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# On January 1, 2010, Dave invests 70% of his retirement savings in Anta

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Math Expert
Joined: 02 Sep 2009
Posts: 48067
On January 1, 2010, Dave invests 70% of his retirement savings in Anta  [#permalink]

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29 Apr 2015, 04:09
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7
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Difficulty:

95% (hard)

Question Stats:

51% (03:23) correct 49% (03:31) wrong based on 190 sessions

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On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then x is between

A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60

Kudos for a correct solution.

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Posts: 1247
Location: Ukraine
Concentration: Entrepreneurship, Technology
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Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta  [#permalink]

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29 Apr 2015, 08:00
1
1
Bunuel wrote:
On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then x is between

A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60

Kudos for a correct solution.

Let's $$s$$ be common savings, than
$$large = 0.7s*1.05*0.9 = 0.66s$$
$$middle = 0.2s*1.1*0.8=0.17s$$
$$small = 0.1s*1.15*x = 0.12sx$$

and we can make equation
$$large + middle + small = s$$
$$0.66s + 0.17s + 0.12sx = s$$
$$0.12sx = 0.17s$$
$$x = 1.41$$

So x = 41%

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Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta  [#permalink]

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29 Apr 2015, 09:52
Hi Harley..

Even I got the answer as D, but the percentage I got was around 47 %.

Harley1980 wrote:
Bunuel wrote:
On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then x is between

A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60

Kudos for a correct solution.

Let's $$s$$ be common savings, than
$$large = 0.7s*1.05*0.9 = 0.66s$$
$$middle = 0.2s*1.1*0.8=0.17s$$
$$small = 0.1s*1.15*x = 0.12sx$$

and we can make equation
$$large + middle + small = s$$
$$0.66s + 0.17s + 0.12sx = s$$
$$0.12sx = 0.17s$$
$$x = 1.41$$

So x = 41%

_________________

Kudos to you, for helping me with some KUDOS.

Retired Moderator
Joined: 06 Jul 2014
Posts: 1247
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta  [#permalink]

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29 Apr 2015, 10:00
shriramvelamuri wrote:
Hi Harley..

Even I got the answer as D, but the percentage I got was around 47 %.

I think that's mean that I or you have made a mistake. If you write your way of solving we can check
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Posts: 48067
Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta  [#permalink]

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04 May 2015, 04:15
1
3
Bunuel wrote:
On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then x is between

A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

The difficulty of this “percent change” problem is not so much conceptual as it is “executional”—you want to be able to solve it quickly, easily, and of course accurately. Let’s get to the workout!

You’ve got three investments (at various percent allocations) changing by various other percents over two time periods. The numbers don’t look too ugly, but you might suspect that the result will be hard to compute exactly, because the problem only asks for a range. Thus, you should be ready to switch to estimation at some point.

Pick a smart number for the total retirement savings Dave starts with—say, $10,000. (If you pick$100, you’ll wind up needing to track decimals, so give yourself a couple more zeros to start with.)

Here are the starting values:

L = $7,000 M =$2,000
S = $1,000 Apply the first year’s changes, so that you have these numbers on 1/1/2011: Newer L =$7,000 + 5% = $7,350 Newer M =$2,000 + 10% = $2,200 Newer S =$1,000 + 15% = $1,150 Now apply the second year’s changes to L and M: Newest L =$7,350 – 10% = $7,350 –$735 = $6,615 Newest M =$2,200 – 20% = $2,200 –$440 = $1,760 Add these to get$8,375. So the newest S must be $10,000 (the target final total of Dave’s retirement savings) minus$8,375, or $1,625. The dollar change in S from 1/1/11 to 1/1/12 is$1,625 – $1,150 =$475. So the question is this: what percent change does $475 represent, from a starting point of$1,150? Since $1,150 is a nasty divisor, switch to benchmarks: 10% of$1,150 = $115. So 20% is just double that, or$230.

And 40% is double that, or $460. Since$475 is just slightly larger than $460 (but not enough to get you to 50%, which would be$460 + $115), x must be between 40 and 50. Intuitively, it should make sense that you’d need a much bigger positive percent change in the smallest investment (S) to make up for even a moderate downturn in the larger investments (L and M), so if you were completely stuck for time and needed to guess in a hurry, you should favor C/D/E over A or B. The correct answer is D. _________________ Intern Joined: 25 Apr 2015 Posts: 7 Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta [#permalink] ### Show Tags 10 May 2015, 05:27 Let's s be common savings, than large=0.7s∗1.05∗0.9=0.66s middle=0.2s∗1.1∗0.8=0.17s small=0.1s∗1.15∗x=0.12sx and we can make equation large+middle+small=s 0.66s+0.17s+0.12sx=s 0.12sx=0.17s x=1.41 So x = 41% Answer is D Understood the concept. But can someone please tell me why the value of large stocks 0.66s is not added to 0.17 ? Intern Joined: 17 Mar 2014 Posts: 1 Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta [#permalink] ### Show Tags 24 Jun 2015, 14:25 I conceptually understand this problem, however the rounding taken place in this problem causes me to get answer C (I rounded up the medium stock calculation). Ex: medium stock = 0.2s*(1.1)*(0.8) = .176s If you round this number down you get and answer D. Can someone please give me some insight on this problem? Retired Moderator Joined: 06 Jul 2014 Posts: 1247 Location: Ukraine Concentration: Entrepreneurship, Technology GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta [#permalink] ### Show Tags 24 Jun 2015, 14:48 foster22 wrote: I conceptually understand this problem, however the rounding taken place in this problem causes me to get answer C (I rounded up the medium stock calculation). Ex: medium stock = 0.2s*(1.1)*(0.8) = .176s If you round this number down you get and answer D. Can someone please give me some insight on this problem? Hello foster22 If you want make precise calculations you should make it in all calculations: large=$$0.7s∗1.05∗0.9=0.6615s$$ middle=$$0.2s∗1.1∗0.8=0.176s$$ small=$$0.1s∗1.15∗x=0.115sx$$ large+middle+small=s $$0.6615s+0.176s+0.115sx=s$$ $$0.115sx=0.1625s$$ $$x=1.41$$ _________________ Manager Joined: 25 May 2016 Posts: 77 Location: Singapore Concentration: Finance, General Management GMAT 1: 620 Q46 V30 Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta [#permalink] ### Show Tags 21 Jul 2018, 06:56 How can you solve this within 2mins? It took me ard 3.5mins. _________________ 15 Kudos left to unlock next level. Help me by Contributing one for cause .. Please Manick9 If you found my post helpful, kindly press "+1 Kudos" to appreciate Manager Joined: 20 Sep 2016 Posts: 191 Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta [#permalink] ### Show Tags 28 Jul 2018, 07:18 My approach : step 1 :L =$70
M = $20 S =$10

Apply the first year’s changes, so that you have these numbers on 1/1/2011:

Newer L = $7,0 + 5% =$73.5
Newer M = $2,0 + 10% =$22
Newer S = $1,0 + 15% =$11.5

step 2:
Now as per the info the resultant is same ie 100

.9*73.5 +.8*22 + (100+x/100 )11.5 = 100
therefore>>approx values:
<67 + < 16 + >11.5 =100
therefore :
67+16 + >11.5= 100
(100+x/100)11.5 =17

then i approximated that it must lie between 40-50 as greater than 50 would go higher than 17.
Bunuel chetan2u . Is my approach right?
Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta &nbs [#permalink] 28 Jul 2018, 07:18
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