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Register now and save up to $200 Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 ## Simple interest - Difficulty hard tagged by: Alphonsaj This topic has 5 expert replies and 0 member replies Alphonsaj Newbie | Next Rank: 10 Posts Joined 14 Jul 2016 Posted: 8 messages #### Simple interest - Difficulty hard Thu Jul 14, 2016 2:04 am A father left a will of$71 million between his 2 daughters aged 8.5 years and 12 years such that they may get equal amounts when each of them reach the age of 18 years. The father instructed that the original amount of 71mn be invested at 10% pa till such time the daughters turned 18. How much did the elder daughter get at the time of the will?

A.31mn
B.49mn
C.39mn
D.35.5mn
E.40mn

Source : 4Gmat
C

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### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
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Wed Jul 20, 2016 9:50 pm
Of course, I probably should've reduced the above to one equation from the start. We know that

Elder's Daughter Trust * Interest = Younger Daughter's Trust * Interest

or

x * (1 + .1*6) = (71 - x) * (1 + .1*9.5)

One variable, one equation, much easier to see and to solve ... go with this one.

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### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
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Wed Jul 20, 2016 9:56 pm
BTW this is a really neat question: thinking about the setup is a bit baffling (I was stuck for a sec on how they could receive the same amount of money when they each turn 18!), but the equation ends up being so clean! Kudos to the author.

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### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
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Wed Jul 20, 2016 9:50 pm
Of course, I probably should've reduced the above to one equation from the start. We know that

Elder's Daughter Trust * Interest = Younger Daughter's Trust * Interest

or

x * (1 + .1*6) = (71 - x) * (1 + .1*9.5)

One variable, one equation, much easier to see and to solve ... go with this one.

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
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Target GMAT Score:
V51
GMAT Score:
780
Wed Jul 20, 2016 9:56 pm
BTW this is a really neat question: thinking about the setup is a bit baffling (I was stuck for a sec on how they could receive the same amount of money when they each turn 18!), but the equation ends up being so clean! Kudos to the author.

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
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Posted:
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Target GMAT Score:
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780
Wed Jul 20, 2016 9:35 pm
I'd think of it this way.

The elder daughter will get her money in 6 years, so let's run the interest till then first, and call her initial amount x.

Elder daughter's net: x * (1 + .1*6)

The younger daughter's share (let's call that y) is similar:

Younger daughter's net: y * (1 + .1*9.5)

We know that the initial shares sum to 71, so we have (x + y) = 71.

We also know that the two daughters receive the same amounts, so x * (1 + .1*6) = y * (1 + .1*9.5)

We want to solve for x, so let's isolate y: x * (1.6)/(1.95) = y

Then plug this back into our first equation, x + y = 71:

x + x * (1.6)/(1.95) = 71

x * (1 + 160/195) = 71

x * (355 / 195) = 71

x = 195 * (71 / 355) => 195 * (1/5) => 39

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