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
David used part of $100,000 to purchase a house
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 14
- Joined: Sat Nov 24, 2012 4:09 am
-
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Thu Nov 29, 2012 8:37 am
- Location: Toronto, Canada
When you invest different portions of your money and get different rates of return (in this case simple annual interest), your overall rate of return can be calculated as a weighted average, where the portion in each investment is the weight for that interest.
In this case, the weighted average will be twice as close to 6% as it is to 4% (because 6% has double the weight). Take the distance between 4% and 6%, divide it into 3 equal parts (so each part is 2/3%) and pick 5 1/3 % (twice as close to 6% as it is to 4%). Rewrite 5 1/3 % as an improper fraction (you should always do this to make GMAT calculations easier) and you find the overall interest rate on the investments was 16/3 %.
If David had $X left over after he purchased the house, then $16X/300 = $320 (I simply multiplied X by 16/3 % and translated % to 1/100).
Divide that equation by 16 and you'll get x/300=20
Multiply by 300 to get X=$6,000
So the house cost $100,000-$6,000=$94,000
Answer is B.
In this case, the weighted average will be twice as close to 6% as it is to 4% (because 6% has double the weight). Take the distance between 4% and 6%, divide it into 3 equal parts (so each part is 2/3%) and pick 5 1/3 % (twice as close to 6% as it is to 4%). Rewrite 5 1/3 % as an improper fraction (you should always do this to make GMAT calculations easier) and you find the overall interest rate on the investments was 16/3 %.
If David had $X left over after he purchased the house, then $16X/300 = $320 (I simply multiplied X by 16/3 % and translated % to 1/100).
Divide that equation by 16 and you'll get x/300=20
Multiply by 300 to get X=$6,000
So the house cost $100,000-$6,000=$94,000
Answer is B.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Of every 3 dollars invested, $1 earns 4% interest and $2 earns 6% interest.ritumaheshwari02 wrote: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
Average interest earned by every $3 = (1*4 + 2*6)/3 = 16/3% = 16/300.
From here we can plug in the answers, which represent the purchase price of the house.
Answer choice C: 88,000
Amount invested = 100,000 - 88,000 = 12000.
Interest earned = (16/300)(12000) = 640.
Since the interest earned is too great, the purchase price of the house must INCREASE, so that the amount invested DECREASES.
Answer choice B: 94,000
Amount invested = 100,000 - 94,000 = 6000.
Interest earned = (16/300)(6000) = 320.
Success!
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- kevincanspain
- GMAT Instructor
- Posts: 613
- Joined: Thu Mar 22, 2007 6:17 am
- Location: madrid
- Thanked: 171 times
- Followed by:64 members
- GMAT Score:790
Suppose he invested x at 4%. Then he invested 2x at 6% and the price of the home was 100000 - 3x
320 = 0.04x + 0.06(2x) = 0.16x
x = 320/0.16 = 2000
The price of the home was 100000-3(2000) = 94000
320 = 0.04x + 0.06(2x) = 0.16x
x = 320/0.16 = 2000
The price of the home was 100000-3(2000) = 94000
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
GMAT Instructor
Gmatclasses
Madrid
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?ritumaheshwari02 wrote: ↑Thu Nov 29, 2012 8:40 amDavid 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
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