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21 Jan 2025, 01:30
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E
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Difficulty:
25%
(medium)
Question Stats:
78% (01:38) correct
22%
(01:08)
wrong
based on 83
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A sum of $12000 was distributed among five individuals - A, B, C, D, and E. What was C's share?
(1) A received \(\frac{1}{3}\)rd more than what B did and B received \(\frac{1}{4}\)th more than what D did.
(2) C received \(\frac{1}{2}\) more than what E did.
(1) A received \(\frac{1}{3}\)rd more than what B did and B received \(\frac{1}{4}\)th more than what D did.
(2) C received \(\frac{1}{2}\) more than what E did.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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21 Jan 2025, 06:15
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Given A+B+C+D+E = $12000
(1) A received 1/3rd more than what B did and B received 1/4th more than what D did.
This gives us
B= \(\frac{5}{4}\)*D
A= \(\frac{4}{3}*\frac{5}{4}*D= \frac{5}{3}*D\)
Hence the equation becomes:
\(\\
(\frac{5}{3}+\frac{5}{4}+1)*D + C+E = 12000\\
\\
\)
As there are 03 variables Hence not sufficient
(2) C received 1/2 more than what E did.
This gives us
C= \(\frac{3}{2}\)*E
Hence the equation becomes:
\(A+B+D+(1+\frac{3}{2})*E\) = 12000
As there are 04 variables, Hence not sufficient
1 & 2
\((\frac{5}{3}+\frac{5}{4}+1)*D + (1+\frac{3}{2})*E = 12000\)
Still two variables, who can have decimal values, hence many solutions can be made. Hence Not Sufficient
IMO Ans E
(1) A received 1/3rd more than what B did and B received 1/4th more than what D did.
This gives us
B= \(\frac{5}{4}\)*D
A= \(\frac{4}{3}*\frac{5}{4}*D= \frac{5}{3}*D\)
Hence the equation becomes:
\(\\
(\frac{5}{3}+\frac{5}{4}+1)*D + C+E = 12000\\
\\
\)
As there are 03 variables Hence not sufficient
(2) C received 1/2 more than what E did.
This gives us
C= \(\frac{3}{2}\)*E
Hence the equation becomes:
\(A+B+D+(1+\frac{3}{2})*E\) = 12000
As there are 04 variables, Hence not sufficient
1 & 2
\((\frac{5}{3}+\frac{5}{4}+1)*D + (1+\frac{3}{2})*E = 12000\)
Still two variables, who can have decimal values, hence many solutions can be made. Hence Not Sufficient
IMO Ans E
21 Jan 2025, 07:35
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Given:
- A sum of $12,000 was distributed among five individuals: A, B, C, D, and E.
- We need to find C's share.
(1) A received more than B, and B received more than D.
- This gives us some relationships between A, B, and D, but it doesn't give us enough direct information about C and E.
- Insufficient on its own.
(2) C received more than E.
- This tells us about the relationship between C and E but doesn't provide any information about how the money is split among A, B, C, D, and E.
- Insufficient on its own.
Combining (1) and (2):
- Even with the relationships from both statements, we don't have enough direct information to calculate C's exact share because we still don't know how the total sum was divided between the individuals.
- So, combining the two statements doesn't help us find C's share.
Answer: E. Both statements together are still insufficient.
- A sum of $12,000 was distributed among five individuals: A, B, C, D, and E.
- We need to find C's share.
(1) A received more than B, and B received more than D.
- This gives us some relationships between A, B, and D, but it doesn't give us enough direct information about C and E.
- Insufficient on its own.
(2) C received more than E.
- This tells us about the relationship between C and E but doesn't provide any information about how the money is split among A, B, C, D, and E.
- Insufficient on its own.
Combining (1) and (2):
- Even with the relationships from both statements, we don't have enough direct information to calculate C's exact share because we still don't know how the total sum was divided between the individuals.
- So, combining the two statements doesn't help us find C's share.
Answer: E. Both statements together are still insufficient.
