a, b, and c are 3 integers such that a

Question

a, b, and c are 3 integers such that  a<b<c . Is the sum of a, b, and c positive?

(1) Two of the numbers are negative
(2) Distance between a and b on the number line is greater than distance between b and c on the number line.

IanStewart · Answer

Each statement is clearly insufficient alone.

If b was exactly halfway between a and c, then we'd have an equally spaced set of three numbers, and b would be the median, and therefore the average. So if we knew the distance from a to b was equal to the distance from b to c, the average of the three numbers would be negative, and thus their sum would be negative too. But here, we know the distance from a to b is larger, so a is smaller (i.e. even more negative) than it would be if the numbers were equally spaced. So the sum will be negative for sure, and the answer is C.

Alternatively you can use algebra: if d is the distance from b to c, then c = b + d, and since the distance from b to a is even larger, a < b - d. So our three numbers are a, b and b + d, which sum to a + 2b + d, and since a < b - d, this sum is less than b - d + 2b + d, so is less than 3b, and since b is negative, the sum is negative.

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem • a < b < c …(i) https://www.dropbox.com/s/88adkmhmbwhtw5o/20.jpg?dl=1 We need to find whether the sum of three integers is positive or not. • a + b + c > 0 or positive or not. Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: Two of the numbers are negative. • From equation (i), and this statement, we can say o a and b are negative o Since We don’t know anything about the magnitude of the integers, we cannot answer the question. Hence, statement 1 is not sufficient, we can eliminate answer options A and D. Statement 2: Distance between a and b on the number line is greater than the distance between b and c. • b-a> c - b • 2b > a + b • a + b + c < 3b • Since we don’t whether the integers are positive or negative. We cannot find the answer to the given question. Hence, statement 2 is also not sufficient, we can eliminate the answer options B Step 3: Analyse Statements by combining. From statement 1: a and b are negative From statement 2: a + b + c < 3b. By combining both the statements, we have • a + b + c < 0 Hence, the correct answer is Option C.

Sinhabhishek · Answer

To find out if a+b+c>0.

1) From Statement 1, a,b <0; It is clearly insufficient on its own

2) From statement 2,
b-a>c-b
Or, 2b>a+c
Adding b both sides,
3b>a+b+c

This is also insufficient on it's own. However, from statement 1, b is also less than zero. Hence, a+b+c <0

So, answer is C

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Dhruv1212 · Answer

What I dont get how do we conclude that a and b are negative

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Bunuel · Answer

We are given that two of the numbers are negative, and since we also know that a < b < c, these two numbers must be a and b.

a, b, and c are 3 integers such that a < b < c. Is the sum of

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