On a vacation, Rose exchanged $500.00 for euros at an exchange rate of

Question

On a vacation, Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar and spent $\frac{3}{4}$ of the euros she received. If she exchanged the remaining euros for dollars at an exchange rate of $1.20 per euro, what was the dollar amount she received?

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00

mikemcgarry · Accepted Answer

Dear AbdurRakib , This is a great question! Thanks for posting it! I'm happy to respond. :-)

Step #1 She exchanges $500 for euros at 0.8 euro/dollar. Set up a proportion, where x is the number of euros she originally received (x/$500) = (0.8 euro)/($1) Cross-multiply and use the doubling & halving rule: x = 0.8*500 = 0.4*1000 = 400 euros Step #2 She spends 3/4, so after her wild days in Europe, she is left with just 100 euros. Step #3 She exchanges 100 euros back to dollars at $1.20 per euro. Again set up a proportion, where y is the number of dollars she gets back. y/100 = $1.20/(1 euro) Cross-multiply: y = $1.20*100 = $120 Answer = (D) Does all this make sense? Mike :-)

umg · Answer

No Need to convert $ to Euro and Vice-versa.

Exchange rate of $ to Euro = 0.80
Exchange rate of Euro to $ = 1.20

% of Money Received if she exchanges $500 to Euro and back = 0.8 * 1.2 = 0.96 = 96%

Therefore, there is a 4% Net loss of Money due to exchange.

$ left after Expenditure =  500*\frac{1}{4} = $125 
Loss due to Exchange = 4% of 125 =  \frac{(125*4)}{100}= $5

Net $ she is left with = 125 - 5 = $120

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=laTW2Nz_zG8

sauravpaul · Answer

Rose got 400 Euros
She spent 300 Euros
Remaining Euros = 100 Euros
She got $120 (@ $1.20 per euro)

ScottTargetTestPrep · Answer

We are given that Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar. Since 1 dollar = 0.8 euros, 500 dollars = 500 x 0.8 = 400 euros.

Since she spent spent 3/4 of her euros, she was left with 1/4 x 400 = 100 euros.

Finally, she exchanged her remaining euros for dollars at a rate of 1.20 dollars per euro.

Since 1 euro = 1.20 dollars, she ended up with 100 x 1.2 = 120 dollars.

Answer: D

VinitSanghvi800 · Answer

Let me try to help in a simple manner.

$500*0.8*1/4*1.2
= $500*4/5*1/4*6/5
= $120

Posted from my mobile device

EMPOWERMathExpert · Answer

On a vacation, Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar and spent $\frac{3}{4}$ of the euros she received. If she exchanged the remaining euros for dollars at an exchange rate of $1.20 per euro, what was the dollar amount she received?

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00

Since nations have their own unique currencies, the need to change from one currency to another is important when one travels from one country to another. This question is based on this scenario.

Step 1: The amount of dollars Rose exchanged originally into euros = $500.00 at the rate of 0.80 euro per dollar.

Step 2: At the rate of 0.8 euro per dollar, $500.00 = 500 x 0.8 = 400 euros. This means that Rose collected 400 euros for the $500 exchanged.

Step 3: Since Rose spent ¾ of the 400 euros she received; the amount she spent is given as: ¾ x 400 = 300 euros. The remaining number of euros that Rose has after spending 300 euros is 400 -300 = 100 euros.

Step4: Rose exchanged the 100 euros that remained back to dollars at an exchange rate of $1.20 per euro. The dollar amount Rose received from this transaction is calculated as follows: 100 x $1.20

Therefore, Rose received  D .

anum23 · Answer

i got it correct but in 2.28 min coz i confused the starting point to be 500 euros and then converted the 'spent' amount in euros finally instead of dollars!

1hopefulone · Answer

Like many others I solved this the same way. What I did however was to change the decimals to fractions. So 500$ x 4/5 = 400. Then she spent 3/4 of that so 400 x 3/4 = 300. (Or to save time she saved 1/4 of that leading to 100). Then she exchanged 100 euros back to dollars at 1.2. Thus 100 x 1.2 = 120.

