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Alex deposited x dollars into a new account that earned 8

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Alex deposited x dollars into a new account that earned 8 [#permalink] New post 23 Jan 2012, 12:12
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Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)

I thought as
1.08x+2x(1.08) = w
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jan 2012, 17:39, edited 1 time in total.
Edited the answer choices
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Re: Alex deposited x dollars into a new account [#permalink] New post 23 Jan 2012, 15:37
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Hi there! I'm happy to contribute to this one! :)

The question: Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w?

So first, Alex puts in x dollars.

One year goes by, and the x dollar accrues interest ---> x(1.08)

Then, Alex adds another x dollars --> x + x(1.08)

Then the second year goes by, and that whole amount gets multiplied by 1.08 ---> [x + x(1.08)]*(1.08) = x(1.08) + x(1.08)^2 = x[1.08 + (1.08)^2]

We are told this amount, the sum total after two years, equals w, so w = x[1.08 + (1.08)^2]

Dividing by the brackets to solve for x, we get x = w/(1.08 + (1.08)^2)

The answer choices as they appear in your post are technically incorrect, because they are lacking parentheses. If you underestimate the importance of parentheses, they will bite you in the butt over and over again on the real GMAT. Assuming the parentheses were in the right places, the answer would be
[Reveal] Spoiler:
D
.

The key idea is: the x dollar amount that was in there for both years is multiplied twice by the multiplier. That's why there has to be a factor of (1.08)^2 floating around somewhere.

Does this make sense? Please let me know if you have any questions on what I've said.

Mike :)
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Re: Alex deposited x dollars into a new account [#permalink] New post 23 Jan 2012, 17:38
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kajolnb wrote:
Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)

I thought as
1.08x+2x(1.08) = w


Account at the end of the first year would be 1.08x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.08x+x) dollars. Account at the end of the second year would be (1.08x+x)*1.08=w --> x(1.08^2+1.08)=w --> x=w/(1.08+1.08^2).

Answer: D.
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Re: Alex deposited x dollars into a new account that earned 8 [#permalink] New post 17 Sep 2013, 06:24
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Re: Alex deposited x dollars into a new account [#permalink] New post 22 Sep 2013, 04:58
Bunuel wrote:
kajolnb wrote:
Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)

I thought as
1.08x+2x(1.08) = w


Account at the end of the first year would be 1.08x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.08x+x) dollars. Account at the end of the second year would be (1.08x+x)*1.08=w --> x(1.08^2+1.08)=w --> x=w/(1.08+1.08^2).

Answer: D.


I did the math, 1.08x + x = 2.08x
2.08x * 1.08 = 2.2464
couldn't spot the answer after 2+ mins.

How are we supposed to know to leave (1.08x + x) in order to see the cube to 1.08^2 x?
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Re: Alex deposited x dollars into a new account [#permalink] New post 22 Sep 2013, 05:07
Expert's post
Skag55 wrote:
Bunuel wrote:
kajolnb wrote:
Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)

I thought as
1.08x+2x(1.08) = w


Account at the end of the first year would be 1.08x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.08x+x) dollars. Account at the end of the second year would be (1.08x+x)*1.08=w --> x(1.08^2+1.08)=w --> x=w/(1.08+1.08^2).

Answer: D.


I did the math, 1.08x + x = 2.08x
2.08x * 1.08 = 2.2464
couldn't spot the answer after 2+ mins.

How are we supposed to know to leave (1.08x + x) in order to see the cube to 1.08^2 x?


On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

For this question this would give you a hint that you shouldn't calculate 1.08^2+1.08.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Alex deposited x dollars into a new account [#permalink] New post 22 Sep 2013, 07:51
Got it, wasn't aware of this. Thanks!
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Re: Alex deposited x dollars into a new account [#permalink] New post 05 Feb 2014, 01:45
Bunuel wrote:
kajolnb wrote:
Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)

I thought as
1.08x+2x(1.08) = w


Account at the end of the first year would be 1.08x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.08x+x) dollars. Account at the end of the second year would be (1.08x+x)*1.08=w --> x(1.08^2+1.08)=w --> x=w/(1.08+1.08^2).

