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Math Expert V
Joined: 02 Sep 2009
Posts: 58332

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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 V Joined: 02 Sep 2009 Posts: 58332 Re M21-32 [#permalink] Show Tags 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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Intern  Joined: 17 Sep 2015
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GMAT 1: 760 Q50 V42 GPA: 3.65

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Struggling to see how this can be done in 2 min... Bunuel, any thoughts?
Manager  Joined: 18 May 2016
Posts: 67
Concentration: Finance, International Business
GMAT 1: 720 Q49 V39 GPA: 3.7
WE: Analyst (Investment Banking)

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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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Manager  Joined: 18 Jan 2010
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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  B
Joined: 12 Jan 2017
Posts: 1
Location: United States
Concentration: Finance, Technology
GMAT 1: 720 Q49 V41 WE: Information Technology (Military & Defense)

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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 B
Joined: 23 Nov 2016
Posts: 70
Location: United States (MN)
GMAT 1: 760 Q50 V42 GPA: 3.51

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Has anyone tried this with Linear Algebra? Trying to find a faster way..
Senior Manager  S
Joined: 08 Jun 2015
Posts: 420
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33

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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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Intern  B
Joined: 06 Jul 2015
Posts: 23

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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  B
Joined: 27 Apr 2011
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Location: India
GMAT Date: 06-13-2017

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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  B
Joined: 27 Apr 2011
Posts: 52
Location: India
GMAT Date: 06-13-2017

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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 V
Joined: 02 Sep 2009
Posts: 58332

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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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Intern  B
Joined: 20 May 2018
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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!
Director  V
Joined: 12 Feb 2015
Posts: 917

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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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Director  G
Joined: 22 Nov 2018
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GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Show Tags

I think this is a high-quality question and I agree with explanation.
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Manager  B
Joined: 09 Nov 2018
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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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