Question: Many Variables vs. 2

Comment on Many Variables vs. 2

Suppose if we multiply both sides by k in 3rd step, then
2k-5?2k
2k-5-2k?2k-2k
-5<0

By this way, 0 becomes big
Should not the answer be D? Please correct me if I am wrong anywhere..
greenlight-admin's picture

Remember that k is a negative value, and we can't multiply both sides by a negative value (see https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...).
HOWEVER, since -k must be a positive value, we can multiply both quantities by -k to get.....
Quantity A: -2k + 5 and Quantity B: -2k
Then add -2k to both sides to get....
Quantity A: 5 and Quantity B: 0

Answer = A

I so appreciate how dedicated, effective, and talented you are as a teacher!

The "last" step, in which Qty A equals [2 - (5/k)], at 1:07, could be a bit confusing.
I refer to this step:

Qty A = 2 - (5/k)
Qty B = 2

I think we can simplify a little further.

Subtract 2 from both quantities.

1. Before
Qty A = 2 - 5/k
Qty B = 2

2. Now subtract 2 from both. Result:

Qty A = -5/k
Qty B = 0

It is given that k<0.
In other words, k is NEGATIVE

Thus, the denominator of the fraction in Qty A is a NEGATIVE number. So too is the numerator (-5).

Hence we can say:
Qty A = (-5/k) = (NEG/NEG) = POSITIVE

Now we have
Qty A = some POSITIVE number
Qty B = 0

Any positive number (Qty A) is greater than 0 (Qty B), so the answer is "A."
Just a thought. :)
greenlight-admin's picture

Thanks for the kind words!
Your proposed solution is perfect and probably easier to follow than mine at the end.
Great work!!

Simplifying 2k/k is obviously 2, but if k is 0 then it is undefined. How come there is no proviso for this? Thanks.
greenlight-admin's picture

The proviso is at the very top where we say that k < 0

K can also be -5 and 5/-5= -1. multiply that by a negative on the outside then it's a positive then multiply by 2 they are equal.
greenlight-admin's picture

Be careful, Kentrell.
If k = -5, then Quantity A evaluates to be 3 (not 2)

Cheers,
Brent

Why can't we eliminate k-1 if k=1
greenlight-admin's picture

This is covered in the previous video at https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Here's a modified version of the question.
Let's say we want to simplify (2k - 2)/(5k - 5)
We can factor top and bottom to get: 2(k - 1)/5(k - 1)
At this point, we probably want to cancel the (k-1) to get 2/5
HOWEVER, we can only do so if k ≠ 1

Here's why:
If k = 1, then (2k - 2)/(5k - 5) = 0/0, which does NOT equal 2/5
So, if k = 1, we can't say that (2k - 2)/(5k - 5) = 2/5

However, for ANY OTHER value of k, we can say that (2k - 2)/(5k - 5) = 2/5
For example,
- if k = 3, then (2k - 2)/(5k - 5) = (6 - 2)/(15 - 5) = 4/10 = 2/5
- if k = 8, then (2k - 2)/(5k - 5) = (16 - 2)/(40 - 5) = 14/35 = 2/5
- if k = -2, then (2k - 2)/(5k - 5) = (-4 - 2)/(-10 - 5) = -6/-15 = 2/5
etc

Cheers,
Brent

Understood. Thanks

Hello,
But in the case that k=-0.001
The answer will vary.
2-(5/k)
Is there something I am missing so I an getting another answer.
Thank you
greenlight-admin's picture

If k = -0.001, then 5/k = 5/(-0.001) = -5000
So, 2 - (5/k) = 2 - (-5000) = 5002
This means Quantity A is still greater than Quantity B.

Does that help?

Cheers,
Brent

In your reply, you mentioned a case where the value would not be 2/5. If Quantity B were to be 2/5, would the answer be D? (I.e. because the LHS will not be 2/5 if k=1)?
greenlight-admin's picture

I'm not 100% sure what you're asking.

In the above discussion, I say that (2k - 2)/(5k - 5) = 2/5 for MOST values of k.
However, if k = 1, then (2k - 2)/(5k - 5) does NOT equal 2/5
My example, (2k - 2)/(5k - 5) = 2/5, it's just that, an example.

Notice that this equation does not match the equation in the original video question above. It's just an example I used to illustrate an important property.

-------------------------
In your question you ask, "If Quantity B were to be 2/5, would the answer be D?

Are you referring to the original question, or my modified question (with Quantity A = (2k - 2)/(5k - 5))?

Hello Brent, I'm unable to watch the video because it says "Private Video. Sorry, you don’t have permission to watch". Pls help rectify
greenlight-admin's picture

Very odd. I'll get my programmer on it.

It works now
greenlight-admin's picture

Good stuff!

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