Proportions

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shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 amFollowed by: 1 member; Thanked: 3 times

by shanice » Wed Aug 15, 2012 10:17 am

Guys, I need your help in the proportion topic.

What is direct proportionality,inverse proportionality and linear growth means? Please give some examples.

Really appreciate the help as I'm pretty weak in this area.

Thank you.

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Source: Beat The GMAT — Problem Solving | Wed Aug 15, 2012 10:17 am

Kobe_Kassidy: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Aug 06, 2012 8:06 am; Thanked: 1 times

by Kobe_Kassidy » Wed Aug 15, 2012 12:13 pm

shanice wrote:Guys, I need your help in the proportion topic.

What is direct proportionality,inverse proportionality and linear growth means? Please give some examples.

Really appreciate the help as I'm pretty weak in this area.

Thank you.

Direct proportionality means that, in a proportion, as one element increases/decreases, the other element increases/decreases as well. Example: If it takes 5 hours to make 10 shirts, how many shirts can be made in 15 hours? The answer is 30. As the number of hours increases, so does the number of shirts you can make.

Inverse proportionality means the exact opposite. In a proportion, as one element increases/decreases, the other element decreases/increases, meaning it moves in the opposite direction. Example: If it takes 10 hours to drive to your mom's house at a speed of 50mph, how long would it take to make the same trip driving at a speed of 100mph? The answer is 5 hours. As your rate of speed increases, the time taken to cover a specified distance decreases.

Linear growth means to grow at a fixed amount per unit of increase (i.e. growth that can be graphed using a straight line). Example: It costs $10 dollars to manufacture one widget. As you manufacture more widgets, your total cost will increase by $10 per additional widget.

Hope this helps.

-KK

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Wed Aug 15, 2012 1:00 pm

shanice wrote:Guys, I need your help in the proportion topic.

What is direct proportionality,inverse proportionality and linear growth means? Please give some examples.

Really appreciate the help as I'm pretty weak in this area.

Thank you.

x is directly proportional to y
In terms of an algebraic formula it means
x = k*y
where, k is a constant and is called constant of proportionality
OR
If y = 0, then x = 0, and as we increment y by 1 unit, x increases by k units.

x is inversely proportional to y
This means
x = k/y
Speed-distance-time is an example for this.
T = D/S
If the distance is constant. Speed is said to be inversely proportional to Time.
If you increase the speed, time decreases and vice versa.

x grows linearly as y is incremented
x = k*y + c

If y = 0, then x = c, and as the value of y is incremented by 1 unit, value of x increments by k units.
Direct proportionality is also an example of linear growth. In this case, c = 0.

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shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 amFollowed by: 1 member; Thanked: 3 times

by shanice » Wed Aug 15, 2012 7:46 pm

Kobe_Kassidy & rijul007,

Your explanation about this topic is really good. I understand it clearly and can't wait to do some questions on proportions.

Thanks for helping out guys.

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