Lesson: QC Strategy - Number Sense

(2x - 6)/5 TIMES 10 = 10(2x - 6)/5

= 2(2x - 6)/1

= 2(2x - 6)

= 4x - 12

Glad you like it!

You're referring to the question that starts at 0:20 in the above video.

Your point would be true IF x could equal -4. However, the given condition (x > 3) states that x must be greater than 3.

I'm happy to help.

Question link: https://gre.myprepclub.com/forum/40076-2395.html

We started with:
Quantity A: (40076)(90042)
Quantity B: (40075)(90043)

I wanted to get these two quantities to look more alike (since they're easier to compare when they share certain values)

We can rewrite 40076 as (40075 + 1), and rewrite 90043 as (90042 + 1) to get:
Quantity A: (40075 + 1)(90042)
Quantity B: (40075)(90042 + 1)

Notice that each quantity now has 40075, and each quantity now has 90042

Expand each to get:
Quantity A: (40075)(90042) + 90042
Quantity B: (40075)(90042) + 40075

----------ASIDE---------------------
For quantity A, we can think of it this way:
(40075 + 1)(90042) = (90042)(40075 + 1)
From here, we can use the distributive property to multiply these values.

In general, the distributive property says x(y + z) = xy + xy
For example: 5(2 + 6) = (5)(2) + (5)(6)
And 3(x + 1) = 3x + 3
Likewise, (90042)(40075 + 1) = (40075)(90042) + 90042

And, for quantity B, (40075)(90042 + 1) = (40075)(90042) + 40075

For more on the distributive property, you can watch: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1057 (starting at 4:07)

Also, you can watch this one on expanding expressions: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...
-----------------------------------

Please let me know if that helps clear things up.

Cheers,
Brent

You're referring to 0:54 in the video.

In order to eliminate both fractions, we can multiply both values by the least common multiple (LCM) of the two denominators. Here, the denominators are 5 and 2, so the LCM is 10.

Notice that something nice happens when we multiply both quantities by 10.

Given:
QUANTITY A: (2x - 6)/5
QUANTITY B: (2 - x)/2

Multiply both quantities by 10 to get:
QUANTITY A: 10(2x - 6)/5
QUANTITY B: 10(2 - x)/2

We can rewrite both values as follows:
QUANTITY A: (2x - 6)(10/5)
QUANTITY B: (2 - x)(10/2)

Simplify the fractions to get:
QUANTITY A: (2x - 6)(2)
QUANTITY B: (2 - x)(5)

Expand each quantity:
QUANTITY A: 4x - 12
QUANTITY B: 10 - 5x

Does that help?

For more on the above strategy, watch: https://gmatclub.com/forum/if-x-and-y-are-positive-numbers-is-x-1-y-1-x-...