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Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 03 Sep 2012, 04:47 1 This post received KUDOS Expert's post 4 This post was BOOKMARKED 00:00 Difficulty: 5% (low) Question Stats: 79% (02:23) correct 21% (01:22) wrong based on 1024 sessions ### HideShow timer Statistics Lucy invested$10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 Practice Questions Question: 31 Page: 156 Difficulty: 600 [Reveal] Spoiler: OA _________________ Math Expert Joined: 02 Sep 2009 Posts: 37073 Followers: 7241 Kudos [?]: 96278 [6] , given: 10730 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]

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03 Sep 2012, 04:47
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SOLUTION

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705

The value of the account today would be $$10,000*1.1*1.05*0.9$$. Now, the question is how to calculate this efficiently.

$$10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}$$ --> 10,000 will cancel and we'll get: $$11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395$$.

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03 Sep 2012, 05:51
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Bunuel wrote:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705

This is a question of successive % change. This question ultimately reduces to a multiplication problem.
Final value after successive % change on $10,000 =$10,000 X 1.1 X 1.05 X .9
1.1 X 1.05 X .9 = 1.0395
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07 Sep 2012, 02:06
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SOLUTION

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705

The value of the account today would be $$10,000*1.1*1.05*0.9$$. Now, the question is how to calculate this efficiently.

$$10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}$$ --> 10,000 will cancel and we'll get: $$11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395$$.

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19 Oct 2012, 01:06
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Stupid lucy! If she sees that there is a crisis in the world and her accounts diminishes every year, why hasn't she redraw her money after the second year?!?... I multiplied the last year with 1.1 instead of 0.9 and i got the D answear... This is lucy's fault! :D
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 15 Dec 2012, 11:14 Bunuel wrote: SOLUTION Lucy invested$10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 The value of the account today would be $$10,000*1.1*1.05*0.9$$. Now, the question is how to calculate this efficiently. $$10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}$$ --> 10,000 will cancel and we'll get: $$11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395$$. Answer: B. Thank you for the answer Bunuel, but i was just wondering. When you chose the denominators for the different fractions, was your goal to get 10 000 in the denominator so we could cancel Lucy's initial investment? Smart move by the way Intern Joined: 24 Apr 2012 Posts: 48 Followers: 0 Kudos [?]: 22 [1] , given: 1 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]

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16 Dec 2012, 03:07
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Ans::
the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10395. So the answer is (B).
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 02 May 2013, 10:12 .10x10,000=$1,000 end of y1 = 11,000
.05x11,000= $550.00 end of y2 = 11,550 .10x11,550= 1,150 -1,155 (subtract y2 with the loss of y3) end of y3= 10,395 GMAT Club Legend Joined: 09 Sep 2013 Posts: 13910 Followers: 589 Kudos [?]: 167 [0], given: 0 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]

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06 Aug 2014, 21:37
Percent increase over time: 1.1 * 1.05 * 0.9 = 1.0395

1.0395 * 10,000 $= 10,395$

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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 10 Sep 2014, 02:43 Bunuel wrote: Lucy invested$10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 Practice Questions Question: 31 Page: 156 Difficulty: 600 10,000*1.1--> 10% increase in the first year. 11000*1.05 --> 5% increase in second year 10% decrease from 11550 --> 10395 Intern Joined: 06 Nov 2014 Posts: 13 Followers: 0 Kudos [?]: 1 [1] , given: 0 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]

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16 Nov 2014, 07:51
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I cut corners this way:
10% of 10 000=1000 (move the dot one spot)
next year you have 11 000
5% of 11 000= 550 (move the dot one spot 1100 = 10%, divide by two to get 5% 1100/2=550)
So then you have 11 550, and subtract 10% from this --> 11 550 - 1155. Well it has to be less than 11 000 since more than 1000 is subtracted (eliminating D & E), and it has to end in 5 since you're subtracting a number ending in five (eliminating A & C) that leaves only B.
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19 Dec 2015, 08:19
year 1 Increases 10% 1000 Value became 11000
Year 2 increase 5% 550 value became 11550
Year 3 decrease 10% 1155 value became 11550-1155 = $10395. _________________ Discipline does not mean control. Discipline means having the sense to do exactly what is needed. Director Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 613 Location: United States (CA) Followers: 23 Kudos [?]: 251 [2] , given: 2 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]

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25 May 2016, 08:01
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Bunuel wrote:
Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705

To determine the value of the account today we want to set up an expression showing the various percent increases and decreases.

Remember we are multiplying each percent increase or decrease against the original value of $10,000. Also, we must remember that a 10% increase is the same as multiplying by 1.1, a 5% increase is the same as multiplying by 1.05, and a 10% decrease is the same as multiplying by 0.9. That is: 10,000(1.1)(1.05)(0.9) Because the multiplication may get a bit complicated in the equation above, we should convert each decimal to a fraction, allowing us to reduce before multiplying. Thus, we have: 10,000(11/10)(105/100)(9/10) This is equivalent to: 10,000(11 x 105 x 9/10,000) Thus we see the the two values of 10,000 cancel out, and we are left with: 11 x 105 x 9 = 99 x 105 = 10,395 Note: If you did not want to perform the multiplication of the final step, you could have used a combination of units digits and estimation to come to the correct answer. Keep in mind that the product of 99 and 105 will have a units digit of 5. That leaves us with only B ($10,395) and E ($12,705) as possible answer choices. Next, by rounding up 99 to 100 and multiplying 100 by 105 we get a product of 10,500. Because we rounded up and answer choice E is LARGER than 10,500, it’s not a possible answer choice. Thus, the correct answer is B,$10,395.
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