Alex deposited x dollars into a new account that earned 8 : GMAT Problem Solving (PS)
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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]

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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.
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Re: Alex deposited x dollars into a new account [#permalink]

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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]

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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).

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Re: Alex deposited x dollars into a new account that earned 8 [#permalink]

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17 Sep 2013, 06:24
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Re: Alex deposited x dollars into a new account [#permalink]

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22 Sep 2013, 04:58
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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).

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]

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22 Sep 2013, 05:07
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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).

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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Re: Alex deposited x dollars into a new account [#permalink]

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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]

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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).

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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05 Feb 2014, 10:11
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]

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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.
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Re: Alex deposited x dollars into a new account that earned 8 [#permalink]

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08 Jul 2015, 09:48
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Alex deposited x dollars into a new account that earned 8 [#permalink]

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18 Sep 2015, 00:46
See attachment for the solution
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Re: Alex deposited x dollars into a new account that earned 8 [#permalink]

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03 Aug 2016, 14:38
BrainLab wrote:
See attachment for the solution

might be a dumb question but at the end of 2nd year, why is it being multiplied by 1.08? should not it be multiplied by 0.08 since it is 8 %? then the resulting amount can be added back to the amount at the end of first year
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Alex deposited x dollars into a new account that earned 8 [#permalink]

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24 Sep 2016, 15:37
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)

[Reveal] Spoiler:
I tried it this way

Lets say Alex starts with $100 (X) and earns$8 as 1st year interest

Year 2 Alex has 108 in his account and deposits another (X) 100, starting off year 2 with $208 in his account By the end of year 2 Alex has earned another 8% ($16.64) on his money ($208) Now Alex has$224.64 (W) in his account, lets round it up to $225. So X = 100 and W = 225, ie W = 2.25 X B is W/1.08+1.16 = W/2.24 Last edited by Vyshak on 24 Sep 2016, 22:15, edited 3 times in total. Topic Merged. Refer to the above discussions Intern Joined: 23 Jun 2016 Posts: 45 Followers: 0 Kudos [?]: 5 [0], given: 13 Alex deposited x dollars [#permalink] ### Show Tags 12 Oct 2016, 23:07 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)+(1.08^3)] Math Expert Joined: 02 Sep 2009 Posts: 36520 Followers: 7065 Kudos [?]: 92890 [0], given: 10528 Re: Alex deposited x dollars into a new account that earned 8 [#permalink] ### Show Tags 12 Oct 2016, 23:19 Akuthiala 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)+(1.08^3)] Merging topics. Please search before posting. Thank you. _________________ Senior Manager Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 491 Location: United States (CA) Followers: 19 Kudos [?]: 175 [0], given: 2 Re: Alex deposited x dollars into a new account that earned 8 [#permalink] ### Show Tags 14 Oct 2016, 04:48 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) We start by determining the new value of the x dollars Alex deposited into his account that earned 8 percent annual interest. At the end of the first year the amount of money in the account was 1.08x and then he added another x dollars to the account, so the account then had a total value of 1.08x + x dollars. The 1.08x + x dollars earned another 8 percent interest for the year. Thus, the total value of his account at the end of the second year is: 1.08(1.08x + x) = (1.08^2)x + 1.08x Since the new total value is equal to w, we can set up the following equation: w = (1.08^2)x + 1.08x Now we must get x in terms of w. w = x(1.08^2 + 1.08) w/(1.08^2 + 1.08) = x Answer: D _________________ Jeffrey Miller Scott Woodbury-Stewart Founder and CEO Re: Alex deposited x dollars into a new account that earned 8 [#permalink] 14 Oct 2016, 04:48 Similar topics Replies Last post Similar Topics: If Scott has earned x dollars by working 3 days a week at a constant 7 01 Aug 2016, 04:53 If$ 5,000 is invested in an account that earns 8% interest compounded 1 03 Jan 2016, 11:17
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