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# M21-32

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Math Expert
Joined: 02 Sep 2009
Posts: 47983

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16 Sep 2014, 01:15
2
12
00:00

Difficulty:

95% (hard)

Question Stats:

54% (02:41) correct 46% (03:06) wrong based on 98 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: 47983 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
Posts: 12
GMAT 1: 760 Q50 V42
GPA: 3.65

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15 Oct 2015, 15:09
2
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!

Senior Manager
Joined: 18 Jan 2010
Posts: 254

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30 May 2016, 04:53
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

Intern
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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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.
Manager
Joined: 23 Nov 2016
Posts: 76
Location: United States (MN)
GMAT 1: 760 Q50 V42
GPA: 3.51

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08 Sep 2017, 22:57
Has anyone tried this with Linear Algebra? Trying to find a faster way..
Director
Joined: 08 Jun 2015
Posts: 529
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38

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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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Intern
Joined: 06 Jul 2015
Posts: 24

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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;
Re: M21-32 &nbs [#permalink] 15 Dec 2017, 19:50
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# M21-32

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