# Lesson: Ratios and Rates

## Comment on Ratios and Rates

### How do I know when to use

How do I know when to use ratios and when to use the speed-distance-time formulas?

### You can use ratios for

You can use ratios for simpler motion if/when you're able to rewrite the information as "for every x there is y" (as mentioned in the video)

### Will we have calculators for

Will we have calculators for these type of questions?

### Unfortunately no.

Unfortunately no.

No calculators are permitted during the Math section of the GMAT.

### Hi Brent,

Hi Brent,
Kindly explain the following DS question:
What was the percent increase in population of city K from 1980 to 1990?
(1) In 1970 the population of city k was 160,000
(2) In 1980 the population of city k was 20 percent greater than it was in 1970, and in 1990 the population of city k was 30 percent greater than it was in 1970
Ans B

### Hi bent, is the official

Hi Brent. Is the Official Guide the best material for practice? I can see people in online forums suggesting that the Official Guide is not a good material and that it has only questions that are retired from GMAT. Is this true?

### The Official Guide questions

The Official Guide questions are, by far, the best questions to practice with.

I'm not sure who's suggesting that the Official Guide (OG) questions are not good, but, whoever they are, they're incorrect. The practice questions in the OG's are retired questions, which means they were once part of the official test bank you'll work with on test day. All other third-party practice questions are simply the authors' attempts to replicate official practice questions (like the ones in the OG).

Cheers,
Brent

### Brent,

Brent,
In looking up 239 DS OG 2020 question, I'm not sure I follow your explanation. I'm confused on how you got the following from S1:
Since the ratio of blue : yellow : red = 2 : 3 : 1, we can conclude that we need:
20/3 quarts of blue paint
10 quarts of yellow paint
20/6 quarts of red paint
I would not have thought about dividing 20/3 for blue and so on. Could you help me see how you derived that?
https://gmatclub.com/forum/a-certain-mixture-of-paint-requires-blue-yellow-and-red-paints-in-243443.html#p1894209

Good question. I should have made that clearer in my solution.
Since the ratio of blue : yellow : red = 2 : 3 : 1, we can see that:
- within 6 quarts of mixture, 2 quarts are blue
- within 6 quarts of mixture, 3 quarts are yellow
- within 6 quarts of mixture, 1 quarts are red

In other words, 2/6 of the mixture is blue, 3/6 of the mixture is yellow, and 1/6 of the mixture is red.
In other words, 1/3 of the mixture is blue.
So, if we have 20 quarts of mixture, then 1/3 of that mixture will be blue.
Other words, 20/3 quarts are blue.

Does that help?

### Hi Brent,

Hi Brent,

Damian needs 1/4 of the wood in the shed on the first day and 2/9 of the remaining wood on the second day to make a tree-house in his backyard. Given that 2/5 of the wood in the shed is unusable due to fungal damage what fraction of usable wood is left once he has completed the tree-house ?

### Since we are asked to find a

Since we are asked to find a certain FRACTION, we can save ourselves some time buy assigning a "nice" value to the amount of wood in the shed.
By "nice" I mean a number that works well with the given information (1/4, 2/9 and 2/5).

The least common multiple of 4, 9 and 5 is 180.
So, let's say there are 180 equal-sized pieces of wood in the shed

1/4 of 180 = 45
So Damian used 45 pieces of wood on the first day

180 - 45 = 135
So there are 135 pieces of wood remaining
2/9 of 135 = 30
So Damian used 30 pieces of wood on the second day

45 + 30 = 75
So, Damian used 75 pieces of wood in total
------------------------

If 2/5 of the wood is unusable, then the other 3/5 of the wood must be usable
3/5 of 180 = 108
So, 108 pieces of wood are USABLE.
-----------------------

108 - 75 = 33
So there are 33 pieces of USABLE wood remaining.

Fraction of usable would remaining = 33/108 = 11/36

Cheers,
Brent

### fraction would be 33/108

fraction would be 33/108 right?
because total wood left is now 108.

### Good catch! I've edited my

Good catch! I've edited my response accordingly.
Cheers and thanks,
Brent

### Hi Brent,

Hi Brent,

Could you pls solve this qs - https://gmatclub.com/forum/a-20-kg-metal-bar-made-of-alloy-of-tin-and-silver-lost-2-kg-63907.html