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

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New post 27 Jun 2018, 01:59
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

47% (00:58) correct 53% (01:06) wrong based on 64 sessions

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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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New post 27 Jun 2018, 02:58
In My Opinion Answer should be E

We are not given the initial amount of t
if t=10 then 10% increase leads to t=11
if t=100 then 10% increase leads to t=110

This day is full of confusions, I missed several concepts I thought I've already mastered :)
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Re: The relationship between the cost (c) and time (t) is given by the equ  [#permalink]

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New post 27 Jun 2018, 03:30
MathRevolution 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.


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The relationship between the cost (c) and time (t) is given by the equ  [#permalink]

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New post 27 Jun 2018, 06:18
\(c=mt+b\). If the time is increased by \(10\), by how many dollars is the cost increased?

\(c(1)=mt+b\)
\(c(2)=m(t+10)+b\)

\(c(2)-c(1)=m(t+10)+b-(mt+b)=10m\) - increase will depend on value of m only

\(1) m=20\) - Suff
\(2) b=30\) - Not Suff

Answer (A)
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New post 29 Jun 2018, 01:14
=>
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
\(m(t + 10) + b – (mt + b) = 10m\). As this depends on the variable m only,
condition 1) is sufficient.

Therefore, the answer is A.

Answer: A
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Re: The relationship between the cost (c) and time (t) is given by the equ  [#permalink]

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New post 29 Jun 2018, 02:07
The simplest way here seems for me is to think about what slope of a line represents.

Here, delta(cost)/delta(time) = m <- the slope
we are given delta(time) = 10
We need slope for delta(cost)

Statement 1 is sufficient.

Statement 2 does not tell us what the slope is. Not sufficient.

Answer: A
Re: The relationship between the cost (c) and time (t) is given by the equ &nbs [#permalink] 29 Jun 2018, 02:07
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