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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # In 2001, John invests x dollars in a special account that yields y%  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 50544 In 2001, John invests x dollars in a special account that yields y% [#permalink] ### Show Tags 28 Jul 2017, 07:50 1 12 00:00 Difficulty: 65% (hard) Question Stats: 61% (02:05) correct 39% (02:55) wrong based on 180 sessions ### HideShow timer Statistics In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has$250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y? (A) 5 (B) 25 (C) 200 (D) 205 (E) 210 _________________ Senior PS Moderator Joined: 26 Feb 2016 Posts: 3301 Location: India GPA: 3.12 Re: In 2001, John invests x dollars in a special account that yields y% [#permalink] ### Show Tags 28 Jul 2017, 10:22 2 The interest accrued over 2 years is 20$ which is 10$per year Since this amount x had been invested for 7 years, the total interest is 70$

Total = Interest + Principal(x)
Principal(x) = Total - Interest = 270 - 70 = 200
Since 10 is 5% of 200 , y=5
Therefore the amount was invested at an annual rate of 5%(which is y) and amount invested(x) = 200

Sum of x and y = 200 + 5 = 205(Option D)
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Re: In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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21 Aug 2017, 08:41
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Top Contributor
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Bunuel wrote:
In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has$270 in his account, what is x + y?

(A) 5

(B) 25

(C) 200

(D) 205

(E) 210

With simple interest, the annual interest accrued is the SAME each year

We're told that in 2 years (from 2006 to 2008), the investment increases by $20 (from$250 to $270) So, EACH YEAR, the investment increases by$10
There are 7 years from 2001 (the year of John's initial investment of x dollars) to 2008 (when John's investment reaches $270) In those 7 years, John's ANNUAL interest is$10. So, the TOTAL interest accrued in 7 years = (7)($10) =$70

So, in 2001, John's initial investment = $270 -$70 = $200 So, x = 200 We now know that: John's initial investment =$200. The ANNUAL interest is $10. 10/200 = 5/100 = 5% So, the annual interest RATE = 5%. In other words, y = 5 So, x + y = 200 + 5 = 205 Answer: D RELATED VIDEO FROM OUR COURSE _________________ Brent Hanneson – GMATPrepNow.com Senior Manager Joined: 02 Apr 2014 Posts: 471 GMAT 1: 700 Q50 V34 Re: In 2001, John invests x dollars in a special account that yields y% [#permalink] ### Show Tags 07 Feb 2018, 12:13 one quick approach (might not work always) given amount increased by 20$ from 250 (2006) to 270 (2008)
so 2xy/100 = 20
=> xy = 1000
quickly scanning through choice and pick x = 200, y = 5 , option D fits well
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Re: In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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23 Sep 2018, 15:41
Bunuel wrote:
In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has$270 in his account, what is x + y?

(A) 5

(B) 25

(C) 200

(D) 205

(E) 210

Since he has $250 in his account in 2006 and$270 in 2008, it must be true that the amount of interest is $20 during these two years. Since it’s a simple interest, it must mean the amount of interest is$10 per year.

Therefore, in 2001, 5 years before 2006, it must have accumulated $50 in interest, which means the amount in 2001 is$200. So x = 200. Since 10/200 = 5/100 = 5%, y = 5. Therefore, x + y = 205.

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In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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Updated on: 26 Sep 2018, 23:52
To start, we can find the amount earned from 2006 to 2008:$$\270 - \250 = \20$$.

This means that John earned $$\20$$ in $$2$$ years, so the interest earned per year is $$\20 \div 2 = \10 \ per \ year$$.

Using the rate of $$\10/year$$, we can find the amount invested in 2001 by subtracting $$\10$$ every preceding year.

Since $$x$$ is the amount invested in 2001, then $$x = 200$$.

To find the annual interest rate, we use $$\200$$ as the principal.

Rate per year = Interest per year $$\div$$ Principal Rate per year $$= \10 \div \200$$

Rate per year = $$0.05$$ or $$5\%$$

Since $$y\%$$ is the annual interest rate, then $$y = 5$$.

Thus, the value of $$x + y = 200 + 5 = 205$$.

The final answer is .

Attachment:

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Originally posted by EMPOWERMathExpert on 26 Sep 2018, 23:34.
Last edited by Bunuel on 26 Sep 2018, 23:52, edited 1 time in total.
Fixed external link issue.
In 2001, John invests x dollars in a special account that yields y% &nbs [#permalink] 26 Sep 2018, 23:34
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# In 2001, John invests x dollars in a special account that yields y%

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