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# Manhattan GMAT Prep - Mistake in 6th Edition - Algebra

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Intern
Joined: 18 Feb 2017
Posts: 18
Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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15 Dec 2017, 20:11
Page 133:

Question 6

The retailer has ... twice as many radios as clocks....

"twice as many radios as clocks" should be 2r = c but for some reason they state this as 2c = r??

wtf?
I am a native speaker and this doesn't make sense to me?

if I have 4 apples and 2 oranges, then I would say "I have twice as many apples as oranges" or in variable form "2a=o"
Intern
Joined: 18 Feb 2017
Posts: 18
Re: Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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15 Dec 2017, 20:52
manhattan rep: Please reply to this post

I have further discovered another question with similar wording:

At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

A. 6 to 1
B. 3 to 2
C. 2 to 3
D. 1 to 5
E. 1 to 6

using the same word/math translation, I have answered this question as 3:2 (B) which is correct.

Twice as many English majors as History majors -> H=2E
Three times as many english majors as mathematics majors -> M=3E

Multiplying (h=2e)3 and (m=3e)2 (common factors I guess you could call that)
gives you

3h=6e AND 2m=6E

the ratio of h:m is 3:2

So if using this question, I have proven that the Manhattan GMAT Prep mistake isn't lack of cognitive function on my part. I thought I was going crazy for the last 2 hours.
I will refrain from dishing out expletives!
Math Expert
Joined: 02 Sep 2009
Posts: 55271
Re: Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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16 Dec 2017, 00:17
1
mrcentauri wrote:
Page 133:

Question 6

The retailer has ... twice as many radios as clocks....

"twice as many radios as clocks" should be 2r = c but for some reason they state this as 2c = r??

wtf?
I am a native speaker and this doesn't make sense to me?

if I have 4 apples and 2 oranges, then I would say "I have twice as many apples as oranges" or in variable form "2a=o"

You say yourself that if you have 4 apples and 2 oranges, then you have twice as many apples as oranges, (4 apples) = 2*(2 oranges), a = 20, NOT 2a=o.

Similarly, "twice as many radios as clocks" means r = 2*c, there are more radios than clocks (twice as many), so you should multiply the number of clocks by 2 to get the number of radios.

The question you mention in your second post is discussed here: https://gmatclub.com/forum/at-a-certain ... 85632.html

Hope it helps.
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Joined: 02 Sep 2009
Posts: 55271
Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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16 Dec 2017, 00:20
1
mrcentauri wrote:
Page 133:

Question 6

The retailer has ... twice as many radios as clocks....

"twice as many radios as clocks" should be 2r = c but for some reason they state this as 2c = r??

wtf?
I am a native speaker and this doesn't make sense to me?

if I have 4 apples and 2 oranges, then I would say "I have twice as many apples as oranges" or in variable form "2a=o"

15. Word Problems

On other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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16 Dec 2017, 08:45
I think you have made a genuine mistake.

I want to find out how many apples or oranges I have.
if I have twice as many apples as oranges this is a ratio of 2x:1x = 3x (where x is the unknown multiplier) so if I have 4 apples I have (x=4/2) thus x=2 so I only have 2 oranges.

so your math isn't adding up here

let's break it down further

twice as many apples as oranges
2 X a : o
so 2*a : o

for every 2 apples we have 1 orange
4 apples = 2 oranges

you are trying to conceptualize 4 apples as if they equal 1 and 2 oranges as if it were equal to 2 meaning 1 *(4) = 2 * (2) which makes zero sense whatsoever

if i have 4 apples and 2 oranges, I have a ratio of 2:1

why are you multiplying 2 * o when it is clear o = 1 and a = 2 ??

we could even argue that a = a/2 where the left side is apples and right is oranges (a/2 represents oranges)

I hope this helps to resolve the fallacy that twice as many x as y is 2y=x (which is incorrect and defies logic),
twice as many X as Y is actually 2x=y (this is correct)
Intern
Joined: 18 Feb 2017
Posts: 18
Re: Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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16 Dec 2017, 09:12
mrcentauri wrote:
I think you have made a genuine mistake.

I want to find out how many apples or oranges I have.
if I have twice as many apples as oranges this is a ratio of 2x:1x = 3x (where x is the unknown multiplier) so if I have 4 apples I have (x=4/2) thus x=2 so I only have 2 oranges.

so your math isn't adding up here

let's break it down further

twice as many apples as oranges
2 X a : o
so 2*a : o

for every 2 apples we have 1 orange
4 apples = 2 oranges

you are trying to conceptualize 4 apples as if they equal 1 and 2 oranges as if it were equal to 2 meaning 1 *(4) = 2 * (2) which makes zero sense whatsoever

if i have 4 apples and 2 oranges, I have a ratio of 2:1

why are you multiplying 2 * o when it is clear o = 1 and a = 2 ??

we could even argue that a = a/2 where the left side is apples and right is oranges (a/2 represents oranges)

I hope this helps to resolve the fallacy that twice as many x as y is 2y=x (which is incorrect and defies logic),
twice as many X as Y is actually 2x=y (this is correct)

ok I think I just got it... I was wrong I admit it!

if I have 4 apples and 2 oranges, then I have twice as many apples as I have oranges

so a=2o makes sense because as an equation 4 apples must equal 4 of something else

so 4 apples is equal to 2 * (2 oranges)

my logic was

o=2a which is (2 oranges) = 2 * (4 apples) and 2=8 isn't a valid sum at all.

so yes you were right,
Intern
Joined: 18 Feb 2017
Posts: 18
Re: Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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16 Dec 2017, 09:19
on a further note

if anyone requires help with this tricky wording please remember the following

twice as many x as y -> means we have 2x's and 1 y so in equation term they both must equal one another (verbal to math is tricky)

so we know that we have 2x and 1y, which means x (we have 2 x) = (is equal to) 2 (we have 1 y) -> 2 = 2(1) (2 can't be equal to 4! this is invalid!)

don't let the wording fool you, it's converting that wording to math that will make the difference
another way of looking at it is as follows

we have twice as many x as y
so we have 2 x's and 1 y

y=x/2 which is the same as having written x=2y

I hope this makes sense to those who are struggling (I am a native speaker and I struggled!)
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Joined: 18 Feb 2017
Posts: 18
Re: Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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16 Dec 2017, 09:20
I think I deserve some kudos for this, anyone that feels this was useful, feel free to hit the button
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Re: Manhattan GMAT Prep - Mistake in 6th Edition - Algebra  [#permalink]

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21 Mar 2019, 08:06
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Re: Manhattan GMAT Prep - Mistake in 6th Edition - Algebra   [#permalink] 21 Mar 2019, 08:06
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# Manhattan GMAT Prep - Mistake in 6th Edition - Algebra

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