# Lesson: Introduction to Fractions

## Comment on Introduction to Fractions

### M is the sum of the

M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?

(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!

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:

Cheers,
Brent

### Hi Brent, they are nice

Hi Brent, they are nice questions.
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,

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

Hey, I was trying to solve this question and I got it wrong. Also, the answers in that page did not make sense to me. I was wondering if you could kindly explain it to me.

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