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# Notation of ratios

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Intern
Joined: 17 Dec 2016
Posts: 1

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12 Oct 2017, 03:32
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.

Math Expert
Joined: 02 Sep 2009
Posts: 44298

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12 Oct 2017, 03:49
asdusz wrote:
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.

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

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

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

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

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.

Discussed HERE.

Hope it helps.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 44298

### Show Tags

12 Oct 2017, 03:50
asdusz wrote:
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.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 44298

### Show Tags

12 Oct 2017, 08:18
asdusz wrote:
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.

3. Fractions, Decimals, Ratios and Proportions

Check below for more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
_________________
Intern
Joined: 17 Jun 2017
Posts: 9

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14 Nov 2017, 17:18
asdusz wrote:
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.

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?

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
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Re: Notation of ratios   [#permalink] 14 Nov 2017, 17:18
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