Robin invested a total of $12,000 in two investments, X and Y, so that the investments earned the same amount of simple annual interest. How many dollars did Robin invest in investment Y ?
(1) Investment X paid 3 percent simple annual interest, and investment Y paid 6 percent simple annual interest.
(2) Robin invested more than $1,000 in investment X.
GMAT Official Guide 2019 Robin invested a total of $12,000
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- 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
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Since X and Y constitute a total investment of $12,000, we get;BTGmoderatorDC wrote:Robin invested a total of $12,000 in two investments, X and Y, so that the investments earned the same amount of simple annual interest. How many dollars did Robin invest in investment Y ?
(1) Investment X paid 3 percent simple annual interest, and investment Y paid 6 percent simple annual interest.
(2) Robin invested more than $1,000 in investment X.
X + Y = 12,000
Statement 1:
Since 3% of X must yield the same amount of interest as 6% of Y, we get:
0.03X = 0.06Y
Since we have two variables (X and Y) and two distinct linear equations (X+Y=12000 and 0.03X=0.06Y), we can solve for the two variables.
Thus, the value of Y can be determined.
SUFFICIENT.
Statement 2:
It's possible that X = 2000 and Y = 10,000.
It's possible that X = 3000 and Y = 9,000.
Since Y can be different values, INSUFFICIENT.
The correct answer is A.
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
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
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Let X = The number of dollars invested in investment XBTGmoderatorDC wrote:Robin invested a total of $12,000 in two investments, X and Y, so that the investments earned the same amount of simple annual interest. How many dollars did Robin invest in investment Y ?
(1) Investment X paid 3 percent simple annual interest, and investment Y paid 6 percent simple annual interest.
(2) Robin invested more than $1,000 in investment X.
Let Y = The number of dollars invested in investment Y
Target question: What is the value of Y?
Given: Robin invested a total of $12,000 in two investments, X and Y, so that the investments earned the same amount of simple annual interest.
If the total investment is $12,000, we can write: X + Y = 12,000
Statement 1: Investment X paid 3 percent simple annual interest, and investment Y paid 6 percent simple annual interest.
So, the annual interest paid by investment X = 0.03X and the interest paid by investment Y = 0.06Y
Since the annual interest on the two investments are EQUAL, we can write: 0.03X = 0.06Y
We now have the following system of linear equations:
X + Y = 12,000
0.03X = 0.06Y
Since we COULD solve this system for Y, we COULD answer the target question with certainty (but we would never waste valuable time actually solving the system!)
Since we could answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: Robin invested more than $1,000 in investment X.
Since we don't know the exact value of the amount Robin invested in X, and since we don't know anything about the interest rates for the investments, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT
ASIDE: If you're not convinced that statement 2 is not sufficient, consider these two cases:
Case a: X = 6,000, Y = 6,000, and the interest rate for each investment is 10%. Notice that the interest for each investment will be equal. Here, the answer to the target question is Y = 6,000
Case b: X = 2000, Y = 10,000, the interest rate for investment X is 50%, and the interest rate for investment Y is 10%. Notice that the interest for each investment will be equal. Here, the answer to the target question is Y = 10,000
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent