3 siblings - Alan, Betty and Carl - were the only ones to receive part

Question

3 siblings - Alan, Betty and Carl - were the only ones to receive part of a $300,000 inheritance. Did any of the three receive more than forty percent of the total inheritance?

(1) Carl received a larger inheritance than Alan and a larger inheritance than Betty.
(2) The combined total of Alan’s and Betty’s inheritances was equal to three times Betty’s inheritance.

QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 4 3 siblings - Alan, Betty and Carl...

48 Hour Window Answer & Explanation Window   
 Earn KUDOS!  Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation

camlan1990 · Answer

We know A+B+C =100%. A =Alan, B = Betty, and C = Carl
Question: Any of three person holds for over 40%???

1) Carl received a larger inheritance than Alan and a larger inheritance than Betty.
=> C >A and C>B

If A, B = 32% => C = 36% < 40%
If A, B = 20% => C = 60% > 40%

Insufficient

2) The combined total of Alan’s and Betty’s inheritances was equal to three times Betty’s inheritance

A+B = 3B => A = 2B

=>A+B+C = 3B+C

3B+C = 100% => C= 100% - 3B
When B is lower than 20%, C is higher than 40%
When B is equal or higher than 20% => A is higher than 40% and C is lower than 40%

In both cases, any of three holds for over 40%

=> Sufficient

ANS: B

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

3 siblings - Alan, Betty and Carl - were the only ones to receive part of a $300,000 inheritance. Did any of the three receive more than forty percent of the total inheritance?

1) Carl received a larger inheritance than Alan and a larger inheritance than Betty.
2) The combined total of Alan’s and Betty’s inheritances was equal to three times Betty’s inheritance.

There are 3 variables (A,B,C) and one equation (A+B+C=300,000(100%)) in the original condition, 2 more equations in the given conditions, giving high chance (C) will be our answer.
Looking at the conditions together, 
C>A=2B, C>B, A+B+C=100%, 2B+B+C=100%, 3B+C=100%, B=(100%-C)/3. If this is substituted in C>2B, 
C>2(100%-C)/3, 3C>2(100%-C)=200%-2C --> 5C>200%, C>40%.
Therefore, C is greater than 40%, and the answer becomes (C).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

KS15 · Answer

Hi Rich,

I was down to C and E but chose E. Please find below my observations

Case 1: If A gets 80k, B gets 40k and C gets 120k, then None will get more than 40%
Case 2: If A gets 100k, B gets 50k and C gets 150k, then C gets more than 40%. 
So we have two different cases here. Could you please tell me where I am going wrong? Also, statement 1 means that C gets more than A and B right?

Thanks.

EMPOWERgmatRichC · Answer

Hi camlan1990,

With Fact 2, you've correctly deduced at A = 2B, but we don't know how C relates to the other two variables. The question asks if any of the three received MORE than 40%. You've come up with a couple of examples in which one of the three received more than 40%, but is it possible that NONE of them received more than 40%.....

IF....
B = 20%
A = 2(20%) = 40%
C = 40%

In this scenario, NONE of the three received more than 40%, so the answer to the question would be NO. Combined with the work that you've already done, we have proof that Fact 2 is INSUFFICIENT.

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

EMPOWERgmatRichC · Answer

Hi KS15,

The idea to TEST VALUES here is a good one. In your first example though, you've made a small mistake - the three values don't total $300,000 (80k + 40k + 120k = 240k). In that example, using the values for A and B that you've selected, C would end up with 180k (which IS more than 40%).

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

EMPOWERgmatRichC · Answer

Hi All,

From the prompt, we can immediately create an equation:

A + B + C = 300,000

The question asks if any of the three receives MORE than 40% of the $300,000 inheritance. We can 'rewrite' the question as "does any of the three receive MORE than $120,000?" You can work through this prompt in terms of the $300,000 and $120,000 OR you can work through it in terms of the percents involved. Either way, we're dealing with a YES/NO question.

1) Carl received a larger inheritance than Alan and a larger inheritance than Betty.

This tells us that C > A and that C > B. We don't know the relative values of any of the three though, so we can TEST VALUES to prove that there's more than one possibility...

