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Inequality type question...

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by nysnowboard » Wed Apr 28, 2010 12:43 am
I got this from the free Manhattan flashcards, the EIV set.

I don't really get the explanation. If someone could clarify what they mean I would really appreciate it!

Question:
If c < 4, what is the range of possible
values of d for the equation
3c = −6d?

Answer:

Answer: d > -2
We can actually replace c with its extreme value, which is "less
than 4." The equation will read 3(less than 4) = −6d. So (less
than 12) = −6d. Divide by −6, and remember to flip the sign,
because we're dividing by a negative. Thus we have (greater
than −2) = d.


Although I am not a quant master, I am not exactly a slouch either. This explanation makes no sense to me, specifically the parenthesized items. "The equation will read 3(less than 4) = -6d...." how exactly does this look in a formula?

From their explanation I am seeing:

3 > 4 = -6d
>12 = -6d
<2 = d

This is nonsensical to me... Any takers?
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by Fiver » Wed Apr 28, 2010 7:41 am
I suggest taking a logical approach.

We are asked the range of a variable 'd', hence it is best to identify the max or the min value of d.
Given c<4. This means that 'c' can take a value miniscule away from 4.
So to take 4 as the ending point of c will make sense.

3*4 = -6d
d = -2 when 'c' is just out of the range on the max side.
For other declining values of 'c' the LHS will take a lower value and subsequently |d| will also be lower than 2.
Since 'd' we know is negative, it is logical to say that d>-2.
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by nysnowboard » Thu Apr 29, 2010 1:39 am
Thank you. I understand your approach and it is more logical than the original solution.

What does "LHS" stand for in your post?

I can either see the solution to these kinds of problems within a minute or I am lost forever...

Is there any standard way to approach them or do I just need to practice them until I can handle new ones efficiently?
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by Fiver » Thu Apr 29, 2010 11:34 pm
nysnowboard wrote:Thank you. I understand your approach and it is more logical than the original solution.

What does "LHS" stand for in your post?

I can either see the solution to these kinds of problems within a minute or I am lost forever...

Is there any standard way to approach them or do I just need to practice them until I can handle new ones efficiently?
Sorry about that. LHS stands for Left Hand Side, left of any sign 'equality' , inequality etc.

Talking about standard methods, they vary based on the problem presented and i have always tried to first devise a logical approach and only then look for standard(s) that may help.
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by nysnowboard » Thu Apr 29, 2010 11:41 pm
Ah, got it =). Your explanation is 100% clearer now that I know what LHS means.
Payment: One crisp, new Bgmat thank you!
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by Fiver » Thu Apr 29, 2010 11:59 pm
nysnowboard wrote:Payment: One crisp, new Bgmat thank you!
Just got richer :D
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by tyronetan82 » Thu Jul 29, 2010 4:13 am
For other declining values of 'c' the LHS will take a lower value and subsequently |d| will also be lower than 2.

Any fast way to figure out/prove how declining values of 'c' will subsequently have |d| be lower than 2? The way I did it to figure this out was to plug in numbers where c<4 which in GMAT time will take tooooo long.

Any tips or tricks will be greatly appreciated! Thanks
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