If (3c + 2d) / 2cd = 1, Then d = ?
a) 3c / (2c - 1)
b) c / (3c + 2)
c) 3c / (2c - 2)
d) (3c -1) / c
e) 3c / 2
If it CAN be solved with PIN, can someone please explain how?
If it CANNOT be solved with PIN, why not?
HELP! Can this problem be solved with Plugging in Numbers?
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- Ian Stewart
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It would be a pretty awkward problem to solve by plugging in numbers - I think if you were adept enough at math to see how to do that quickly, you'd likely find the actual algebra even quicker. You'd first need to find values of c and d that work in the equation given (for example, c = 2 and d = 3), then plug your value of c into each answer choice until you find one which is equal to d. If you find more than one answer that is equal to d, you'd need to pick a new set of numbers to differentiate between the remaining choices (if you try c = 2 and d = 3, you'll find that both answers C and E give you the correct value for d - that's just coincidence, so you need to try a different set of numbers to see which answer choice *always* gives the right value for d). I don't find that fast to do.
Algebraically, it's a four step problem. First cross multiply:
3c + 2d = 2cd
Then get terms with d in them to one side, since we want to solve for d:
3c = 2cd - 2d
Then factor out the d:
3c = d(2c - 2)
then divide on both sides by the thing in brackets:
3c/(2c- 2) = d
That's quite a standard sequence of steps to need to carry out in GMAT algebra, and it's much, much faster than plugging in numbers here, so it's worth learning.
Algebraically, it's a four step problem. First cross multiply:
3c + 2d = 2cd
Then get terms with d in them to one side, since we want to solve for d:
3c = 2cd - 2d
Then factor out the d:
3c = d(2c - 2)
then divide on both sides by the thing in brackets:
3c/(2c- 2) = d
That's quite a standard sequence of steps to need to carry out in GMAT algebra, and it's much, much faster than plugging in numbers here, so it's worth learning.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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- acaba007
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Thanks so much, Ian.
The way you solved it algebraically is much more condensed than the way Knewton did in the explanation of the answer, which is great!
I would like to know, though, what makes this problem jump out at you that it can be solved algebraically? I'm asking because there are variables in the question stem, as well as in the answer choices. I was taught that this usually means use PIN.
How can I differentiate between this problem and others in which PIN would be a good strategy?
The way you solved it algebraically is much more condensed than the way Knewton did in the explanation of the answer, which is great!
I would like to know, though, what makes this problem jump out at you that it can be solved algebraically? I'm asking because there are variables in the question stem, as well as in the answer choices. I was taught that this usually means use PIN.
How can I differentiate between this problem and others in which PIN would be a good strategy?