Lesson: Expanding Expressions

Comment on Expanding Expressions

ab < 0
bc > 0

QUANTITY A: ac
QUANTITY B: 0


GIVEN: ab is NEGATIVE and bc is POSITIVE

So, (ab)(bc) = (NEGATIVE)(POSITIVE) = NEGATIVE
Simplify left side to get: ab²c = NEGATIVE
Rewrite as: (ac)(b²) = NEGATIVE
Since b² must be positive, we can write: (ac)(POSITIVE) = NEGATIVE
This tells us that ac must be NEGATIVE

So, we get:
QUANTITY A: NEGATIVE
QUANTITY B: 0

0 is greater than a NEGATIVE number
Answer: B

Cheers,
Brent

Crazily, I saw this whole algebraic thing as two relationships, in which (A) is the toxic union of two people, a and b. It is toxic because their result value is less than zero (<0), so one of them two is the toxic potentiator. Then I see that b conjoined with c and had a positive result (>0), so a is the one that messes things up, and makes the end result negative. In a relationship of a and c nothing good can come out of it since it's got a included, so the result will be negative as well, being less than zero. Crazy, but it worked for my abstract mind. Advice: Stay away from a.
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/ab-0-bc-3666.html

Ha! Great reasoning!

Cheers,
Brent

At 7:07, is that a typo? Wouldn't (5y^3) (4y^4) = 20y^7 and not 20x^7?
greenlight-admin's picture

Good catch - thanks!
I'll fix that shortly.

Cheers,
Brent

Regarding the 2nd question from the activities (https://gre.myprepclub.com/forum/x-is-different-from-zero-9213.html). I like your approach better than what I did, but I want to know if what I did is allowed. So, I had 3x^2 vs 9x^2 and then subtracted 3x^2 from both sides. At that point I had 0 vs 6x^2. I reasoned that no matter what x is, x^2 will be positive, so 6 times a positive number will always be positive, so B is greater than A. So, B is the answer.
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/x-is-different-from-zero-9213.html

That's perfectly sound reasoning.
Nice work!

Cheers,
Brent

Hello Brent,
Please, can you explain a little more how did you get to know those values?

You mentioned the following in the solution:

"We already know that 72.42 = 72 + 42/100"

https://gre.myprepclub.com/forum/gre-math-challenge-14-72-42-k-24-n-333.html
Thank you
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/gre-math-challenge-14-72-42-k-24-n-333....

Let's do a few conversions from decimals to fractions:
0.5 = 5/10 (aka 1/2)
0.7 = 7/10
0.24 = 24/100 (aka 6/25)
0.86 = 86/100 (aka 43/50)
0.123 = 123/1000
0.811 = 811/1000
0.125 = 125/100 (aka 1/8)

So, we know that 0.42 = 42/100

Also, 72.42 = 72 + 0.42
= 72 + 42/100

Likewise, 13.549 = 13 + 0.549
= 13 + 549/100

For more on conversions from decimals to fractions, watch https://www.greenlighttestprep.com/module/gre-arithmetic/video/1066

Does that help?

Cheers,
Brent

Help! I think my brain imploded.

Regarding the linked practice question (same as the one to which you linked above)

(https://gre.myprepclub.com/forum/gre-math-challenge-14-72-42-k-24-n-333.html)

Here is the prompt:

If 0 < n < 100
and
72.42 = k(24 + n/100),
then k + n =

I did the algebra, made the same deductions as those in your solution, and initially got the reportedly correct answer (i.e., k+n=17).

But then I noticed something that now has me confused.

From the given info, it seems that the value of k depends on the value of n.

So ...

1) If n = 90:
72.42 = k(24 + 90/100)
72.42 = k(24.9)
k = [72.42/24.9] = approximately 2.9
Then (k+n)=(2.9+90)= approx. 92.9

2) If n=10:
72.42 = k(24 + 10/100)
72.42 = k(24.1)
k = [72.42/24.1] = approximately 3
Then (k+n)=(3+10)= approx. 13

In case 1, (k+n) = 92.9
In case 2, (k+n) = 13

Am I missing something?
greenlight-admin's picture

You're absolutely right!!
I just added a proviso to the question so that it has just one solution.
Check it out: https://gre.myprepclub.com/forum/gre-math-challenge-14-72-42-k-24-n-333....

So In this case you assume that 72 is equal to 24K. And the rest is the decimal. Is there any other approach to solve this exercise that you may know?
Thank you
greenlight-admin's picture

Hey Brent what does in front mean in terms of math like is this side front (A) [5] (B) or is this side front?
greenlight-admin's picture

If Joe and Sue are in line to get into a theatre, and Joe is IN FRONT of Sue, then that means Joe get into the theatre before Sue will.

So, here's one possible scenario: (Back of line)(other people)(Sue)(other people)(Joe)(theatre entrance)
Here's another scenario: (Back of line)(other people)(Sue)(Joe)(other people)(theatre entrance)

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