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Comment on Introduction to Fractions
M is the sum of the
(A) 1/3 < M < 1/2
(B) 1/5 < M < 1/3
(C) 1/7 < M < 1/5
(D) 1/9 < M < 1/7
(E) 1/12 < M < 1/9
Hi Brent,
Grateful to give me your version of solution to the above mentioned question.
Many thanks
Fatima-Zahra
Hi Fatima-Zahra,
Hi Fatima-Zahra,
Here's my step-by-step solution: https://www.beatthegmat.com/m-is-the-sum-of-the-reciprocals-of-the-conse...
Cheers,
Brent
Thank you Brent!
I really do not understand the principle the extreme value!!
Grateful for your help
Fatima-Zahra
Here are a few more questions
Here are a few more questions involving extreme values and maximization:
- https://gmatclub.com/forum/if-4-x-7-and-6-y-3-which-of-the-following-spe...
- https://gmatclub.com/forum/are-at-least-10-percent-of-the-people-in-coun...
- https://gmatclub.com/forum/1-7-1-8-1-9-is-in-between-239519.html
- https://gmatclub.com/forum/the-minimum-of-the-integers-x-y-and-z-is-10-a...
- https://gmatclub.com/forum/a-certain-meter-records-voltage-between-0-and...
Cheers,
Brent
Hi Brent, they are nice
I could not understand this question's solution. Is there a simpler way?
https://gmatclub.com/forum/are-at-least-10-percent-of-the-people-in-country-x-who-are-65-years-122734.html
Did you happen to see my
Did you happen to see my solution at https://gmatclub.com/forum/are-at-least-10-percent-of-the-people-in-coun... ?
Statement 2: Among Country X's seniors, 20 percent of the men and 10 percent of the women are employed
One approach is to think of this question as mixing two salt solutions.
So, rather than having a group of men in which 20% are employed, we can think of solution A as consisting of 20% salt.
Likewise, rather than having a group of women in which 10% are employed, we can think of solution B as consisting of 10% salt.
If we combine a 20% solution and a 10% solution, the concentration of salt in the resulting solution will range from 10% to 20%.
In other words, we can conclude that the resulting mixture will consist of AT LEAST 10% salt.
In other words, we can conclude that, in the resulting mixture OF SENIORS, AT LEAST 10% of them will be employed.
Does that help?
Cheers,
Brent
PS: For more on the above concepts, you can watch: https://www.gmatprepnow.com/module/gmat-statistics/video/805
Hi Brent,
Thank you. I believe I got it.
After some thinking I solved the statement 2 like this:
Lets say the total population is 100 people, where 20 people are men and 10 are women giving in total 30 people. Thus we get answer on the question.
Does this thinking work?
That interpretation is close,
That interpretation is close, but the percentages mentioned in statement to refer to seniors only.
So far example, we COULD have 100 senior men (of which 20 are unemployed) and 100 senior women (of which 10 are unemployed). So, in this case, we have a total of 200 seniors, and among those seniors there are 30 unemployed people. 30/200 = 15%. So, the answer to the target question is "YES, at least 10% of the seniors are unemployed.
It COULD be the case that we have 10 senior men (of which 2 are unemployed) and 100 senior women (of which 10 are unemployed). So, in this case, we have a total of 110 seniors, and among those seniors there are 12 unemployed people. 12/110 ≈ 10.9%. So, the answer to the target question is still "YES, at least 10% of the seniors are unemployed.
If we keep testing various cases, will find that we keep getting the same answer to the target question (YES).
Does that help?
Hey, I was trying to solve
The question is:(4th one from reinforcement activity)
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def ?
(A) 27/4
(B) 27/8
(C) 3/4
(D) 3/8
(E) 1/4
Here's my solution: https:/
Here's my solution: https://gmatclub.com/forum/if-a-b-1-3-b-c-2-c-d-1-2-d-e-3-and-e-f-1-4-th...
I took the approach of plugging in values for a, b, c, d, e, and f that satisfy all of the given conditions (e.g., a/b = 1/3, b/c = 2, etc)
Does that help?
Cheers,
Brent
Hi Brent, why is the need to
I believe you're referring to
I believe you're referring to my solution here: https://gmatclub.com/forum/if-a-b-1-3-b-c-2-c-d-1-2-d-e-3-and-e-f-1-4-th...
In my solution, I found values for a, b, c, d, e, and f that satisfied the given information.
There are other values that would yield the same answer.
Given: a/b = 1/3
Let a = 1 and b = 3 (these are the values you chose)
Let's continue with these values.
Given: b/c = 2
Since b = 3, it must be the case that c = 1.5 (since 3/1.5 = 2)
Given: c/d = 1/2
Since c = 1.5, it must be the case that d = 3 (since 1.5/3 = 1/5)
Given: d/e = 3
Since d = 3 , it must be the case that e = 1
Given: e/f = 1/4
Since e = 1 , it must be the case that f = 4
So, abc/def = (1)(3)(1.5)/(3)(1)(4)
= 4.5/12
Divide numerator and denominator by 1.5 to get the equivalent fraction 3/8 (Answer A)
Understand now thanks Brent.
Yes, that's exactly why I
Yes, that's exactly why I used 2.
Fewer fractions often means fewer mistakes :-)
Great thanks Brent for