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Comment on 2's, x's and an Inequality
can we work on quant A and B
first taking the reciprocals then multiplying by 2 then subscribing 2 then multiplying by -1 to get (1 for A) and (2-2/x for B) we already know that (2-2/x < 0) so A=1 is bigger
Sorry, can you please
Sorry, can you please elaborate on your solution? I'm not sure what you are doing in each step.
Cheers,
Brent
Hi Brent, why can’t we
That approach also works.
That approach also works.
GIVEN: 2 - 2/x < 0
Subtract 2 from both sides to get: -2/x < -2
Divide both sides by -2 to get: 1/x > 1
IMPORTANT: If 1/x > 1, then we know that x is POSITIVE
So, we can safely multiply both sides by x to get: 1 > x
This means Quantity A is greater.
Cheers,
Brent
why can't you just start by
Regardless of whether one
Regardless of whether one quantity is zero, we can't multiply both quantities by a variable unless we are 100% certain that the variable is POSITIVE
Consider this example:
QUANTITY A: 1/x
QUANTITY B: 0
Multiply both quantities by x to get:
QUANTITY A: 1
QUANTITY B: 0
Quantity A is greater. So, the answer is A (or is it?).
See the problem here?
-----------------------------------
Consider the two cases where x is either positive or negative
If x is POSITIVE, then we get:
QUANTITY A: 1/x = 1/POSITIVE = POSITIVE
QUANTITY B: 0
In this case, Quantity A is greater.
If x is NEGATIVE, then we get:
QUANTITY A: 1/x = 1/NEGATIVE = NEGATIVE
QUANTITY B: 0
In this case, Quantity B is greater.
So, the correct answer is actually D
-----------------------------------
Does that help?
Cheers,
Brent
How can we multiply both
I was comparing 2 < 2/x and reasoned that x must be less than 2 for the inequality be true, therefore A is the answer. Is my reasoning correct here?
Thanks in advance!
Starting at 0:50 in the video
Starting at 0:50 in the video, I explain how we know that x is positive. It goes like this.
Given: 2 - 2/x < 0
Add 2/x to both sides: 2 < 2/x
If 2/x is greater than 2, we know that 2/x is POSITIVE
If 2/x is POSITIVE, then x must be POSITIVE
Cheers,
Brent