means b+c = 4a. But we do not have necessary information to calculate exact values. Insufficient. option 2

Now consider option 1 and 2 together , we can derive the value of a =10.

Ans: Option C
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Statement 1
c = 4a - 6, substituting this in original equation we get:
a + b + 4a - 6 = 50 or 5a + b = 56.
But until we know the value of b, we cannot find 'a'. So not sufficient.

Statement 2
Given, (b+c)/2 = 2a or b+c = 4a. Substituing this in original equation we get:
a + 4a = 50 or 5a = 50 or a=10. This is sufficient.

Hence B answer

1) C=4A-6 but there is no info about b insufficient

2) b+c/2 = 2a b+c = 4a

a+b+c = 50 substitute above value 5a=50 a =10

(B) imo
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now we know b+c = 4a

we have a+b+c=50
now substitute in the above value
a+4a = 50

a= 10

(B)
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Hi Bunuel

Answer here is shwn as D. How can one proceed to find the value of a with Statement 1 only?

Thanks

The correct answer is B. Edited. Thank you.
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Average of b+c = 2a , which means b+c = 4a.

Replace b+c = 4a in the given equation and you will get

a + 4a = 50

a = 10

Sufficient (B)
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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 be able to solve for the variables.

We know that each condition would usually give us an equation, resulting in a total of 3 equations, one each from the original condition, condition (1), and condition (2). Since we need 2 more equations to match the numbers of variables and equations in the original condition, an equal number of equations and variables should logically give us an 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.

=> We have to find the value of 'a' : Given a + b + c = 50


Second and the third step of Variable Approach: From the original condition, we have 3 variables (a, b and c) and 1 Equation ( a + b + c = 50). To match the number of variables with the number of equations, we need 2 more 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 the condition together.

Condition(1) tells us that c = 4a - 6 and Condition (2) tells us that the average of b and c is 2a.

=> Average of b and c is 2a: b + c = 2 * 2a = 4a

=> b + 4a - 6 = 4a . Therefore , b = 6.

=> a + c = 44 and 4a - c = 6. Both equation will give us value of a.

Since the answer will be unique, both the conditions combined together are sufficient by CMT 2.

The answer should be C.

But this is a Common Mistake Type Concept4(A) in which if it easy to find C as an answer choose A or B as an answer. This is applied to key questions that involve integers, statistics, inequality. [watch our lessons to learn this tips]

Let's take each condition separately

Condition(1) tells us that c = 4a - 6

As there is no information about 'b', we cannot find the unique value of 'a'

[b]Since the answer is not unique, the condition is not sufficient by CMT 2.[/b]


Condition(2) tells us that b + c = 4a

=> a + b + c = 50

=> a + 4a = 50

=> a = 10

[b]Since the answer is unique, the condition is sufficient by CMT 2.[/b]


Condition (2) alone is sufficient.

So, B is the correct answer.

Answer: B