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Re: If x dollars is invested at 10 percent for one year and y [#permalink]
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) $1,108
(E) $1,200

2% = 56
1% = 28
10% = 280
100% 2800

0.10x - 0.8y = 56
X + y = 2000
X = 2000 - Y

0.10 (2000 – Y ) – 0.8Y = 56

200 – 0.10Y – 0.8Y = 56

-0.18Y = -144

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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2 equations with 2 unknowns

10x / 100 - 8y / 100 = 56

and

x + y = 2000

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

Answer B.
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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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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.
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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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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

Answer: B
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Re: If x dollars is invested at 10 percent for one year and y dollars is [#permalink]
everyone above has mentioned the conventional method. Which almost takes 2 mins. if anyone could suggest an approach for easy POE. Bunuel chetan2u sayantanc2k
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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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AdityaHongunti wrote:
everyone above has mentioned the conventional method. Which almost takes 2 mins. if anyone could suggest an approach for easy POE. Bunuel chetan2u sayantanc2k



Aditya two ways ..
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 [#permalink]
Agreed. Can someone please explain this? Thanks

amit2k9 wrote:
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.
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Re: If x dollars is invested at 10 percent for one year and y [#permalink]
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Hi Pankaj0901,

The principal amount invested in an account is NOT income, so the short answer is that amit2k9's interpretation of the prompt is not correct. The income in this case is any 'new' money that is placed into the account from the interest that is generated on that account. If you wanted to approach this Algebraically, then you could create the following 2 equations (and then solve via Substitution or Combination):

X + Y = 2000
.1X - .08Y = 56

As an alternative, you would likely find TESTing THE ANSWERS to be a lot faster.

GMAT assassins aren't born, they're made,
Rich
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Re: If x dollars is invested at 10 percent for one year and y [#permalink]
1
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Thank you EMPOWERgmatRichC
Your first statement clarifies my doubt - The principal amount invested in an account is NOT income.

EMPOWERgmatRichC wrote:
Hi Pankaj0901,

The principal amount invested in an account is NOT income, so the short answer is that amit2k9's interpretation of the prompt is not correct. The income in this case is any 'new' money that is placed into the account from the interest that is generated on that account. If you wanted to approach this Algebraically, then you could create the following 2 equations (and then solve via Substitution or Combination):

X + Y = 2000
.1X - .08Y = 56

As an alternative, you would likely find TESTing THE ANSWERS to be a lot faster.

GMAT assassins aren't born, they're made,
Rich
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Re: If x dollars is invested at 10 percent for one year and y [#permalink]
y = 2000 - x


.1x - .08(2000-x) = 56

.-160+.18x = 56

x = 1200 and y = 800

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

Answer: B




Why it is 0.10x = 0.08y + 56
and not
1.1x-1.08y=56 ??
kindly Help
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Re: If x dollars is invested at 10 percent for one year and y [#permalink]
1
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Expert Reply
Nsp10 wrote:
JeffTargetTestPrep wrote:
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

Answer: B




Why it is 0.10x = 0.08y + 56
and not
1.1x-1.08y=56 ??
kindly Help



Hi Nsp10,

The principal amount invested in an account is NOT income, so that interpretation of the prompt is not correct. The income in this case is any 'new' money that is placed into the account from the INTEREST that is generated on that account. If you wanted to approach this Algebraically, then you could create the following 2 equations (and then solve via Substitution or Combination):

X + Y = 2000
.1X - .08Y = 56

As an alternative, you would likely find TESTing THE ANSWERS to be a lot faster.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com
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Re: If x dollars is invested at 10 percent for one year and y [#permalink]
Thank you EMPOWERgmatRichC.
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Re: If x dollars is invested at 10 percent for one year and y [#permalink]
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