To find the median

[gmattesttaker2]

Hello,

Can you please tell me if my solution is correct here?


Set S is made up of positive integers a, b, and c. What is the median of set S?

1) a - b = 2
2) c - a < 0

OA: E


1) Let a = 2 and b = 4 => a - b = 2
c could be 3 => c is the median
c could be 5 => b is the median. Hence in-suff

2) Let a = 4 and c = 2 => c - a < 0
b could be 3 => b is the median
b could be 1 => c is the median
b could be 5 => a is the median. Hence in-suff

1 and 2:

a - b = 2 and c - a < 0

Let a = 4, b = 2, c = 1 => b is the median
Let a = 4, b = 2, c = 3 => c is the median

Hence, in-suff.


Thanks a lot,
Sri

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Hi Sri,

This question is perfect for TESTing Values. Your logic is great, but there are lots of typos in your explanation.

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

[Brent@GMATPrepNow]

Set S is made up of positive integers a, b, and c. What is the median of set S?

1) a - b = 2
2) c - a < 0

Hi Sri,

Your approach of plugging in numbers is great.
Here's an approach that uses some number sense.

Target question: What is the median of set S?
We have 3 numbers in set S, so our goal is to determine which number is the MIDDLE NUMBER, when the 3 values are arranged in ASCENDING order.

Statement 1: a - b = 2
If a - b equals 2, we can conclude that a IS GREATER THAN b (it's 2 greater)
Let's write: b < a
Since we don't know anything about c, there's no way to determine the median.
So, statement 1 is NOT SUFFICIENT

Statement 2: c - a < 0
Take this inequality and add a to both sides to get: c < a
Since we don't know anything about b, there's no way to determine the median.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that b < a
Statement 2 tells us that c < a
So, all we know is that a is greater than both b and c. In other words, a is the biggest of the three numbers.
Since we have no idea whether b or c is the middle value, we cannot determine the median.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

[gmattesttaker2]

Hi Sri,

This question is perfect for TESTing Values. Your logic is great, but there are lots of typos in your explanation.

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

Hello Rich,

Thanks for the feedback. Was just wondering if the typos had to do with in-correct values or more on the lines of not phrasing properly. Thanks for all your help.

Best Regards,
Sri

[gmattesttaker2]

Set S is made up of positive integers a, b, and c. What is the median of set S?

1) a - b = 2
2) c - a < 0

Hi Sri,

Your approach of plugging in numbers is great.
Here's an approach that uses some number sense.

Target question: What is the median of set S?
We have 3 numbers in set S, so our goal is to determine which number is the MIDDLE NUMBER, when the 3 values are arranged in ASCENDING order.

Statement 1: a - b = 2
If a - b equals 2, we can conclude that a IS GREATER THAN b (it's 2 greater)
Let's write: b < a
Since we don't know anything about c, there's no way to determine the median.
So, statement 1 is NOT SUFFICIENT

Statement 2: c - a < 0
Take this inequality and add a to both sides to get: c < a
Since we don't know anything about b, there's no way to determine the median.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that b < a
Statement 2 tells us that c < a
So, all we know is that a is greater than both b and c. In other words, a is the biggest of the three numbers.
Since we have no idea whether b or c is the middle value, we cannot determine the median.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Hello Brent,

Thanks a lot for the detailed explanation.

Best Regards,
Sri