• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

OG 13: DS Q#77

This topic has 3 expert replies and 2 member replies

OG 13: DS Q#77

Post
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

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
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

  • +1 Upvote Post
  • Quote
  • Flag
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
Post
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.

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member
Joined
14 Aug 2012
Posted:
1556 messages
Followed by:
34 members
Upvotes:
448
Target GMAT Score:
750
GMAT Score:
650
Post
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

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
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

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

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
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

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

Top First Responders*

1 fskilnik@GMATH 91 first replies
2 Brent@GMATPrepNow 50 first replies
3 Jay@ManhattanReview 40 first replies
4 GMATGuruNY 25 first replies
5 Rich.C@EMPOWERgma... 24 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

176 posts
2 image description Scott@TargetTestPrep

Target Test Prep

118 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

103 posts
4 image description Max@Math Revolution

Math Revolution

89 posts
5 image description Jay@ManhattanReview

Manhattan Review

73 posts
See More Top Beat The GMAT Experts