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agalstia
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Post subject: The value of an investment increases by x%  Posted: Wed Jun 30, 2010 2:37 pm |
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The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ?
A) 200x/100 + 2x
B) x(2 + x)/(1 + x)2
C) 2x/1 + 2x
D) x(200 + x)/10,000
E) 100-(10,000/100 + x)
Answer is E).
I found this on a CAT exam, and I understand the explanation in the solution. However, I tried solving the equation in different ways and I do not get the same answer. Please help.
These are my calculations:
I(1+x/100)(1-y/100)=I
(1+x/100)(1-y/100)=1
1-y/100+x/100-xy/10,000=1 (I distributed the 2 equations)
x/100-xy/10,000-y/100=0
x/100=xy/10,000+y/100
x=xy/100+y (I multiplied denominators by 100)
100x=xy+100y ( I multiplied denominator by 100 again to cancel it out)
100x=y(x+100)
100x/(x+100)=y
The denominator is correct, but not the numerator. Where did I go wrong?
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adiagr
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Post subject: Re: The value of an investment increases by x% Posted: Thu Jul 01, 2010 2:08 am |
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agalstia wrote: The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ?
A) 200x/100 + 2x
B) x(2 + x)/(1 + x)2
C) 2x/1 + 2x
D) x(200 + x)/10,000
E) 100-(10,000/100 + x)
Answer is E).
I found this on a CAT exam, and I understand the explanation in the solution. However, I tried solving the equation in different ways and I do not get the same answer. Please help.
These are my calculations:
I(1+x/100)(1-y/100)=I
(1+x/100)(1-y/100)=1
1-y/100+x/100-xy/10,000=1 (I distributed the 2 equations)
x/100-xy/10,000-y/100=0
x/100=xy/10,000+y/100
x=xy/100+y (I multiplied denominators by 100)
100x=xy+100y ( I multiplied denominator by 100 again to cancel it out)
100x=y(x+100)
100x/(x+100)=y
The denominator is correct, but not the numerator. Where did I go wrong? You have calculated correctly. (E) when simplified works out to 100x/(x+100)=y, which you have calculated.
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tim
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Post subject: Re: The value of an investment increases by x% Posted: Thu Jul 08, 2010 2:09 pm |
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| ManhattanGMAT Staff |
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Posts: 2242
Location: Southwest Airlines, seat 21C
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good work!
_________________
Tim Sanders
Manhattan GMAT Instructor
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tsayashi
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Post subject: Re: The value of an investment increases by x% Posted: Wed Sep 07, 2011 9:06 am |
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Location: Tokyo
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Yeah, I solved this question in the same way as agalstia did. Took me about 30 min. to figure out that
100x/(x+100)
is actually the same thing as E)'s
100-(10,000/100 + x).
I'm clear now that these things are identical to each other, but, I still wonder, if I was faced with this question in a real test, how should I be able to notice that among the answer choices, there's a converted version of the thing you got in your calculation...? When I was solving this question in the CAT2, I had no idea/couldn't notice at all that I had the correct answer in a wrong format, so I had to give up on choosing the right one, and to skip to the next question.
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JohnHarris
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Post subject: Re: The value of an investment increases by x% Posted: Fri Sep 09, 2011 11:23 pm |
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tsayashi wrote: ...but, I still wonder, if I was faced with this question in a real test, how should I be able to notice that among the answer choices, there's a converted version of the thing you got in your calculation... Basically, without enough experience, you punt (after ignoring the question until you are through with the 'less difficult' ones) or, if you are taking an exam with a #right minus #wrong for the score, you ignore the problem until you have finished the 'easy' problems and, no answer at the end, don't answer. One of the things that help in situations like this is that there is some similarity in the answers. The only answer which seems to fit is the one with the same denominator [it is a very simple expression and would be hard to get rid of]. So, thinking (E) looks complicated, you try to reduce it. In this case you would be successful.
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tim
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Post subject: Re: The value of an investment increases by x% Posted: Fri Sep 16, 2011 10:46 pm |
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| ManhattanGMAT Staff |
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Posts: 2242
Location: Southwest Airlines, seat 21C
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John, this is a ridiculous answer. Please take a closer look at how the GMAT works. You cannot do questions out of order or skip them without penalty. tsayashi, the real thing to do is to take your best guess on the actual test without spending too much time on the problem. Of course, in preparing for the GMAT, you will want to stick with this problem until you get it and thoroughly understand it. That's what you should do with every practice problem, so that you minimize your chances of being faced with the situation you describe on the actual test..
_________________
Tim Sanders
Manhattan GMAT Instructor
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JohnHarris
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Post subject: Re: The value of an investment increases by x% Posted: Fri Sep 16, 2011 11:58 pm |
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tim wrote: John, this is a ridiculous answer. Please take a closer look at how the GMAT works. You cannot do questions out of order or skip them without penalty. ... That being the case, it was a wrong answer in so far as the statement about "ignoring the question ..at the end, don't answer." goes and I thank you for correcting it for the students sake. I do wonder though if you would have said the same thing if an instructor had made a mistake on part of the problem answer or maybe it is just Guests that get their answers called ridiculous. But then maybe you don't think "punt" is really what you do when you "take your best guess" and that the suggestion to look at the answers in comparison to what you got as an answer is also ridiculous. If that is the case, then I think your answer is even more "ridiculous" than mine.
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tim
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Post subject: Re: The value of an investment increases by x% Posted: Fri Sep 23, 2011 5:05 pm |
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Posts: 2242
Location: Southwest Airlines, seat 21C
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Actually John, your advice about punting was fine. The thing that made your answer ridiculous was the inference that a student could go back to a question after doing all the easier ones (as well as your assumptions about how the test is graded). To answer your other question, i would have been much harder on another instructor if they gave the kind of advice that ignored the reality of the test; instructors are paid to know how the test works.. :)
_________________
Tim Sanders
Manhattan GMAT Instructor
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tsayashi
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Post subject: Re: The value of an investment increases by x% Posted: Sat Oct 01, 2011 4:50 am |
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John and tim, thank you both for your responses. I do see a point in what John wrote, to find a similarity between an answer choice and my own answer, and to punt at the denominator, since it's usually a thing hard to get rid of. That's a smart tip.
And John, don't worry about it, because I first didn't even understand what you meant by the part around "you ignore the problem until you have finished the 'easy' problems." Until tim came in, I had kept thinking you whipped out something in a very slangish English, that non-natives never get. :)
And of course, I also hope that I just won't get in a situation like the one I described above, in the next real exam I will take...
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tim
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Post subject: Re: The value of an investment increases by x% Posted: Tue Oct 04, 2011 7:43 am |
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Location: Southwest Airlines, seat 21C
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Thanks tsayashi, I’m glad John and I were able to help you..
_________________
Tim Sanders
Manhattan GMAT Instructor
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