Lesson: Operations with Fractions

Comment on Operations with Fractions

To solve this problem:

Let p = the product of all the odd integers between 500 and 598, and let q = the product of all the odd integers between 500 and 602. In terms of q, what is the value of 1/p + 1/q?

Are we to memorize the prime numbers between 500 and 1000? If yes then what are the set of numbers for which we should memorize the prime numbers for?
gmat-admin's picture

I think you might be mixing up ODD numbers with PRIME numbers.

Here's my full solution to your question: https://gmatclub.com/forum/let-p-the-product-of-all-the-odd-integers-bet...

ASIDE: As far as memorizing prime numbers goes, I think it's fine to remember the primes from 2 to 97

Sorry to mention this, but there is a typo in your answer to this question:
https://gmatclub.com/forum/if-x-1-10-1-12-1-13-1-14-1-15-then-which-of-the-following-i-229134.html
in this statement:
So, we know that x must be greater than 1/3 AND less than 1/3
I am certain you meant it to be:
So, we know that x must be greater than 1/3 AND less than 1/2
gmat-admin's picture

Good catch!! Thanks Aladdin!
I have edited my response.

Cheers,
Brent

Can you please explain the concept of the smallest number that denominator divides into? How to find that?
gmat-admin's picture

The technique for finding the Lowest Common Denominator is the same as finding the Least Common Multiple (LCM).

So, for example, when adding 1/12 and 7/15, we must first find the LCM of 12 and 15.

Here's a video on finding the LCM: https://www.gmatprepnow.com/module/gmat-integer-properties/video/835

Cheers,
Brent

nice tricks!

Hi Brent,
Need help with the following question:
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of sixth year, the tree was 1/5 taller than it was at the end of 4th year. By how many feet the height of the tree increase each year?
A 3/10
B 2/5
C 1/2
D 2/3
E 6/5
gmat-admin's picture

I have seen examples where the numerators and denominators both have 2 fractions (total of 4 fractions). For example: 1/2 divided by 10/33 is the numerator, and the denominator is 1/3 divided by 25/11.

I assume the reciprocal approach applies here as well, and do it 3 times, or is there a better technique? Thanks!
gmat-admin's picture

I would evaluate the numerator and the denominator separately, and then complete the last division. Three divisions in total.

Yulia's picture

Hi Brent,
To be honest I didn’t understand the solution for this question https://gmatclub.com/forum/let-p-the-product-of-all-the-odd-integers-between-500-and-154251.html

Let p = the product of all the odd integers between 500 and 598, and let q = the product of all the odd integers between 500 and 602. In terms of q, what is the value of 1/p + 1/q?

A. 1/600q
B. 1/359,999q
C. 1,200/q
D. 360,000/q
E. 359,999q

However, I answered correctly and approach it by using a number sense if I can say like this. I could understand that the product of odd integers would be a large number therefore 1 in numerator can’t be thus A and B choices is out. E is out too because sum operation could not result in 359,999q (at least I could not see any ways to get such a reply). I discarded C because the numerator is too small since we have integers between 500 and 598 and 500 and 602, so for sure LCM will be large resulting also the numerators to increase.

I looked through the solutions but honestly could not understand them. Any advice on it?
gmat-admin's picture

Question link: https://gmatclub.com/forum/let-p-the-product-of-all-the-odd-integers-bet...

That's good that you got the correct answer, but I'm not sure I follow your rationale for eliminating A and B.
Can you elaborate?

Aside: The correct answer (360000/q) simplifies to be approximately 1/100000000000......, where the denominator has over 100 zeros,

Yulia's picture

Hi Brent,
Thank you for your reply.

What does "In terms of q, what is the value of 1/p+ 1/q" mean? Dont really understand expression "in terms of q"

In your solution I understand this:
p = (501)(503)(505)...(597)
q = (501)(503)(505)...(597)(599)(601)

After that I am lost. Why q = (p)(599)(601)?
gmat-admin's picture

"in terms of q" tells us to rewrite the mathematical relationship using only the variable q (and other numbers).

For example, let's say that we're told: x + y = 7
If we want to express x in terms of y, we can write: x = y - 7

We already know that: p = (501)(503)(505)...(597).
This means we can replace (501)(503)(505)...(597) with p, since the two values are equivalent.
So, we can take: q = (501)(503)(505)...(597)(599)(601)
and replace (501)(503)(505)...(597) with p to get: q = (p)(599)(601)

Does that help?

Yulia's picture

Thank you Brent.

Now it is very clear.

https://gmatclub.com/forum/let-p-the-product-of-all-the-odd-integers-between-500-and-154251.html

For this question, if my brain is just fool enough to get how I can do this, what should I do?
gmat-admin's picture

On test day, if you're stuck on a question, my best advice is to make your best guess and move on. The GMAT isn't about getting every question correct; it's about maximizing your score.

That said, for this particular question, you can start with my solution here: https://gmatclub.com/forum/let-p-the-product-of-all-the-odd-integers-bet...

Let me know if you have any questions after reading the solution.

Office Hours

Have questions about your preparation or an upcoming test? Need help modifying the Study Plan to meet your unique needs? No problem. Just book a Skype meeting with Brent to discuss these and any other questions you may have. 

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and a GMAT expert will answer it as fast as humanly possible.

Free “Question of the Day” emails!