Answer: D.



I did quick math (1.08)^2 = 1.16 and selected option B.

I know option D is more precise, but can GMAC give two option different only by third decimal digit (1.16 Vs 1.1664)?
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Re: Alex deposited x dollars into a new account [#permalink] New post 05 Feb 2014, 10:11
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idinuv wrote:
I did quick math (1.08)^2 = 1.16 and selected option B.

I know option D is more precise, but can GMAC give two option different only by third decimal digit (1.16 Vs 1.1664)?

Dear idinuv,
I'm happy to respond. :-)
The short answer to your question is: "absolutely." Math is all about precision. Yes, in many Quant questions, GMAC spreads out the answer choices and allows for estimation and quick approximations, but that is not always the case. One way to think about it is that, for a pure mathematician, there is a continuous infinity of decimals between 1.16 and 1.1664 --- more decimals in that separation than the number of grains of sand it would take to fill the Universe. For a pure mathematician, there is just equal or completely unequal, and any inequality, no matter how small, is vast beyond all reckoning. Another perspective is what business people care about. Suppose, for the sake of argument, that x = $100,000,000 --- then, whether we divide by 1.16 or 1.1664 results in a difference of $437,014.52 : do you want that discrepancy to come out of your paycheck, because you were the person who rounded to two decimal places? Small decimal difference get very big in a hurry when one starts dealing with numbers in the millions & billions --- which values, of course, are typical in some industries. ------ Both the perspective of the pure mathematician and the perspective of big business are very important in informing the design of GMAT Quant questions, and from the point of view of both of these perspectives, the difference between 1.16 and 1.1664 could be tremendously important, not something to overlook.
Does all this make sense?
Mike :-)
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Re: Alex deposited x dollars into a new account [#permalink] New post 05 Feb 2014, 10:48
mikemcgarry wrote:
idinuv wrote:
I did quick math (1.08)^2 = 1.16 and selected option B.

I know option D is more precise, but can GMAC give two option different only by third decimal digit (1.16 Vs 1.1664)?

Dear idinuv,
I'm happy to respond. :-)
The short answer to your question is: "absolutely." Math is all about precision. Yes, in many Quant questions, GMAC spreads out the answer choices and allows for estimation and quick approximations, but that is not always the case. One way to think about it is that, for a pure mathematician, there is a continuous infinity of decimals between 1.16 and 1.1664 --- more decimals in that separation than the number of grains of sand it would take to fill the Universe. For a pure mathematician, there is just equal or completely unequal, and any inequality, no matter how small, is vast beyond all reckoning. Another perspective is what business people care about. Suppose, for the sake of argument, that x = $100,000,000 --- then, whether we divide by 1.16 or 1.1664 results in a difference of $437,014.52 : do you want that discrepancy to come out of your paycheck, because you were the person who rounded to two decimal places? Small decimal difference get very big in a hurry when one starts dealing with numbers in the millions & billions --- which values, of course, are typical in some industries. ------ Both the perspective of the pure mathematician and the perspective of big business are very important in informing the design of GMAT Quant questions, and from the point of view of both of these perspectives, the difference between 1.16 and 1.1664 could be tremendously important, not something to overlook.
Does all this make sense?
Mike :-)


Thanks for your clear explanation Mike !

I totally concede with both the perspectives you have put-forth. My perspective about the design of incorrect answers has been that the incorrect answers generally are Partial answers, Wrong path answers, Simple manipulation answers etc. As suggested, I would now also lookout for 'Precision' based on the range of answer choices given.
Re: Alex deposited x dollars into a new account   [#permalink] 05 Feb 2014, 10:48
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