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# M19-13

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Math Expert
Joined: 02 Sep 2009
Posts: 45219

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16 Sep 2014, 01:05
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Difficulty:

65% (hard)

Question Stats:

57% (00:51) correct 43% (01:16) wrong based on 170 sessions

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1000 dollars were converted into pounds and then the pounds were converted back into dollars at the same exchange rate of $$x$$ pounds per dollar. If a commission of $$y\%$$ is levied on any exchange operation, what dollar amount was left after the exchanges?

(1) $$x = 0.6$$

(2) $$y = 5$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:05
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Official Solution:

Whatever the value of $$x$$, the first exchange turned 1000 dollars into the equivalent of $$1000(1 - \frac{y}{100})$$ dollars. This amount, in turn, became $$1000(1 - \frac{y}{100})^2$$ dollars after the second exchange. To answer the question we need to know the value of $$y$$.
Statement (1) by itself is insufficient. S1 tells us the value of$$x$$, not $$y$$.

Statement (2) by itself is sufficient. S2 tells us the value of $$y$$.

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Joined: 04 Aug 2014
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GMAT 1: 620 Q44 V31
GMAT 2: 620 Q47 V28
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18 Dec 2015, 02:11
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HI BRUNEL

CAN U PLS ELABORATE THE LOGIC BEHIND

1000(1−y/100) dollars
Manager
Joined: 08 Jul 2015
Posts: 56
GPA: 3.8
WE: Project Management (Energy and Utilities)

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26 May 2016, 02:32
sidagar wrote:
HI BRUNEL

CAN U PLS ELABORATE THE LOGIC BEHIND

1000(1−y/100) dollars

sidagar: the question said y% means y% = y/100.

Also, final value you receive after exchange = begin - commission (on begin value) = 1000 - 1000*y% = 1000 (1-y%) = 1000(1-y/100).

Cheers.
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Senior Manager
Joined: 31 Mar 2016
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Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
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20 Aug 2016, 04:56
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I think this is a high-quality question and I agree with explanation.
Intern
Joined: 03 Jul 2016
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10 Oct 2016, 07:42
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I agree with the impact of Y on exchange but what about x, once the exchange operation is done what about the loss through exchange rate, I believe that should also be converted.
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Joined: 07 May 2015
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04 Nov 2016, 02:37
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chetanyasahu1 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I agree with the impact of Y on exchange but what about x, once the exchange operation is done what about the loss through exchange rate, I believe that should also be converted.

CASE #1 Exchange Rate X = 0.6 (£0.6 = $1) •$1000 --> £600
• (-) Commission 5%  £570
• £570--> $950 • (-) Commisson 5% $902.5

CASE #2 Exchange Rate X = 2 (£2 = $1) •$1000 --> $2000 • (-) Commission 5% --> £1900 • £1900 -->$950
• (-) Commisson 5% --> \$902.5

SO, exchange rate does not matter.
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Joined: 09 Aug 2017
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09 Aug 2017, 08:46
neither of these two answers are logic and do not answer the question. The question was how much dollars you have after two exchanges. These two answers are more like conditions of task.
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Joined: 08 Jun 2015
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GMAT 1: 640 Q48 V29

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09 Aug 2017, 09:47
+1 for option B. We need value of "y". Only option B gives us the amount of dollars to be paid. The answer is B.
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Joined: 09 Nov 2016
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10 Aug 2017, 05:18
sidagar wrote:
HI BRUNEL

CAN U PLS ELABORATE THE LOGIC BEHIND

1000(1−y/100) dollars

Hi,
Its simple math..
1000-y% of 1000 = 1000 - $$\frac{y}{100}*1000$$ is what would remain for conversion to pounds.

Intern
Joined: 05 Jul 2017
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17 Aug 2017, 22:52
Bunuel wrote:
Official Solution:

Whatever the value of $$x$$, the first exchange turned 1000 dollars into the equivalent of $$1000(1 - \frac{y}{100})$$ dollars. This amount, in turn, became $$1000(1 - \frac{y}{100})^2$$ dollars after the second exchange. To answer the question we need to know the value of $$y$$.
Statement (1) by itself is insufficient. S1 tells us the value of$$x$$, not $$y$$.

Statement (2) by itself is sufficient. S2 tells us the value of $$y$$.

exchange rate X must be equal to a fraction i.e. [pound][/dollar] or [p][/d] .
Now after first conversion the amount would be = $$1000(1 - \frac{y}{100})$$ . [p][/d]

Now when we convert again the pound to dollar the fraction would be inverted to [d[/p]
and the new dollar value that would be remaining = $$1000(1 - \frac{y}{100})^2$$ . [p][/d] . [d[/p] = $$1000(1 - \frac{y}{100})^2$$

=> the Answer is B, as we just need to know the value of Y .
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Joined: 10 Sep 2015
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Concentration: Finance, Human Resources
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08 Nov 2017, 11:03
i am still confused on y% of what.
When converting from dollar to pound then y% of dollar and when from pound to dollar then y% of pound.

Please confirm if my understanding is correct
Intern
Joined: 26 Nov 2017
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02 May 2018, 05:03
question doesn't says that commission is charged on dollars or pound. confused.
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12 May 2018, 14:44
I think this is a high-quality question and the explanation isn't clear enough, please elaborate.
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Re M19-13   [#permalink] 12 May 2018, 14:44
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# M19-13

Moderators: chetan2u, Bunuel

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