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# If x dollars is invested at 10 percent for one year and y dollars is

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Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 100
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
If x dollars is invested at 10 percent for one year and y dollars is  [#permalink]

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17 May 2011, 08:33
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Difficulty:

45% (medium)

Question Stats:

70% (02:32) correct 30% (02:33) wrong based on 93 sessions

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If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by \$56. If \$2,000 is the total amount invested, how much is invested at 8 percent?

a. \$280
b. \$800
c. \$892
d. \$1108
e. \$1200
Senior Manager
Joined: 24 Mar 2011
Posts: 367
Location: Texas
Re: If x dollars is invested at 10 percent for one year and y dollars is  [#permalink]

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17 May 2011, 08:41
3
2 equations with 2 unknowns

10x / 100 - 8y / 100 = 56

and

x + y = 2000

Solving these 2 equations, x = 1200 and y = 800

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Re: If x dollars is invested at 10 percent for one year and y dollars is  [#permalink]

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17 May 2011, 09:29
annual income = principal + interest

for x @ 10% x + 10/100 * x = 1.1 x
for y @ 8% y + 8/100 * y = 1.08y

x+y = 2000

1.1x - 1.08y = 56
1.1 (2000-y) - 1.08y = 56
2200-1.1y-1.08y = 56
2.08y = 2144

y= 2144/2.18 = 983.46

so the question stem must say the annual interest difference rather than annual income difference.
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
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Re: If x dollars is invested at 10 percent for one year and y dollars is  [#permalink]

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18 May 2011, 20:11
Lucky twins -the answer is B or E
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Re: If x dollars is invested at 10 percent for one year and y dollars is  [#permalink]

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13 Jun 2017, 11:12
1
tonebeeze wrote:
If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by \$56. If \$2,000 is the total amount invested, how much is invested at 8 percent?

a. \$280
b. \$800
c. \$892
d. \$1108
e. \$1200

We are given that x = the number of dollars invested at 10% and y = the number of dollars invested at 8%. We are also given that the total amount invested is \$2000, and thus we have x + y = 2000 or x = 2000 - y. Finally, we are given that the annual income from the 10% investment exceeds the annual income from the 8% investment by \$56, so we can create the following equation to determine the value of y:

0.10x = 0.08y + 56

0.10(2000 - y) = 0.08y + 56

200 - 0.10y = 0.08y + 56

144 = 0.18y

14400 = 18y

y = 14400/18 = 800

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Re: If x dollars is invested at 10 percent for one year and y dollars is  [#permalink]

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28 Jul 2018, 03:27
everyone above has mentioned the conventional method. Which almost takes 2 mins. if anyone could suggest an approach for easy POE. Bunuel chetan2u sayantanc2k
Math Expert
Joined: 02 Aug 2009
Posts: 7041
Re: If x dollars is invested at 10 percent for one year and y dollars is  [#permalink]

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28 Jul 2018, 05:29
everyone above has mentioned the conventional method. Which almost takes 2 mins. if anyone could suggest an approach for easy POE. Bunuel chetan2u sayantanc2k

1) 8% would require at least two 0s to ensure that the difference is an integer
Otherwise say amount is 780...8% will result in a decimal
So answer will be 800, 1000 or 1200..
If it is 1000 each.. difference is 100 for 10% and 80 for 8%, so 100-80=20
But we want 56>20
So if you want to increase the difference, the greater should increase and smaller decrease, so only possible value 800

Otherwise
1) 56 has a units digit of 6 which is 10-4..
So 8*z should have units digit as 4.. 8*800 /100 will give 4 as units digit
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Re: If x dollars is invested at 10 percent for one year and y dollars is &nbs [#permalink] 28 Jul 2018, 05:29
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