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
OA D
Source: Magoosh
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In 2001, John invests x dollars in a special account that yi
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BTGmoderatorDC
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Jay@ManhattanReview
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Given that the sum $x amounted to $250 in 2006 and to $270 in 2008, we can deduce that the simple interest on $x for 2 years = 270 - 250 = $20BTGmoderatorDC 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
OA D
Source: Magoosh
Thus, 20 = x*y*2/100 => xy = 1,000
Again, since the sum $x invested in 2001 amounted to $250 in 2006, SI for 5 years is $(250 - x).
Thus, 250 - x = x*y*5/100
25,000 - 100x = 5xy
Plugging-in the value of xy = 1,000 in 25,000 - 100x = 5xy, we have x = $200 and y = 5. Thus, x + y = 200 + 5 = 205.
The correct answer: D
Hope this helps!
-Jay
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The interest accrued over 2 years is 20$ which is 10$ per year.
Since this amount x had been invested for 7 years, the total interest is 70$.
Total = Interest + Principal(x)
Principal(x) = Total - Interest = 270 - 70 = 200.
Since 10 is 5% of 200, y = 5.
Therefore the amount was invested at an annual rate of 5%(which is y) and amount invested(x) = 200.
Sum of x and y = 200 + 5 = 205.
Since this amount x had been invested for 7 years, the total interest is 70$.
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.
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Scott@TargetTestPrep
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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 simple interest, it must mean that the amount of interest is $10 per year.BTGmoderatorDC 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
OA D
Source: Magoosh
Therefore, in 2006, 5 years since 2001, the account must have accrued $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.
Answer: D
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