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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6616
GMAT 1: 760 Q51 V42
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The relationship between the cost (c) and time (t) is given by the equ  [#permalink]

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27 Jun 2018, 00:59
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Difficulty:

45% (medium)

Question Stats:

51% (01:09) correct 49% (01:32) 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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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 13 Feb 2018 Posts: 135 The relationship between the cost (c) and time (t) is given by the equ [#permalink] Show Tags 27 Jun 2018, 01:58 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 Senior Manager Joined: 04 Aug 2010 Posts: 310 Schools: Dartmouth College Re: The relationship between the cost (c) and time (t) is given by the equ [#permalink] Show Tags 27 Jun 2018, 02:30 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. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Senior Manager Joined: 29 Dec 2017 Posts: 385 Location: United States Concentration: Marketing, Technology GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37 GMAT 3: 710 Q50 V37 GPA: 3.25 WE: Marketing (Telecommunications) The relationship between the cost (c) and time (t) is given by the equ [#permalink] Show Tags 27 Jun 2018, 05:18 $$c=mt+b$$. 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) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6616 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The relationship between the cost (c) and time (t) is given by the equ [#permalink] Show Tags 29 Jun 2018, 00:14 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Joined: 20 Apr 2018
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Concentration: Technology, Nonprofit
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Re: The relationship between the cost (c) and time (t) is given by the equ  [#permalink]

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29 Jun 2018, 01:07
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.

Re: The relationship between the cost (c) and time (t) is given by the equ &nbs [#permalink] 29 Jun 2018, 01:07
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