IF...
A = 20%
B = 20%
C = 60%
And the answer to the question is YES.

IF...
A = 30%
B = 30%
C = 40%
And the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) The combined total of Alan’s and Betty’s inheritances was equal to three times Betty’s inheritance.

This Fact can be translated into...

A + B = 3B
A = 2B

We don't know how C relates to the other two variables though...

IF...
A = 10%
B = 20%
C = 70%
And the answer to the question is YES.

IF...
A = 20%
B = 40%
C = 40%
And the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know....
C > A and C > B
A = 2B

Using our prior work as a basis for comparison, we can use the following TEST to define how the variables relate to one another...

IF...
A = 20%
B = 40%
C = 40%
Then C is NOT greater than B, so this TEST is NOT permissible. For C to be BIGGER than B, both A and B would have to be smaller (which would increase C past 40%).

For example...

IF...
A = 19%
B = 38%
C = 43%
Thus, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer:  C

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

umg · Answer

Nice Question. Here is my solution:
Share of Alan, Betty and Carl = A, B & C respectively.

Given: A + B + C = 300k
Question: Is A/B/C > 40% of 300k or 120k?

When I am given absolutely no info about the variables in the question, I Always start with Statement 2 because Statement 1 is generally designed to plant a subtle constraint in mind which we carry forward to Statement 2.

II

A + B = 3B
=> A = 2B

Cases => A = $2; B = $1 and rest for C =>  Answer Yes 
A = 40%; B = 20%; C = 40% =>  Answer No
 
I picked 40% for A because it is the terminal value as mentioned in the question. Greater than 40% -> Yes; Less than or Equal to 40% -> No. They must have picked it for some specific reason.
So, make it a note: ALWAYS check the answers for Terminal values.

I.

C > A
C > B
Doesn't really say anything. We can have either cases:
C = 34%; A = 33% ; B = 33%  Answer No 
and 
C = 50%; A = 20%; B = 30%  Answer Yes

Taking I & II together

A = 2B
Therefore, A > B
And Hence, C > A > B

Now is the tricky part..

Maximum value that B can have < 20%
Because if B = 20%; A = 40% & C = 40%
Thus violating Statement I

If we put B = 19%,
=> A = 38% & C = 43%

For B = 15%, A = 30% and C = 55%

So, we can see that C is increasing beyond 40% with decreasing B. Therefore, Correct answer is C.

mysterymanrog · Answer

This is how I approached it:

1) C>A, C>B 
Many cases. Clearly not NS but for completeness sake: 
Case 1: C=90%, B=5% A=5% (yes)
Case 2: C=40%, B=40% A=20% (no)

2) A+B=3B, A=2B - clearly insuff we don't know anything about C.

3) Now:
A=2B
C>2B
C>B
and by definition, A>B
the minimum value that C can recieve is marginally higher than the case when C=2B.
Therefore we can make this eqauation:
A+B+C=300,000
2B+B+2B=300,000
5B=300,000
B=60000
therefore, B will at most receive (60,000/300,000=1/5) and A gets 2/5 (which is equal to 40%) and C gets 2/5 which is equal to 40% as well. 
As this is the minimum value for C, that means that C will receive always more than 2/5, which means that C will always get more than 40%. Therefore, C is the correct answer.

NipunSyn · Answer

Hey GC team, here's how I approached the question and ended up at E, even though the answer given is C. 
Please tell me where I am going wrong.

A, B, C receive a "part" of the total inheritance, and we don't know how much that is - could be 100K, 200K, or the full 300K.

Which means, A+B+C = X (which is an unknown)

Statement1: C > A and C > B. Doesn't really help me. Could be 50K, 30K, 20K, or any other possible combination.
Statement2: A + B = 3C. Again, could be anything. 10K, 20K, 30K. Or 20K, 30K, 50K, and so on
Combining: Again, I don't see how this will help me, as there are still a lot of combinations possible.

Thus, E.

3 siblings - Alan, Betty and Carl - were the only ones to receive part

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

3 siblings - Alan, Betty and Carl - were the only ones to receive part

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards