ritumaheshwari02 wrote: ↑

Thu Nov 29, 2012 8:40 am

David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?

A. $96,000
B. $94,000
C. $88,000
D. $75,000
E. $40,000

STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also solve the question algebraically. However, since I can already see we can immediately eliminate two answer choices, I know that I need only test ONE answer choice.
So I'm going to start testing answer choices

First recognize that the correct answer can't be A or D. Here's why:
If the correct answer were choice A ($96,000), then David invested the remaining $4000, which means he invested 1/3 of $4000 at an interest rate of 4% and 2/3 of $4000 at an interest rate of 6%.
The problem is that $4000 isn't divisible by 3.
So, for example, 1/3 of $4000 = $1333.33333...., which means David invested $1333 and one-third of a penny at 4%.
Since we can't invest one-third of a penny, answer choice A is disqualified.
We can apply the same logic to eliminate answer choice D.

Of the remaining three answer choices (B, C and E), I'll test the middle answer...
(C) $88,000
If David spent $88,000 of his $100,000 on his house, then he invested the remaining $12,000
1/3 of $12,000 is $4000, which means David invested $4000 at a 4% simple interest rate, which means the interest after 1 year = 4% of $4000 = $160
2/3 of $12,000 is $8000, which means David invested $8000 at a 6% simple interest rate, which means the interest after 1 year = 6% of $8000 = $480
So, the TOTAL income from the two investments = $160 + $480 = $640

The question tells us that the total income from the two investments is $320, which means we can eliminate choice C.
Also, since we want the total income to be LESS THAN $640, we need David to invest less than $12,000.
In other words, we need the house price to be greater than $88,000, which means we can also eliminate answer choice E.

By the process of elimination, the correct answer must be B.

Answer: B