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Register now and save up to $200 Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code ## OG 13: DS Q#77 tagged by: ProGMAT This topic has 1 expert reply and 3 member replies ProGMAT Senior | Next Rank: 100 Posts Joined 24 Jul 2013 Posted: 35 messages Thanked: 2 times Target GMAT Score: 730 #### OG 13: DS Q#77 Fri Aug 16, 2013 8:34 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) 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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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Sat Aug 17, 2013 4:32 am
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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 GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "Thank" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Thanked by: ProGMAT, faraz_jeddah 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. faraz_jeddah Master | Next Rank: 500 Posts Joined 18 Apr 2013 Posted: 358 messages Followed by: 7 members Thanked: 42 times Test Date: 17-Nov Target GMAT Score: 690 GMAT Score: 730 Wed Sep 25, 2013 4:43 am 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. theCodeToGMAT Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Thanked: 448 times Target GMAT Score: 750 GMAT Score: 650 Wed Sep 25, 2013 5:08 am 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} _________________ R A H U L ### GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8718 messages Followed by: 461 members Thanked: 2747 times GMAT Score: 800 Wed Sep 25, 2013 11:31 pm 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.

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

_________________
Contact Rich at Rich.C@empowergmat.com

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