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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   55% (hard)

Question Stats: 54% (01:23) correct 46% (01:37) wrong based on 186 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) $$y = 5$$

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Math Expert V
Joined: 02 Sep 2009
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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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Intern  B
Joined: 04 Aug 2014
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GMAT 1: 620 Q44 V31 GMAT 2: 620 Q47 V28 GPA: 3.2

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HI BRUNEL

CAN U PLS ELABORATE THE LOGIC BEHIND

1000(1−y/100) dollars
Intern  Joined: 08 Jul 2015
Posts: 40
GPA: 3.8
WE: Project Management (Energy and Utilities)

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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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I think this is a high-quality question and I agree with explanation.
Intern  Joined: 03 Jul 2016
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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.
Intern  S
Joined: 07 May 2015
Posts: 41
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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. Intern  Joined: 09 Aug 2017 Posts: 1 Re: M19-13 [#permalink] Show Tags 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. Senior Manager  S Joined: 08 Jun 2015 Posts: 420 Location: India GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33 Re: M19-13 [#permalink] Show Tags +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. _________________ " The few , the fearless " Manager  S Joined: 09 Nov 2016 Posts: 53 Location: India Re: M19-13 [#permalink] Show Tags 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. Hope this answers your question. Intern  B Joined: 05 Jul 2017 Posts: 26 Re: M19-13 [#permalink] Show Tags 1 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 $$y$$. Answer: B Adding to bunuel's solution 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 . Manager  S Joined: 10 Sep 2015 Posts: 67 Location: India Concentration: Finance, Human Resources GMAT 1: 640 Q47 V31 GMAT 2: 660 Q47 V35 GMAT 3: 700 Q49 V36 GPA: 4 Re: M19-13 [#permalink] Show Tags 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  B Joined: 26 Nov 2017 Posts: 4 Re M19-13 [#permalink] Show Tags question doesn't says that commission is charged on dollars or pound. confused. Manager  B Status: Turning my handicaps into assets Joined: 09 Apr 2017 Posts: 122 Re M19-13 [#permalink] Show Tags I think this is a high-quality question and the explanation isn't clear enough, please elaborate. _________________ If time was on my side, I'd still have none to waste...... Intern  B Joined: 20 Apr 2018 Posts: 31 Location: United States (DC) GPA: 3.84 Re: M19-13 [#permalink] Show Tags I just used logic here. For example, say we have$1000 dollars and the exchange rate of dollars to pounds is 1/3, then $1000 dollars gives us 3000 pounds. The exchange rate remains the same, thus 3000 pounds at 1/3 is still$1000 dollars. Thus, we only need to find Y to get the actual amount.

Please correct me if I am wrong.
Intern  B
Joined: 29 Jun 2017
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Hi,

I understand that the commission(y) needs to be deducted from the amount so converted. But the question asks us to find the amount left after deducting the commission. In that case, isn't the value of x i.e the exchange rate important? Only after knowing the value of x will we be able to find the remaining amount.

Senior Manager  P
Joined: 09 Jun 2014
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Megha1119 wrote:
Hi,

I understand that the commission(y) needs to be deducted from the amount so converted. But the question asks us to find the amount left after deducting the commission. In that case, isn't the value of x i.e the exchange rate important? Only after knowing the value of x will we be able to find the remaining amount.

No.I think a unit is converted into from pound to dollar and then from dollar to pound..doesnt matter how many dollar is equal to how many pounds..because the value will change and the unit will get back to original value..
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Joined: 18 Jul 2018
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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 $$y$$.

Hi Bunuel

Instead of calculating exchange difference at the first exchange and then the second exchange, can we approach the Q in the following manner instead???

exchange rate => £x = $1 first exchange with y% commission =$1000 = £1000x(y/100) = £10xy

second exchange with y% commission = (10xy/x)(y/100) = $y^2/10 Q is asking what dollar amount was left after the exchanges? Hence, we need to know value of y. Manager  B Joined: 18 Jul 2018 Posts: 52 Location: United Arab Emirates M19-13 [#permalink] Show Tags Xylan Sorry to bother you again! Instead of calculating exchange difference at the first exchange and then at the second exchange, can we approach the Q in the following manner instead??? exchange rate => £x =$1

first exchange with y% commission = $1000 = £1000x(y/100) = £10xy second exchange with y% commission = (10xy/x)(y/100) =$ y^2/10

Q is asking what dollar amount was left after the exchanges?

Hence, we need to know value of y. Does this make sense ??
Manager  P
Status: The darker the night, the nearer the dawn!
Joined: 16 Jun 2018
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JIAA wrote:
Xylan

Sorry to bother you again!
Instead of calculating exchange difference at the first exchange and then at the second exchange, can we approach the Q in the following manner instead???

exchange rate => £x = $1 first exchange with y% commission =$1000 = £1000x(y/100) = £10xy

second exchange with y% commission = (10xy/x)(y/100) = $y^2/10 Q is asking what dollar amount was left after the exchanges? Hence, we need to know value of y. Does this make sense ?? JIAA It's a beautiful Question, attacking the conscience of the test taker who is in a hurry. Few things to keep in mind: Correctly inferred from the Q-statement: exchange rate =>$ 1 = £ $$x$$
£ 1 = $$$1/x$$ If a commission of $$y$$% is levied on any exchange operation, then the remaining amount(amount that is left after the commission-cost) should be $$Amount*(1 - y/100)$$ 1st exchange with y% commission with starting amount:$ -------> £
$$$1000$$ ------leads to------> £ $$1000*(1 - y/100)*x$$ 2nd exchange with y% commission with starting amount: £ ------->$
£ $$1000*(1 - y/100)*x$$ ------leads to------> \$ $$1000*(1 - y/100)^2$$: the value of x cancels out

Since the value of X cancels out, only Y's value is required to answer the Q.
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