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

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

by Max@Math Revolution » Wed Jun 27, 2018 12:48 am

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[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
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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Jun 27, 2018 2:29 am

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Max@Math Revolution wrote:[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.
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by Max@Math Revolution » Fri Jun 29, 2018 12:04 am

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=>
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
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