Question: Absolute Value with Subtraction

Comment on Absolute Value with Subtraction

In rewatching some of your videos; I was wondering, if you have two different variables, is it possible for them to have the same value? I mean if x=0 than doesn't the variable "y" imply that it is a different value other than 0 (otherwise if the expression wanted to represent the value as 0 than they would have used the variable x repeatedly)?

Also in the GRE 2nd edition book; it states on page 215 that QA would be greater than QB. So why wouldn't this statement be true every time (considering that x and y are two different variables hence representative of two different values)?

Thank you in advance :)
greenlight-admin's picture

Great question. Two different variables can have the same value.
For example, if I say that G = the number of girls at a certain school, and B = the number of boys at a certain school, it's perfectly acceptable for G and B to have equal values.
I checked the textbook you're referring to, and I can't find what you're referring to when you talk about QA and QB. Can you be more specific?

Thanks :) and No problem:

In the GRE Math Review in the Official Guide to the GRE Revised General Test 2nd Edition. On page 215 right before the 1.6 Ratio section, the 3rd bullet from the last was giving examples in regards to absolute values. It states the example used in this particular question is known as the triangle inequality. Than the book gives an example where they plugged in values for the variable a and b.

In the book stating |a+b| is less than or equal to |a| + |b|. Than I thought the equivalence would be |a-b| is greater than or equal to |a|-|b|.

Because I wasn't sure if two different variables could have the same value, I assumed the numbers were different and thought Quantity A was greater than Quantity B.

Thanks again for your help :)
greenlight-admin's picture

Your extension of that rule is correct. |a-b| is greater than or equal to |a|-|b|
The key phrase is "or equal to"
Even if a and b don't have equal values, we can still get |a-b| = |a|-|b|
For example if a = 3 and b = 1, then we get: |3-1| = |3|-|1|

okay I understand, thanks again for all your help :)

You did an amazing job on these resources by the way :D
greenlight-admin's picture

Thanks!

When using the "Plugging In" Method, is it good policy to start with Zero to dwindle the answer choices down, THEN move to a positive (X) value and negative (Y) value?
I ask because perhaps the method would work better if there was some consistency: Starting with the negative then moving to a Positive/Negative number.

Hopefully that makes sense.
greenlight-admin's picture

When plugging in numbers, the most important strategy is to try a variety of numbers (positive, negative, 0, 1, -1, fractions etc).

I'n not sure there's a set order that would be optimal, since each question will present information that will provide hints as to which numbers are best to test.

Consider this example:
QUANTITY A: (x-3)/4
QUANTITY B: (x-3)(x+1)

In this case, it makes the most sense to try x = 3 first, since we can immediately see that both quantities will evaluate to be EQUAL.

As for the which number to test next, it makes most sense to try x = -1, since we can quickly see that QUANTITY B will evaluate to be ZERO, while QUANTITY A will NOT evaluate to be zero (which means the correct answer is D)

So, in the above example, we let the two quantities guide which numbers to plug in.

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