500$ x 4/5 = 400 euros total
400 euros x 1/4 remaining = 100 euros remaining
100 euros x 1.2 exchange rate = 120$

Posted from my mobile device

500$ x 4/5 = 400 euros total
400 euros x 1/4 remaining = 100 euros remaining 
100 euros x 1.2 exchange rate = 120$

Posted from my mobile device

rai000 · Answer

There's a speedy method here, provided that you've memorized your fractions:
Recognize that 0.8 euros can be stated as the fraction 4/5... then you are left with the much faster equation of (500 dollars)*(4/5 euros)=400 euros

If she spends 3/4th of what she has: (400 euros)(3/4)=300 euros. She has 100 euros remaining. Just convert that to dollars:
(100 euros)(1.20 dollars/1 euro)= 120 dollars .

shaonkarim · Answer

Sample☺

Dollar to euro rate is .8
500*.8=400 euro 
Spent =3/4*400=300
Remaining euro =400-300=100 
So, converted to dollar =100*1.2=120 dollar

Answer:D

Posted from my mobile device

Syeedarimshah · Answer

It's said 1euro = 1.2 dollars so dollar is bigger than euro I think we should divide 100/1.2 = 83 dollars respectively

Posted from my mobile device

Bunuel · Answer

Please read both the question and solutions more carefully. The question says: $1.20 per euro, so 1 euro = $1.20. So, 100 euros = $120.

plaverbach · Answer

I think the fastest way is to do all the math at the same time:

1. Convert into fractions
a.  0.80=\frac{4}{5} 
b.  1.2=\frac{6}{5}

2.
 \frac{4}{5}. 500. \frac{1}{4}.\frac{6}{5}

500=100.5=20.5.5

Substitute:
 \frac{4}{5}. 20.5.5. \frac{1}{4}.\frac{6}{5} =

Cancel what you can:
( 4  / 5 ). 5.5 . 20 .(1/  4  ).( 6 / 5 )=
6.20=120

dylanl1218 · Answer

I like taking a more methodical approach to currency translation problems by writing out the translation rates as fractions:

(1) 0.80 Euro to dollar is equivalent to 4 (Euro) / 5 (Dollar), which when you multiply $500 X (4 Euro/5 Dollar) you get 400 euros
(2) Spending 3/4 of the 400 euros means you have 1/4 of your euros remaining, so 400 ( 1/4 ) = 100 Euros
(3) Finally a 1.20 Dollar to euro exchange rate is equivalent to 12 (Dollar) /10 ( Euro ) = 6 (Dollar) / 5 (Euro), so you're left with $120

Abramo · Answer

Attention guys: I have done a very dumb mistake here. I just skipped the part which says she has spent 3/4 of his money which had to be subtracted from the dollar amount.

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=upf2RpjfT0I

ThatDudeKnows · Answer

mikemcgarry  did a great job with the answer here!

But there's another way that might be worth looking at as you move past just thinking about the math content and try to master the test-taking techniques and psychologies that you'll be able to use on other questions.
 
There is an opportunity here to use the answer choices to narrow things down.

If Rose gets $1.20 for every Euro at the end of the trip, I'm skeptical of answer choices B, C, and E, since none of those is evenly divisible but $1.20 (and not only are they not evenly divisible, they require repeating decimals for the number of Euros). I'd feel pretty good that the credited response is going to be either A or D. Maybe I'll try one to see if it works?

D looks a little easier to start with, since dividing by $1.20 is easy peasy. Okay, that would mean Rose had 100 Euros once she was done with the spending on her trip. And that means she had 400 Euros at the start of her trip. Is that what she would have gotten at the 0.80 Euros per dollar exchange rate given? Well, wouldn't you know: it IS!! Answer choice D.

ManifestDreamMBA · Answer

Whenever decimals are involved, I am afraid to check answer choices for multiples since, what if there's some say 1.25 lying there in the calculations which will make my 12 look 15 and lead me to eliminate a potential correct answer choice or make me do the backward calculations all for nothing. Is there a good strategy to identify when this will work vs not, esp. when fractions are involved?

On a vacation, Rose exchanged $500.00 for euros at an exchange rate of

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On a vacation, Rose exchanged $500.00 for euros at an exchange rate of

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