Problem Solving

Judy invests a sum of money in a bank deposit at Bank A at 10%, interest compounded annually. An equal sum of money is invested in a bank deposit for 20% in Bank B compounded annually. After 2 years, the difference between the amount in the Bank A and B is $92. What is the sum of money invested in bank deposit of Bank B??

$400
$350
$800
$200

The answer has not been provided to me. i discussed it with the friend who passed it on to me! V both get $ 400 as the answer. Ill b very grateful if the guru's could help!

Johnrohit wrote:Judy invests a sum of money in a bank deposit at Bank A at 10%, interest compounded annually. An equal sum of money is invested in a bank deposit for 20% in Bank B compounded annually. After 2 years, the difference between the amount in the Bank A and B is $92. What is the sum of money invested in bank deposit of Bank B??

$400
$350
$800
$200

We can PLUG IN THE ANSWERS, which represent the amount invested in each account.

After 2 years, B-A = $92 -- an INTEGER value.
In A, the amount each year increases by 10%, implying that over 2 years the amount in A will be multiplied by 11/10 two times:
(11/10)(11/10)A = (121/100)A.
Implication:
The correct answer choice will be a MULTIPLE OF 100, so that the amount in A after 2 years will be an integer value.

Of the 3 multiples of 100 in the answer choices -- 200, 400, and 800 -- start with the MIDDLE value:

Answer choice A: 400
Bank A:
Amount after 1 year = 400 + (10/100)(400) = 400 + 40 = 440.
Amount after 2 years = 440 + (10/100)(440) = 440 + 44 = 484.

Bank B:
Amount after 1 year = 400 + (20/100)(400) = 400 + 80 = 480.
Amount after 2 years = 480 + (20/100)(480) = 480 + 96 = 576.

Resulting difference:
B-A = 576 - 484 = 92.
Success!

The correct answer is A.

Thanks gmat guru!! cud u plz teme how u got 11/10?

GMATGuruNY wrote:

Johnrohit wrote:Judy invests a sum of money in a bank deposit at Bank A at 10%, interest compounded annually. An equal sum of money is invested in a bank deposit for 20% in Bank B compounded annually. After 2 years, the difference between the amount in the Bank A and B is $92. What is the sum of money invested in bank deposit of Bank B??

$400
$350
$800
$200

We can PLUG IN THE ANSWERS, which represent the amount invested in each account.

After 2 years, B-A = $92 -- an INTEGER value.
In A, the amount each year increases by 10%, implying that over 2 years the amount in A will be multiplied by 11/10 two times:
(11/10)(11/10)A = (121/100)A.
Implication:
The correct answer choice will be a MULTIPLE OF 100, so that the amount in A after 2 years will be an integer value.

Of the 3 multiples of 100 in the answer choices -- 200, 400, and 800 -- start with the MIDDLE value:

Answer choice A: 400
Bank A:
Amount after 1 year = 400 + (10/100)(400) = 400 + 40 = 440.
Amount after 2 years = 440 + (10/100)(440) = 440 + 44 = 484.

Bank B:
Amount after 1 year = 400 + (20/100)(400) = 400 + 80 = 480.
Amount after 2 years = 480 + (20/100)(480) = 480 + 96 = 576.

Resulting difference:
B-A = 576 - 484 = 92.
Success!

The correct answer is A.

AIM TO CRACK GMAT wrote:
...
cud u plz teme how u got 11/10?
...

If the initial value is x and it is increased by 10% the final amount would be:
x + (10% of x)
x + (10/100)x
x [ 1 + 10/100 ]
x [ 1 + 1/10 ]
x [ 11/10 ]

If you again increase this value by 10% you would have to remultiply by 11/10.
This shortcut is very useful on the GMAT

Hope that helps.