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M21-32

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M21-32  [#permalink]

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New post 16 Sep 2014, 00:15
2
13
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

54% (02:41) correct 46% (03:15) wrong based on 112 sessions

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If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 dollars and 4 pounds is equivalent to 56 crowns, 1 pound and 28 crowns is equivalent to how many dollars?

A. $7.00
B. $7.50
C. $8.50
D. $9.00
E. $10.00

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Re M21-32  [#permalink]

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New post 16 Sep 2014, 00:15
1
1
Official Solution:

If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 dollars and 4 pounds is equivalent to 56 crowns, 1 pound and 28 crowns is equivalent to how many dollars?

A. $7.00
B. $7.50
C. $8.50
D. $9.00
E. $10.00


Given:

\(5d+35c=7p\), so \(c=\frac{7p-5d}{35}\);

\(4d+4p=56c\), so \(c=\frac{d+p}{14}\), also if we reduce this equation by 2 we'll get: \(2d+2p=28c\);

From above we have that \(\frac{7p-5d}{35}=\frac{d+p}{14}\), which simplifies to \(p=\frac{5d}{3}\).

Question:

\(p+28c=?\) Since \(2d+2p=28c\), then \(p+28c=p+(2d+2p)=2d+3p=2d+3*\frac{5d}{3}=7d\).


Answer: A
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Re: M21-32  [#permalink]

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New post 15 Oct 2015, 14:09
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Struggling to see how this can be done in 2 min... Bunuel, any thoughts?
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Re: M21-32  [#permalink]

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New post 30 May 2016, 03:23
I find it very hard to sort of discover which way to take and which variable to try to identify when it comes to questions like this. What is the logic that drives the decision to move c on one side? Any advice? many thanks!
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M21-32  [#permalink]

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New post 30 May 2016, 03:53
2
2
Bunuel wrote:
If 5 dollars and 35 crowns is equivalent to 7 pounds, and 4 dollars and 4 pounds is equivalent to 56 crowns, 1 pound and 28 crowns is equivalent to how many dollars?

A. $7.00
B. $7.50
C. $8.50
D. $9.00
E. $10.00


Strategy in such questions is to eliminate each variable one by one.

First Form equations:

Eq. 1: 5d+35c = 7p
Eq. 2 : 4d+4p = 56c


Eliminate 1 variable
From eq 1: p = (5/7)d+5c
Put this in Eq 2:

4d+4{(5/7)d+5c} = 56 c

4d+ (20/7)d+ 20 c = 56 c

(48/7) d = 36 c
c = (4/21)d

Express p also in terms of d
p = (5/7)d+5c

p = (5/7)d+ 5 (4/21) d = (15/21) d + (20/21) d = (35/21) d = (5/3)d

Now come to the question once again: 1 pound and 28 crowns is equivalent to how many dollars?

1p+28c = (5/3)d + 28* (4/21) d = (5/3) d + (16/3) d = (21/3) d = 7 d

Answer : A
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Re: M21-32  [#permalink]

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New post 30 Mar 2017, 17:49
Why do you decide to solve for C first vice any of the others? Or does it matter? I tried solving for P first and it messed me up.
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Re: M21-32  [#permalink]

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New post 08 Sep 2017, 21:57
Has anyone tried this with Linear Algebra? Trying to find a faster way..
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Re: M21-32  [#permalink]

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New post 15 Dec 2017, 08:39
Express the facts given in the two statements as :

5D+35C=7P
4D+4P=56C

We need to find P+28C. Here D stands for dollar, C for Crown , and P for Pound.

Express P in terms of C and C in terms of D. Substitute in P+28C to get the answer as option A.
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Re: M21-32  [#permalink]

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New post 15 Dec 2017, 18:50
I don't know if this is a subtle approach or not; 5,35,7 ,35 is divisible by 7 and 5; 4,4,56 , 56 is divisible by 4 ; 1,28? any number that divides 28, the only number that divides 28 is 7;
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Re: M21-32  [#permalink]

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New post 26 Aug 2018, 04:45
This question involves unnecessarily lengthy calculations, which GMAT normally doesn't ask.
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Re M21-32  [#permalink]

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New post 26 Aug 2018, 04:47
I think this is a poor-quality question and I don't agree with the explanation. This question involves lengthy calculations, which GMAT normally does not ask. Poor quality question.
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Re: M21-32  [#permalink]

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New post 26 Aug 2018, 04:52
VAKRATUNDA wrote:
I think this is a poor-quality question and I don't agree with the explanation. This question involves lengthy calculations, which GMAT normally does not ask. Poor quality question.


The average time of correct answer is 02:35, so the calculations are not that lengthy after all (of course if know what to do and how to do). The question is fine.
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Re: M21-32  [#permalink]

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New post 20 Sep 2018, 01:34
you can even solve it with currencty exchange rate (maybe a bit longer, quite effective tho)
ex. 5x + 35y=35
4x/y + 4/y= 56
Solve them and you ll find x=3/5 and y=4/35
In the end you just have to divide 28 coronas by 4/35 and you ll get 16/5 (which are now pounds) sum it with 1 and you ll get 21/5 (pounds)
By doing 21/5 / 3/5 ypou get 7.00


BTW definitelty a high quality question!
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Re: M21-32  [#permalink]

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New post 12 Oct 2018, 20:51
1
5 dollars and 35 crowns is equivalent to 7 pounds, and 4 dollars and 4 pounds is equivalent to 56 crowns, 1 pound and 28 crowns is equivalent to how many dollars?

7p-35c=5d &
-4p+56c=4d or -p+14c=d or 28c = 2d + 2p

7p-35c=5d
-4p+56c=4d
3p+21c=9d or p+7c = 3d or 4p +28c = 12d or 4p + 2d + 2p = 12d or 6p = 10d

then p + 28c = ? or p + 2d + 2p= ? or 2d + 3p = ? or 2d + \(\frac{5d}{3}\) * 3 = 2d + 5d = 7d (Ans A)
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Re: M21-32 &nbs [#permalink] 12 Oct 2018, 20:51
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