The relationship between the cost (c) and time (t) is given

[Max@Math Revolution]

[GMAT math practice question]

The relationship between the cost (c) and time (t) is given by the equation c=mt+b. If the time is increased by 10, by how many dollars is the cost increased?

1) m=20
2) b=30

[GMATGuruNY]

[GMAT math practice question]

The relationship between the cost (c) and time (t) is given by the equation c=mt+b. If the time is increased by 10, by how many dollars is the cost increased?

1) m=20
2) b=30

Original cost = mt+ b.
When the time increases by 10, we get:
New cost = m(t+10) + b = mt + 10m + b.
Thus:
Increase in the cost = new cost - original cost = (mt + 10m + b) - (mt + b) = 10m.
To determine the increase in the cost, we need to know the value of m.
Question stem, rephrased:
What is the value of m?

Statement 1: m=20
SUFFICIENT.

Statement 2: b=10
No information about m.
INSUFFICIENT.

The correct answer is A.

[Max@Math Revolution]

=>
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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The increase in the cost when the time is increased by 10 is given by
m(t + 10) + b - (mt + b) = 10 m. As this depends on the variable m only,
condition 1) is sufficient.

Therefore, the answer is A.

Answer: A