Generally, we've been taught that you should never divide by a variable unless you are certain that the value of the variable is not 0.
I was reviewing a data sufficiency question in the Manhattan GMAT Algebra Strategy guide (pg 116 in 5th ed) and I noticed that the explanation allowed for division by a variable.
The question reads:
If a = 3bc, what is the value of c?
The book suggests you manipulate a = 3bc to c = a/3b or 1/3(a/b) where if you can find a/b, it's sufficient.
Statement 1) a = 10-b
a/b = (10-b)/b Insufficient
Statement 2) 3a = 4b
a/b = 4/3 Sufficient
How do we distinguish between situations where dividing by a variable is ok? How do we know for sure that neither a,b, or c = 0?
For example, when ab = a, we cannot assume that b = 1. What's different? Does it have to do with simplifying vs. eliminating a variable entirely?
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Dividing by a variable
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[email protected]
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Hi xiamsamx,
What you're asking about is somewhat 'circumstantial' (meaning that the specific information and the specific question that is asked will determine what type of math you should or shouldn't be doing).
There's a difference between 'dividing out' a variable and dividing by a variable.
For example, if you have the equation...
X^2 = X
This equation has 2 solutions. Can you figure them out? What happens if you divide both sides by X first (how many solutions do you end up with then?)? By dividing by a variable, you end up REMOVING one of the solutions to the original equation, which is something that you want to avoid doing.
In contrast, with this example...
3A = 4B
You CAN divide both sides by a variable to find the ratio of the two variables....
A/B = 4/3
Notice that the two examples involved two different questions (what are the values of X vs. what is the ratio of A to B). This is all meant to say that you have to pay careful attention to what you're given and what is asked. As a general rule, dividing by a variable almost always removes a possible answer, so you have to think about how doing that would impact the question that the prompt asks.
GMAT assassins aren't born, they're made,
Rich
What you're asking about is somewhat 'circumstantial' (meaning that the specific information and the specific question that is asked will determine what type of math you should or shouldn't be doing).
There's a difference between 'dividing out' a variable and dividing by a variable.
For example, if you have the equation...
X^2 = X
This equation has 2 solutions. Can you figure them out? What happens if you divide both sides by X first (how many solutions do you end up with then?)? By dividing by a variable, you end up REMOVING one of the solutions to the original equation, which is something that you want to avoid doing.
In contrast, with this example...
3A = 4B
You CAN divide both sides by a variable to find the ratio of the two variables....
A/B = 4/3
Notice that the two examples involved two different questions (what are the values of X vs. what is the ratio of A to B). This is all meant to say that you have to pay careful attention to what you're given and what is asked. As a general rule, dividing by a variable almost always removes a possible answer, so you have to think about how doing that would impact the question that the prompt asks.
GMAT assassins aren't born, they're made,
Rich
Last edited by [email protected] on Wed Jan 13, 2016 3:06 pm, edited 1 time in total.
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ceilidh.erickson
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Great question, xiamsamx! In fact, you caught a mistake in one of our books (no one is perfect!).
The problem should have specified that abc could not equal zero. As written, you're right - it's impossible to divide by any of the variables.
If you're ever confused or think you've caught a mistake in one of our books, check the Errata page on our website: https://www.manhattanprep.com/gmat/errat ... gebra-5ed/
Good eye! And good luck with your studies.
The problem should have specified that abc could not equal zero. As written, you're right - it's impossible to divide by any of the variables.
If you're ever confused or think you've caught a mistake in one of our books, check the Errata page on our website: https://www.manhattanprep.com/gmat/errat ... gebra-5ed/
Good eye! And good luck with your studies.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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chetan.sharma
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Hi,ceilidh.erickson wrote:Great question, xiamsamx! In fact, you caught a mistake in one of our books (no one is perfect!).
The problem should have specified that abc could not equal zero. As written, you're right - it's impossible to divide by any of the variables.
If you're ever confused or think you've caught a mistake in one of our books, check the Errata page on our website: https://www.manhattanprep.com/gmat/errat ... gebra-5ed/
Good eye! And good luck with your studies.
Ceilidh, I am actually impressed that you have accepted that there has ben some error by the source and creating some errors should be normal, given that you all come out with thousands of Q.
In another forum, I pointed out glaring faults of few source, well known in this field otherwise, but they tried defending the defenseless...
Accepting error, if done only brings more respectability to the source..
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ceilidh.erickson
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Thanks, Chetan. The reality is that every question out there - from GMAC or from private companies - is written by a human, and we're all prone to subjectivity and fallibility. And things can get lost going from the writer to the editor to the book publisher.
We're all here to improve, and that definitely includes Manhattan Prep! None of us gain by being stubborn or defensive. We certainly welcome any input on how we can improve: [email protected]
Thanks!
We're all here to improve, and that definitely includes Manhattan Prep! None of us gain by being stubborn or defensive. We certainly welcome any input on how we can improve: [email protected]
Thanks!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
