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Notation of ratios

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Notation of ratios [#permalink]

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New post 12 Oct 2017, 02:32
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.

Thanks already in advance!

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Re: Notation of ratios [#permalink]

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New post 12 Oct 2017, 02:49
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.

Thanks already in advance!


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

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

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


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.
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Re: Notation of ratios [#permalink]

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New post 12 Oct 2017, 02:50
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.

Thanks already in advance!


Please follow the rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Notation of ratios [#permalink]

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New post 12 Oct 2017, 07:18
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.

Thanks already in advance!


3. Fractions, Decimals, Ratios and Proportions



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

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135380 [0], given: 12691

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Re: Notation of ratios [#permalink]

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New post 14 Nov 2017, 16:18
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, 16:18
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