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

Hi All,

While this is an old prompt, it can be solved by TESTing THE ANSWERS.

We're given a number of facts to work with:
1) $2,000 is invested in 2 different accounts.
2) The accounts pay 10% and 8% annual interest (calculated annually, for lack of any additional info)
3) After 1 year, the 10% account will generate $56 MORE than the 8% account.

We're asked for the amount of money invested in the 8% account.

To start, we can do a simple, hypothetical calculation. If we invested $1,000 in each account....
10% of $1,000 = $100
8% of $1,000 = $80
....then the difference would be $20. This is TOO SMALL (it's supposed to be $56), thus MORE than $1,000 is invested at 10% and LESS is invested at 8%. Eliminate Answers D and E.

Among the 3 remaining Answers, let's TEST Answer B: $800

IF....$800 is invested in the 8% account....
10% of $1200 = $120
8% of $800 = $64
...then the difference would be $56, which is an exact MATCH for what we were told. So this MUST be the answer.

Final Answer:

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

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

y = 2000 - x


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

.-160+.18x = 56

x = 1200 and y = 800

my answer is B

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

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.

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.

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
_________________

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
_________________

Agreed. Can someone please explain this? Thanks

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

Thank you EMPOWERgmatRichC
Your first statement clarifies my doubt - The principal amount invested in an account is NOT income.

y = 2000 - x


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

.-160+.18x = 56

x = 1200 and y = 800

Posted from my mobile device

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

Thank you EMPOWERgmatRichC.