Last visit was: 01 Sep 2026, 17:14 It is currently 01 Sep 2026, 17:14
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
avatar
asdusz
avatar
Joined: 17 Dec 2016
Last visit: 24 Oct 2017
Posts: 1
Own Kudos:
2
 [2]
Posts: 1
Kudos: 2
 [2]
Notation of ratios 12 Oct 2017, 03:32
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi everyone,

I have a question about the notation of ratios.
I do understand the math behind it yet sometimes it seems to me that questions use the notation interchangeably.
Here are two examples of what I mean:

1. Example
If a=2b, 1/2b=c and 4c=3d what is the ratio of d to a?

I thought it's 3/1 but the correct answer is 1/3.

2. Example
Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?

Following the first example I answered 13:10 yet here the correct answer is 10:13.

My question:
Can someone please explain the logic behind this and give a rule how to chose the right ratio.

Thanks already in advance!

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 Sep 2026
Posts: 113,017
Own Kudos:
838,443
 [1]
Given Kudos: 111,247
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,017
Kudos: 838,443
 [1]
Notation of ratios 12 Oct 2017, 03:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
asdusz
Hi everyone,

I have a question about the notation of ratios.
I do understand the math behind it yet sometimes it seems to me that questions use the notation interchangeably.
Here are two examples of what I mean:

1. Example
If a=2b, 1/2b=c and 4c=3d what is the ratio of d to a?

I thought it's 3/1 but the correct answer is 1/3.

2. Example
Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?

Following the first example I answered 13:10 yet here the correct answer is 10:13.

My question:
Can someone please explain the logic behind this and give a rule how to chose the right ratio.

Thanks already in advance!
Show more

Quote:
If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a?

A. 1 : 3
B. 3 : 1
C. 3 : 4
D. 1 : 1
E. 4 : 3
Show more


\(\frac{1}{2}*b = c\), thus \(b = 2c\);
\(a = 2b = 4c\).
\(4c = 3d\), thus \(d = \frac{4c}{3}\).

\(\frac{d}{a}=\frac{\frac{4c}{3}}{4c}=\frac{4c}{3}*\frac{1}{4c}=\frac{1}{3}\).

Answer: A. Discussed HERE.


Quote:
Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?

A. 3:4
B. 10:13
C. 5:6
D. 13:10
E. 4:3
Show more

The first nine positive multiples of six are {6, 12, 18, 24, 30, 36, 42, 48, 54}
The first twelve positive multiples of six are {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}

Both sets are evenly spaced, thus their median=mean:
a=30 and b=(36+42)/2=39 --> a/b=30/39=10/13.

Answer: B.

Discussed HERE.

Hope it helps.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 Sep 2026
Posts: 113,017
Own Kudos:
838,443
Given Kudos: 111,247
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,017
Kudos: 838,443
Notation of ratios 12 Oct 2017, 03:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
asdusz
Hi everyone,

I have a question about the notation of ratios.
I do understand the math behind it yet sometimes it seems to me that questions use the notation interchangeably.
Here are two examples of what I mean:

1. Example
If a=2b, 1/2b=c and 4c=3d what is the ratio of d to a?

I thought it's 3/1 but the correct answer is 1/3.

2. Example
Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?

Following the first example I answered 13:10 yet here the correct answer is 10:13.

My question:
Can someone please explain the logic behind this and give a rule how to chose the right ratio.

Thanks already in advance!
Show more

Please follow the rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 Sep 2026
Posts: 113,017
Own Kudos:
838,443
Given Kudos: 111,247
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,017
Kudos: 838,443
Notation of ratios 12 Oct 2017, 08:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
asdusz
Hi everyone,

I have a question about the notation of ratios.
I do understand the math behind it yet sometimes it seems to me that questions use the notation interchangeably.
Here are two examples of what I mean:

1. Example
If a=2b, 1/2b=c and 4c=3d what is the ratio of d to a?

I thought it's 3/1 but the correct answer is 1/3.

2. Example
Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?

Following the first example I answered 13:10 yet here the correct answer is 10:13.

My question:
Can someone please explain the logic behind this and give a rule how to chose the right ratio.

Thanks already in advance!
Show more

3. Fractions, Decimals, Ratios and Proportions



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
User avatar
JaeTPU
User avatar
Joined: 17 Jun 2017
Last visit: 09 Jan 2019
Posts: 15
Own Kudos:
5
Posts: 15
Kudos: 5
Notation of ratios 14 Nov 2017, 17:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
asdusz
Hi everyone,

I have a question about the notation of ratios.
I do understand the math behind it yet sometimes it seems to me that questions use the notation interchangeably.
Here are two examples of what I mean:

1. Example
If a=2b, 1/2b=c and 4c=3d what is the ratio of d to a?

I thought it's 3/1 but the correct answer is 1/3.
Show more

Rephrase "what is the ratio of d to a" algebraically to "d/a=?"

To get a numerical answer for your ratio, you will need the variables to cancel out. Put d in terms of c and a in terms of c (a->b->c)
d=(4/3)c, a=2b=4c. ((4/3)c)/4c = (4/3)/4 = 1/3

Quote:

2. Example
Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
Show more

Same thing. If you rephrase "what is the ratio of a to b" into algebra, you get "a/b=?"

The average of numbers that are evenly spaced apart is the median. The median of the first nine positive multiples of 6 is 30.
Median of the first 12 positive multiples of 6 is the mean of the 6th and 7th positive multiples of 6, so (36+42)/2= 39

30/39 = 10/13
User avatar
ccooley
User avatar
Manhattan Prep Instructor
Joined: 04 Dec 2015
Last visit: 06 Jun 2020
Posts: 931
Own Kudos:
1,665
Given Kudos: 115
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Posts: 931
Kudos: 1,665
Notation of ratios 04 Jun 2019, 09:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
asdusz
Hi everyone,

I have a question about the notation of ratios.
I do understand the math behind it yet sometimes it seems to me that questions use the notation interchangeably.
Here are two examples of what I mean:

1. Example
If a=2b, 1/2b=c and 4c=3d what is the ratio of d to a?

I thought it's 3/1 but the correct answer is 1/3.

2. Example
Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?

Following the first example I answered 13:10 yet here the correct answer is 10:13.

My question:
Can someone please explain the logic behind this and give a rule how to chose the right ratio.

Thanks already in advance!
Show more

If you're unsure about which order to write a ratio in, think about it in terms of actual numbers.

When the problem says "what is the ratio of a to b," you would write the value of a first, then the value of b.

If it says "what is the ratio of d to a," you would write the value of d first, then the value of a.

So, for instance, look at your first problem. One set of numbers that works is a = 2, b = 1, c = 1/2, and d = 2/3.

The ratio of D to A is 2/3 to 2, because D could equal 2/3 and A could equal 2.

Then, simplify that ratio by multiplying by 3:

D to A = 2 to 6

Then, divide by 2:

D to A = 1 to 3

That's how you know it's 1 to 3 and not 3 to 1.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!