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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## OG 13: DS Q#77 tagged by: ProGMAT ##### This topic has 3 expert replies and 2 member replies A total of$60,000 was invested for 1 year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was$4080, what is the value of x?

(1) x=3y/4
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

OA: C

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faraz_jeddah wrote:
Is there a shortcut to this problem?
Maybe structuring it in the "x Equations x variables" format?
We don't have to solve for values.. remember it's Data Sufficiency..

My steps:
Total Interest = Interest in First Slot + Interest in Second Slot
4080 = (A*x*1 + (60000-A)*y*1)/100

Statement 1: We have no information about "A" hence we will not be able to deduce a proper numerical answer
INSUFFICIENT

Statement 2:
First Slot is countable
Second Slot is 2/5*60000
here, we don't have info about the X & y relation.. hence we would be able to deduce numerical answer.
INSUFFICIENT

Combining..
we have all values required..

Answer {C}

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Quote:
A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the$60,000 for that year was $4,080, what is the value of x? (1) x = 3y / 4 (2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2. Since 4080 is between 5% and 10% of 60,000, it is likely that x and y are between 5 and 10. Statement 1: x = (3/4)y It's possible that x=6 and y=8 or that x=6.6 and that y=8.8. To accommodate the desired combination of percentages, we could simply adjust the amount invested at each percentage so that the total amount of interest earned = 4080. Since x can be different values, INSUFFICIENT. Statement 2: The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3/2. Sum of the parts of the ratio = 3+2 = 5. Since the actual amount invested = 60,000, and 60,000/5 = 12000, the two parts of the ratio must be multiplied by 12,000: 12,000(3:2) = 36,000:24,000. Thus, 36,000 earns x% interest and 24,000 earns y% interest. It's possible that x=6 or that x=6.6. To accommodate each value for x, we could simply adjust the value of y so that the total amount of interest earned = 4080. Since x can be different values, INSUFFICIENT. Statements 1 and 2 combined: 32,000 earns x% interest and 24,000 earns y% interest. Since x=(3/4)y, for every 4% of interest earned by the$24,000, 3% interest is earned by the $36,000. If x=3 and y=4: (.03)(36,000) + (.04)(24,000) = 1080+960 = 2040. Since 2040 is half the amount of interest needed, the percentages must be doubled to 6% and 8%. Thus, x=6. SUFFICIENT. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Master | Next Rank: 500 Posts Joined 18 Apr 2013 Posted: 358 messages Followed by: 7 members Upvotes: 42 Test Date: 17-Nov Target GMAT Score: 690 GMAT Score: 730 Is there a shortcut to this problem? Maybe structuring it in the "x Equations x variables" format? _________________ A good question also deserves a Thanks. Messenger Boy: The Thesselonian you're fighting... he's the biggest man i've ever seen. I wouldn't want to fight him. Achilles: That's why no-one will remember your name. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10184 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi faraz_jeddah, Yes, there is a way to use a "system math" rule to answer this question, but you have to be careful about how you deal with the variables in the initial prompt. You can clearly see the variables X and Y, which represent the 2 unknown interest rates. You only need 1 more variable to account for the invested money. M = amount invested at X% (60,000 - M) = amount invested at Y% We're told that M(X/100) + (60,000 - M)(Y/100) =$4080. This is 1 equation with 3 variables

We're asked to solve for X.

Fact 1: X = 3Y/4

Here we have another equation, but this 1 equation isn't enough for us to figure out what X is.
Fact 1 is INSUFFICIENT

Fact 2: This sentence translates into this: M/(60,000 - M) = 3/2

Here we can figure out the value of M, but we don't have enough to figure out what X is.
Fact 2 is INSUFFICIENT

Combining Facts, we have 3 variables and 3 unique equations. You CAN solve this system and get the value of X.

Final Answer: C

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ProGMAT wrote:
A total of $60,000 was invested for 1 year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the$60,000 for that year was $4080, what is the value of x? (1) x=3y/4 (2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2. We are given that$60,000 was invested for 1 year. We are also given that part of the investment earned x percent simple annual interest and the rest earned y percent simple annual interest. We are also given that the total interest earned was $4,080. Let’s start by defining a variable. b = the amount that earned x percent simple interest Using variable b, we can also say: 60,000 - b = the amount that earned y percent simple annual interest Since we know that the total interest earned was$4,080, we can create the following equation:

b(x/100) + (60,000 - b)(y/100) = 4,080

Note that in the equation above, we express "x percent" as x/100 and "y percent" as y/100 in the same way that we would express, say, 24 percent as 24/100.

Statement One Alone:

x = 3y/4

Although we have an equation with x and y, we still need a third equation to be able to determine the value of x because our equation from the given information has three variables. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

From our given information we know that b is the amount that earned interest at the rate of x percent per year and that 60,000 - b is the amount that earned interest at the rate of y percent per year. Thus, we can create the following equation:

b/(60,000 - b) = 3/2

Without a third equation, statement two alone is not sufficient to determine the value of x.

Statements One and Two Together:

From the given information and statements one and two we have the following 3 equations:

1) b(x/100) + (60,000 - b)(y/100) = 4,080

2) x = 3y/4

3) b/(60,000 - b) = 3/2

Since we have 3 independent equations with variables x, y, and b, we are able to determine the value of x.

Answer: C

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