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# M19#13

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Manager
Joined: 07 Jan 2008
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07 Feb 2009, 16:25
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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
B

Source: GMAT Club Tests - hardest GMAT questions
SVP
Joined: 29 Aug 2007
Posts: 2492
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08 Feb 2009, 11:47
topmbaseeker wrote:
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. $$y = 5$$

Dollar to pounds
$1000 = 1000x pounds after commission = 1000x (100 - 5%) pounds = 950x pounds Pounds to Dollar 950x pounds = 950x (1/x) dollar = 950 dollar after commission = 950 dollar (100 - 5%)= 95% of 950 dollar so B got it. _________________ Manager Joined: 20 Oct 2009 Posts: 113 Schools: MIT LGO (Admitted), Harvard (Admitted)) Followers: 8 Kudos [?]: 31 [0], given: 0 Re: M19#13 [#permalink] ### Show Tags 25 Dec 2009, 08:01 I was thinking without any calculations that since the exchange rate did not change x is irrelevant. However Y is still essential. If you are running out of time on the math session, just pick B and move on. If you have some time to spare, then you verify with calculation. topmbaseeker wrote: 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. $$y = 5$$ * Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient [Reveal] Spoiler: OA B Source: GMAT Club Tests - hardest GMAT questions _________________ Dream the impossible and do the incredible. Live. Love. Laugh. Intern Joined: 20 Nov 2009 Posts: 4 GMAT 1: 620 Q V0 Followers: 0 Kudos [?]: 5 [0], given: 0 Re: M19#13 [#permalink] ### Show Tags 26 Dec 2009, 04:18 [strike]Thank you for your very useful tips & explanations.[/strike] Manager Joined: 02 Oct 2008 Posts: 58 Followers: 5 Kudos [?]: 46 [0], given: 0 Re: M19#13 [#permalink] ### Show Tags 27 Dec 2009, 16:34 even my choice is B. Manager Joined: 23 Nov 2009 Posts: 53 Followers: 1 Kudos [?]: 11 [0], given: 1 Re: M19#13 [#permalink] ### Show Tags 29 Dec 2009, 17:30 I thought C, but I guess B is sufficient _________________ A kudos would greatly help Tuhin Senior Manager Joined: 01 Nov 2010 Posts: 295 Location: India Concentration: Technology, Marketing GMAT Date: 08-27-2012 GPA: 3.8 WE: Marketing (Manufacturing) Followers: 10 Kudos [?]: 72 [0], given: 44 Re: M19#13 [#permalink] ### Show Tags 03 Jan 2011, 23:54 b is final choice.. _________________ kudos me if you like my post. Attitude determine everything. all the best and God bless you. Manager Joined: 23 Oct 2010 Posts: 87 Location: India Followers: 3 Kudos [?]: 26 [0], given: 6 Re: M19#13 [#permalink] ### Show Tags 04 Jan 2011, 07:39 B. Conv and reconv ==> (1000*x - 1000*x*y)/x Manager Joined: 25 May 2011 Posts: 157 Followers: 2 Kudos [?]: 55 [0], given: 71 Re: M19#13 [#permalink] ### Show Tags 07 Nov 2011, 01:31 You just need to know that if the exchange rate of converting dollar to pound is $$X$$, then the exchange of converting pound to dollar is $$\frac{1}{X}$$ Manager Joined: 08 Sep 2011 Posts: 75 Concentration: Finance, Strategy Followers: 3 Kudos [?]: 2 [0], given: 5 Re: M19#13 [#permalink] ### Show Tags 05 Jan 2012, 16:52 B. You don't need to know the exchange rate because it will be equal once you convert it back. you need to know how much they charge between conversions Senior Manager Joined: 08 Jun 2010 Posts: 397 Location: United States Concentration: General Management, Finance GMAT 1: 680 Q50 V32 Followers: 3 Kudos [?]: 77 [0], given: 13 Re: M19#13 [#permalink] ### Show Tags 07 Jan 2012, 06:47 I have one little problem with the wording of this problem.. It doesn't mention where the y% is applied. Is it applied after conversion or before (on the total amount)? Different assumptions lead to different answers. First, If you assume the commission is applied to starting amount:$ --> GBP
1000 --> 1000x-10y

1000x-10y --> 1000-10(y/x) -10xy + (10y^2)/100

Second, if you assume the commission is applied to final amount

\$ --> GBP

1000 --> 1000x-10xy

1000x-10xy --> 10y-y^2

Joined: 27 Dec 2012
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Concentration: Technology, Entrepreneurship
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07 Jan 2013, 22:29
1000 dollars = 1000x GBP
after deducting y % commission
1000x-10xy GBP which is nothing but 1000-10y dollars.

again converting back to dollars, divide GBP by x
= 1000-10y - commission
commission = y% of (1000-10y) dollars
=10y - (y^2)/10

so total money left in dollars is 1000 -10y -(10y -(y^2)/10)
=1000-20y+(y^2)/10 which is independent of x because this amount is in dollars. So the catch in the very starting is that question asks about dollars. That should be used to save time.

Two cents.
Manager
Joined: 20 Oct 2013
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Location: United States
Concentration: General Management, Real Estate
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20 Apr 2014, 02:34
The conversion is from dollar to pound and back to dollar at the same exchange rate (x). In the end, we still have 1000 dollars, so x is not important.

To get the remaining amount after levy: 1000*(1-y%)^2

-> (2) is sufficient
Re: M19#13   [#permalink] 20 Apr 2014, 02:34
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# M19#13

Moderator: Bunuel

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