If a, b, and c are three numbers on the number line shown above, is c between a and b?
1) b<0
2) a-b > c
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GMAT Prep Question Pack 1 DS If a, b, and c are three numbe
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richachampion
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Hi richachampion,
This question can be solved by TESTing VALUES. To start though, it's important to note that we don't know the 'relative scale' of this number line. A and B might be 'close together' or 'far apart.' We also don't know if the three variables (A, B and C) are integers or not. We DO know that B is GREATER than A though (since it's farther right on the number line).
We're asked if C is between A and B. This is a YES/NO question.
1) B < 0
This Fact tells us that B is NEGATIVE (so A must ALSO be negative - since it's farther to the left than B is). However, we don't know anything about C.
Fact 1 is INSUFFICIENT
2) (A - B) > C
IF....
A = -2 and B = -1, then (A-B) = -1.... and -1 > C....
IF....
C = -1.5, then the answer to the question is YES
C = -3, then the answer to the question is NO
Fact 2 is INSUFFICIENT
Combined, the two TESTs that I used in Fact 2 fit both Facts and provide different answers to the question (one YES and one NO).
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This question can be solved by TESTing VALUES. To start though, it's important to note that we don't know the 'relative scale' of this number line. A and B might be 'close together' or 'far apart.' We also don't know if the three variables (A, B and C) are integers or not. We DO know that B is GREATER than A though (since it's farther right on the number line).
We're asked if C is between A and B. This is a YES/NO question.
1) B < 0
This Fact tells us that B is NEGATIVE (so A must ALSO be negative - since it's farther to the left than B is). However, we don't know anything about C.
Fact 1 is INSUFFICIENT
2) (A - B) > C
IF....
A = -2 and B = -1, then (A-B) = -1.... and -1 > C....
IF....
C = -1.5, then the answer to the question is YES
C = -3, then the answer to the question is NO
Fact 2 is INSUFFICIENT
Combined, the two TESTs that I used in Fact 2 fit both Facts and provide different answers to the question (one YES and one NO).
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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richachampion
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I have a new learning while solving this question.
Statement 1 alone is not sufficient.
Let us discuss the statement 2 and statement 1 + statement 2.
A finding →
a-b will always lie between a and b irrespective of the sign of a and b.
Precisely, this one →
a-b = - |a-b|
a-b > c doesn't tell anything. That means statement 2 is also discarded.
The combination of statement 1 and statement 2 only tells that we are now dealing with the negative axis, but still, the statement 2 is valid and hence we can't infer whether "C" lies between a and b or away from "a" on the negative axis.
Statement 1 alone is not sufficient.
Let us discuss the statement 2 and statement 1 + statement 2.
A finding →
a-b will always lie between a and b irrespective of the sign of a and b.
Precisely, this one →
a-b = - |a-b|
a-b > c doesn't tell anything. That means statement 2 is also discarded.
The combination of statement 1 and statement 2 only tells that we are now dealing with the negative axis, but still, the statement 2 is valid and hence we can't infer whether "C" lies between a and b or away from "a" on the negative axis.
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
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Brent@GMATPrepNow
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Target question: is c between a and b?richachampion wrote:If a, b, and c are three numbers on the number line shown above, is c between a and b?
1) b < 0
2) a - b > c
Statement 1: b < 0
No information about c, so statement 1 is NOT SUFFICIENT
Statement 2: a - b > c
There are several sets of numbers that meet this condition. Here are two:
Case a: a = -3, b = -1 and c = -2.5 in which case c is between a and b
Case b: a = -3, b = -1 and c = -5 in which case c is not between a and b
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
There are still several sets of numbers that meet this condition. Here are two:
Case a: a = -3, b = -1 and c = -2.5 in which case c is between a and b
Case b: a = -3, b = -1 and c = -5 in which case c is not between a and b
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
