## The value of an investment increases by x%

Math questions from any Manhattan Prep GMAT Computer Adaptive Test.
agalstia
Course Students

Posts: 12
Joined: Thu Sep 10, 2009 8:03 pm

### The value of an investment increases by x%

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)

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?
Students

Posts: 88
Joined: Tue Jan 26, 2010 6:47 am

### Re: The value of an investment increases by x%

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)

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.
tim
ManhattanGMAT Staff

Posts: 5665
Joined: Tue Sep 11, 2007 9:08 am
Location: Southwest Airlines, seat 21C

### Re: The value of an investment increases by x%

good work!
Tim Sanders
Manhattan GMAT Instructor

https://www.manhattanprep.com/gmat/forums/a-few-tips-t31405.html
ss268
Students

Posts: 3
Joined: Fri Sep 17, 2010 2:01 pm
Location: Tokyo

### Re: The value of an investment increases by x%

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.
JohnHarris
Forum Guests

Posts: 35
Joined: Tue Aug 30, 2011 7:38 am

### Re: The value of an investment increases by x%

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.
tim
ManhattanGMAT Staff

Posts: 5665
Joined: Tue Sep 11, 2007 9:08 am
Location: Southwest Airlines, seat 21C

### Re: The value of an investment increases by x%

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

https://www.manhattanprep.com/gmat/forums/a-few-tips-t31405.html
JohnHarris
Forum Guests

Posts: 35
Joined: Tue Aug 30, 2011 7:38 am

### Re: The value of an investment increases by x%

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.
tim
ManhattanGMAT Staff

Posts: 5665
Joined: Tue Sep 11, 2007 9:08 am
Location: Southwest Airlines, seat 21C

### Re: The value of an investment increases by x%

Tim Sanders
Manhattan GMAT Instructor

https://www.manhattanprep.com/gmat/forums/a-few-tips-t31405.html
ss268
Students

Posts: 3
Joined: Fri Sep 17, 2010 2:01 pm
Location: Tokyo

### Re: The value of an investment increases by x%

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...
tim
ManhattanGMAT Staff

Posts: 5665
Joined: Tue Sep 11, 2007 9:08 am
Location: Southwest Airlines, seat 21C

### Re: The value of an investment increases by x%

Tim Sanders
Manhattan GMAT Instructor

https://www.manhattanprep.com/gmat/forums/a-few-tips-t31405.html
catennacio
Course Students

Posts: 26
Joined: Sun Aug 15, 2010 5:33 pm

### Re: The value of an investment increases by x%

This MGMAT question is not cool. I arrived at y=100x/(100+x) and stared at the 5 answer choices for like 4 mins before deciding to guess (which I was wrong) and move on. In the real test, how am I supposed to know which answer choice will reduce into my answer. This is not to mention there are chances that I made mistakes to arrive at my own answer. So I wouldn't risk spending the time to work out on each of the answer (5 of them to reach E) choice and hope that it will arrive at my result. The only thing I agree here is when making a quick glance, only E has the same denominator, which makes it a good contender.
tim
ManhattanGMAT Staff

Posts: 5665
Joined: Tue Sep 11, 2007 9:08 am
Location: Southwest Airlines, seat 21C

### Re: The value of an investment increases by x%

hopefully by the time you get to the real test you will have developed the skills to process this type of question quickly and correctly. the surest way NOT to achieve this goal is to stare at the answer choices for four minutes. you should always try to find something to do with a problem, and then once you're done with your problem set you should review the problem to figure out how to approach it more efficiently. approaching each problem as a learning experience rather than deciding the problem is not cool is definitely the better way to go..
Tim Sanders
Manhattan GMAT Instructor

https://www.manhattanprep.com/gmat/forums/a-few-tips-t31405.html
catennacio
Course Students

Posts: 26
Joined: Sun Aug 15, 2010 5:33 pm

### Re: The value of an investment increases by x%

tim wrote:hopefully by the time you get to the real test you will have developed the skills to process this type of question quickly and correctly. the surest way NOT to achieve this goal is to stare at the answer choices for four minutes. you should always try to find something to do with a problem, and then once you're done with your problem set you should review the problem to figure out how to approach it more efficiently. approaching each problem as a learning experience rather than deciding the problem is not cool is definitely the better way to go..

Advice taken. However on a side note, I don't think GMAC tries to trick the students with such tricks as this one :)
tim
ManhattanGMAT Staff

Posts: 5665
Joined: Tue Sep 11, 2007 9:08 am
Location: Southwest Airlines, seat 21C

### Re: The value of an investment increases by x%

i actually thought immediately of PS209 and DS127 in the OG when i saw this one. not sure what "trick" you're referring to, but it's best to be prepared for anything the GMAT can throw at you on these math questions..
Tim Sanders
Manhattan GMAT Instructor

https://www.manhattanprep.com/gmat/forums/a-few-tips-t31405.html
I_need_a_700plus
Course Students

Posts: 32
Joined: Mon Mar 30, 2009 7:53 am

### Re: The value of an investment increases by x%

What is the best approach to this problem? I tried plugging in values, but got confused with the "simple" numbers that I decided to choose.

Is algebra the best approach for this problem?

Thanks.