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Comment on Inequalities - Part II
Compare y and w
y < x
x+5 < w
----> adding -5 on both sides
x+5-5 < w-5
x < w-5
Now y < x
x < w-5
y < x < w-5
so y < w-5
I did like this . is it correct?... Kindly help
Thanks in advance....
You're referring to the task
You're referring to the task that starts at 4:55.
Your approach is perfect.
If you want to go a little further in comparing y and w, you can recognize that w-5 < w
So, continuing where you left off (y < w-5), we have: y < w-5 < w, which means y < w
Hello I have a question
Explanation stated ""The length of rectangle A is 10 percent greater than the length of rectangle C , or 1.1ℓ."
I don't know how it came out 1.1 liter. Please let me know
Hi jenibae,
Hi jenibae,
Be careful,"ℓ" need not represent liters. It can also be a variable.
In the official solution, they let L = the length of rectangle C (aside: the solution uses lowercase "l", but I'll use capital "L" to avoid confusion)
If the length of rectangle A is 10 percent greater than the length of rectangle C, then the 1.1L = length of rectangle A.
Does that help?
Cheers,
Brent
Thank you for your
L = the length of rectangle C
L = the length of rectangle C
So, 10% of L = (10/100)L = 0.1L
So, if the length of rectangle A is 10% GREATER than the length of rectangle C, then the length of rectangle A = L + 0.1L = 1.1L
More here: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1083 (starting at 7:00 in the video)
Cheers,
Brent
Thank you so much !
Hi Brent,
If the reciprocal of the negative integer x is greater than the sum of y and z, which of the following must be true?
A) x > y+z
B) y and z are positive
C) 1 > x(y+z)
D) 1 < xy + xz
E) 1/x > z-y
If the reciprocal of the negative integer x is greater than y + z then I understand that to be 1/x > y+z.....where 1/x is positive. With that I would choose answer C because one would not change the inequality direction since x is positive. However the official answer given is D; it is stated in the answer explanation the sign changes as x is negative. This seems contradictory to the 1st sentence. Any insight?
Many thanks
Question link: https:/
Question link: https://gre.myprepclub.com/forum/if-the-reciprocal-of-the-negative-integ...
You made a small mistake when you wrote "I understand that to be 1/x > y+z.....where 1/x is POSITIVE"
We're told that x is a NEGATIVE integer.
This means 1/x is NEGATIVE
For example, if x = -2, then 1/x = 1/(-2) = -0.5
Here's my full solution: https://gre.myprepclub.com/forum/if-the-reciprocal-of-the-negative-integ...
Cheers,
Brent
Hi Brent,
In this question, https://gre.myprepclub.com/forum/a-b-8949.html, your solution actually says a<b, but then the answer is A. Would you like to clarify?
I solved the eq. this way: I added the two equations to get a + b/10 > b + a/10, I then added the terms and multiplied 10 with a and b on either side.
I got: 10a - a > 10b - b
9a > 9b
a > b
Are these steps correct?
Thanks,
Ketan
Question link: https:/
Question link: https://gre.myprepclub.com/forum/a-b-8949.html
Good catch! It turns out I accidentally reversed the order of the inequality symbols in both given inequalities.
My edited solution is here: https://gre.myprepclub.com/forum/a-b-8949.html#p37663
Cheers and thanks,
Brent
So I have got the steps right
Thanks,
Ketan
Oops.
Oops.
Yes, your steps are perfect. Nice work!
Cheers,
Brent
https://gre.myprepclub.com/forum
For this problem I added c on both sides and then added the inequalities. I got a+b>0 after adding the inequalities . Is this still a valid way to do it?
I think that sounds right.
I think that sounds right.
Just to be sure, can you tell me the steps you took?
https://gre.myprepclub.com/forum
For this problem when we multiply by 10 for b+a/10<0 we get 10b + a <0 since we want the inequalities to point the same diection, I understand we can multiply by -1 and reverse the sign of the inequality. but could we also rewrite it as 0> 10b+a?
Solution link: https:/
Solution link: https://gre.myprepclub.com/forum/a-b-8949.html#p37663
Let's see what happens.
If we do that, we end up with:
10a + b > 0
0 > 10b + a
At this point we might combine them to get: 10b + a < 0 < 10a + b
This means: 10b + a < 10a + b
Subtract b from both sides: 9b + a < 10a
Subtract a from both sides: 9b < 9a
Divide both sides by 9 to get: b < a
Cheers,
Brent
If √a > b > c^2, which of the
I. a > b > c
II. c > b > a
III. a > c > b
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
I wanted to clarify the details on could be problems, my understanding is if it is a COULD BE TRUE problem, then if one solution satisfies the requirements we can accept that condition, if it fails then disregard, right?
Question link: https:/
Question link: https://gmatclub.com/forum/if-a-1-2-b-c-2-which-of-the-following-could-b...
Sorry, I'm not sure I follow your question.
Notice that a = 100, b = 5 and c = 0 satisfy the given condition (√a > b > c²).
These values of a, b and c satisfy statement I (a > b > c), so, we've shown that statement I COULD be true.
These same values of a, b and c DO NOT satisfy statements II and III, but this doesn't necessarily mean that statements II and III cannot be true; it just means that those two statements aren't true for those particular values of a, b and c.
Does that answer your question?