While practicing Quantitative topics, be sure to practice with both official and unofficial questions.
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Comment on Negative Exponents
Hi Brent
If x is an integer, is x|x|<2^x?
(1)x<0
(2)x=-10
Pls explain i couldn't understand how to substitute values for |x| should i take -ve or + ve
In both statements you are
In both statements you are told that x is negative. So, if you're going to plug in (test) values of x, you must use negative values.
The key thing to recognize here is that 2^x IS POSITIVE for ALL values of x (positive or negative)
For example, if x = 5, then 2^x = 2^5 = 32
And if x = -3, then 2^x = 2^(-3) = 1/8
(1) If x < 0, then x is NEGATIVE
So, we get: (NEGATIVE)(|NEGATIVE|) < 2^NEGATIVE
Evaluate to get: (NEGATIVE)(POSITIVE) < POSITIVE
Simplify: NEGATIVE < POSITIVE
Perfect!
2) Same process here as for statement 1.
Answer: D
Here's a thread discussing this question at greater length: https://gmatclub.com/forum/if-x-is-an-integer-is-x-x-2-x-144342.html
Hi Brent. Can you walk
https://gmatclub.com/forum/if-5n-4n-x-0-788-then-x-n-259657.html
And why/how can you flip each fraction?
Your answer to the question:
Given: 5n/(4n - x) = (0.788)^(-1)
Rewrite as: 5n/(4n - x) = 1/0.788
Flip each fraction: (4n-x)/5n = 0.788
Apply above property: 4n/5n - x/5n = 0.788
Simplify: 4/5 - x/5n = 0.788
Simplify: 0.8 - x/5n = 0.788
So: x/5n = 0.012
Multiply both sides by 5 to get: x/n = 0.06
Rewrite as fraction: x/n = 6/100 = 3/50
Question link: https:/
Question link: https://gmatclub.com/forum/if-5n-4n-x-0-788-then-x-n-259657.html
The main property here is as follows:
If wxyz ≠ 0 and w/x = y/z, then it must also be true that: x/w = z/y
For example, since 4/8 = 1/2, it must also be true that 8/4 = 2/1
Likewise, since 9/6 = 3/2, it must also be true that 6/9 = 2/3
So, when I got to this point: 5n/(4n - x) = 1/0.788...
...I could see that flipping both sides was going to make it much easier to solve the equation.
Does that help?
Cheers,
Brent
Hi Brent,
Could you please show how to solve the question by using just variables?
https://gmatclub.com/forum/x-1-y-1-xy-1-x-y-316172.html
How did you know that x can be 2 and y can be 4?
Since there are no
Since there are no restrictions on the values of x and y, we can assign any values we wish.
I chose x = 2 and y = 4, because they're easy numbers to work with.
I could have also chosen to use x = 6.215 and y = -0.004213, and the algebraic expression would still evaluate to be -1 (but the calculations would be a lot harder to complete.)
https://gmatclub.com/forum/x-1-y-1-xy-1-x-y-316172.html#p2546544
Hi Brent, Could you solve
I'm getting C as the answer, not sure how the OA is D
Here's my full solution:
Here's my full solution: https://gmatclub.com/forum/m26-184464-20.html#p2715815
https://gmatclub.com/forum/if
Hi Brent,
I couldn’t find your solution to this question can you help me with that
Thanks
Here's my full solution:
Here's my full solution: https://gmatclub.com/forum/if-x-and-y-are-integers-is-x-y-143771-20.html...
These 650 questions are
There are several super
There are several super tricky questions in that list.
Be sure to check the difficulty level rating of questions you find difficult.
If they're rated 75 or greater (for example https://gmatclub.com/forum/if-a-b-c-and-d-are-four-consecutive-integers-...), don't worry about them too much, since they are crazy hard.