Lesson: Operations with Signed Numbers - Part II

Comment on Operations with Signed Numbers - Part II

Are there some calculation mistakes in the way in which this problem has been solved?


greenlight-admin's picture

Question link: http://gre.myprepclub.com/forum/if-a-b-0-which-of-the-following-numbers-...

Yes, there were several calculation errors in his response.
I have admin privileges on that site, so I was able to edit the mistakes.
It should be good now.


Abdul Hannan's picture


I have a problem in this question Mr Hanneson. the thing is when you square a negative number you get a negative answer e.g. -3^2=-9.

but when you put a bracket around a negative number and square it we get a positive number e.g. (-3)^2=9

now there is no mention of any bracket so how should i solve it, I am confused. please reply.
greenlight-admin's picture

Hi Abdul,

We can think of this in terms of order of operations (BEDMAS aka PEMDAS)

In both cases, (-5)² and -5², we can think of expressions as having two operations: subtraction and an exponent.

In the case of (-5)², we must first deal with what's happening inside the brackets. So, we have -5 in the brackets.
Then we'll deal with exponent (the power of 2) to get: (-5)² = (-5)(-5) = 25

Conversely, the expression -5² has no brackets. So, according to BEDMAS/PEMDAS, we must deal with the exponent before we deal with the subtraction.
So, -5² = -(5²) = -(25) = -25

Does that help?


confused at this point. is it that -5^2 and (-5^2) are not the same, as such we can't get the same answer
greenlight-admin's picture

-5² and (-5²) are equal.
-5² = -25 and (-5²) = -25
We can say that -5² = -(5²) = -(25) = -25

On the other hand,(-5)² = (-5)(-5) = 25

It's all about notation.

Does that help?


what is the meaning of "yare number"?
Thank you
greenlight-admin's picture

Can you tell me where you saw/heard "yare number"?
That will help me decipher :-)

I read it in the following link:

Thank you
greenlight-admin's picture

Ahhhh! Looks like the original poster didn't place a space between "y" and "are"
It should have read "If x and y are numbers..."
I have edited the question.


where are the practice questions available? Is it the 3rd edition book?
greenlight-admin's picture

There's a lot of duplication between the 1st, 2nd and 3rd edition books. So, in the Reinforcement Activities box above, some linked questions listed as "GRE Official Guide" questions could be from just one edition or all 3. The important thing is that all of the Official questions are actual (retired) GRE questions.

Does that help?


please solve this brent
greenlight-admin's picture

At 4:26 mark, 2+3*4= 20. I think this is wrong. Shouldn't it be 14?

greenlight-admin's picture

You're correct. If you watch the next 20 seconds, you'll see that I say 2 + 3 x 4 = 14
I used the expression 2 + 3 x 4 to set up orders of operations (i.e., PEMDAS and BEDMAS).



Hi Brent,

this question seems very easy, but I can't seem to understand it.
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/x-x-14550.html

In this question, we're told that x ≠ 0 and |x| = -x

ASIDE: Many students will assume that -x must be negative (since we have a negative symbol in front of the x).
However we can't make the conclusion that -x must be negative.
In actuality, -x can be either positive or negative (depending on the value of x)

For example, if x = 1, then -x = -1 (negative)
And, if x = 6.2, then -x = -6.2 (negative)

However, if x = -3, then -x = -(-3) = 3 (positive)
And, if x = -88, then -x = -(-88) = 88 (positive)

Okay back to the question.

Let's examine this part: |x| = -x
We know that |x| is POSITIVE for all nonzero values of x.
So, our equation becomes: some POSITIVE number = -x
This means -x is POSITIVE
In order for -x to be POSITIVE, it must be the case that x is negative (see my examples above)

Does that help?

Sorry for the delayed answer. Understood

Hi Brent, I'm struggling at comprehending this question. Could you please help?

greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/gre-practice-question-if-b-0-and-a-b-56...

Given: a/b > 0 (the product ab is positive)

We know the following from the above video:
i) positive/positive = positive
ii) negative/positive = negative
iii) positive/negative = negative
iv) negative/negative = positive

So, a/b is positive, we know that EITHER a and b are both positive (property i) OR a and b are both negative (property iv).
In other words, we can be certain that a and b are the SAME SIGN

The three statements:
A. a > b
B. b > 0
C. ab > 0

We can see that A and B need not be true (be my solution for counter-examples)

However, if a and b are the SAME SIGN, then the product ab must be positive.
For example, if a and b are both positive, then the product ab is positive.
If a and b are both negative, then the product ab is positive.

So, statement C must be true.

Does that help?

How do the Reinforcement Activities work?

Free “Question of the Day” emails!