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# M21-32

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Math Expert
Joined: 02 Sep 2009
Posts: 58332

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16 Sep 2014, 01:15
2
16
00:00

Difficulty:

95% (hard)

Question Stats:

50% (02:48) correct 50% (03:41) wrong based on 76 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 _________________ Math Expert Joined: 02 Sep 2009 Posts: 58332 Re M21-32 [#permalink] ### Show Tags 16 Sep 2014, 01:15 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 $$p+28c=p+(2d+2p)=2d+3p=2d+3*\frac{5d}{3}=7d$$.

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Joined: 17 Sep 2015
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GMAT 1: 760 Q50 V42
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15 Oct 2015, 15:09
3
Struggling to see how this can be done in 2 min... Bunuel, any thoughts?
Manager
Joined: 18 May 2016
Posts: 67
GMAT 1: 720 Q49 V39
GPA: 3.7
WE: Analyst (Investment Banking)

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30 May 2016, 04:23
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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My debrief: Self-study: How to improve from 620(Q39,V36) to 720(Q49,V39) in 25 days!
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Joined: 18 Jan 2010
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30 May 2016, 04:53
3
4
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

Intern
Joined: 12 Jan 2017
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Location: United States
Concentration: Finance, Technology
GMAT 1: 720 Q49 V41
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30 Mar 2017, 18:49
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.
Current Student
Joined: 23 Nov 2016
Posts: 70
Location: United States (MN)
GMAT 1: 760 Q50 V42
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08 Sep 2017, 22:57
Has anyone tried this with Linear Algebra? Trying to find a faster way..
Senior Manager
Joined: 08 Jun 2015
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15 Dec 2017, 09:39
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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15 Dec 2017, 19:50
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;
Manager
Joined: 27 Apr 2011
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26 Aug 2018, 05:45
This question involves unnecessarily lengthy calculations, which GMAT normally doesn't ask.
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Hope it's clear.
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Manager
Joined: 27 Apr 2011
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GMAT Date: 06-13-2017

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26 Aug 2018, 05:47
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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Hope it's clear.
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Math Expert
Joined: 02 Sep 2009
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26 Aug 2018, 05:52
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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Joined: 20 May 2018
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20 Sep 2018, 02:34
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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12 Oct 2018, 21:51
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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25 Feb 2019, 08:28
I think this is a high-quality question and I agree with explanation.
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Give +1 kudos if this answer helps..!!
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18 Aug 2019, 06:38
I think this is a high-quality question and I agree with explanation.
Re M21-32   [#permalink] 18 Aug 2019, 06:38
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# M21-32

Moderators: chetan2u, Bunuel