José deposited a total of $ 10,000 into two interest-bearing accounts

Hi gmatmania17,

This DS question includes a great algebra "shortcut" that you'll be able to take advantage of a couple of times on Test Day.

We're told that $10,000 is broken into two banks accounts that return 8% interest and 10% interest over the course of one year. We're asked how much money was DEPOSITED into the 10% account.

To start, we can create an equation with 2 variables:

X = amount invested at 8%
Y = amount invested at 10%

X + Y = $10,000

This gives us 1 equation with 2 variables. We are asked to solve for the value of Y.

Fact 1: Total interest = $870

From this, we can create ANOTHER equation...

.08X + .1Y = $870

We now have a "system" of equations - 2 variables and 2 unique equations...which means that we CAN solve for X and Y. The shortcut here is that we DON'T have to - it's enough to know that we have enough information to get the answer, so we can stop working.
Fact 1 is SUFFICIENT

Fact 2: The amount invested at 10% was $3,000 less than the amount invested at 8%

From this, we can create ANOTHER equation...

Y = X - $3,000

As in Fact 1, we have a "system" of equations, so we have enough information and we can stop working.
Fact 2 is SUFFICIENT

Final Answer:

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

Thank you! Can you please help me with the question of the annual rent collected ..?

What exactly is the question?

It is posted in the last page of the topic the annual rent that you can see in the data sufficiency category..

Hi gmatmania17,

I'm not sure what you mean when you say "the annual rent collected", but if you want to know the amount that is in each of the accounts, here's how you can figure it out:

In the original prompt, you have the equation...

X + Y = 10,000

In Fact 1, you have this equation....

.08X + .1Y = 870

Using "system" math, we can use either "substitution" or "combination" to get the value of the 2 variables (although the question just asks for the value of Y).

Let's multiply the entire second equation by -10

-.8X - Y = -8700

And then add it to the first equation...

-.8X - Y = -8700
X + Y = 10,000
---------------
.2X = 1300
X = 6500
Y = 3500

In Fact 2, we have a different "second equation", but we can do the same type of math that we did in Fact 1:

X + Y = 10,000
Y = X - 3,000

X + (X - 3,000) = 10,000
2X = 13,000
X = 6500
Y = 3500

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