What is the sum of 3 consecutive integers?

let the three numbers be \((x-1),x,(x+1)\)

from statement (1), \((x-1) + x + (x+1) < (x+1)\)
so \(3x < x+1\) ,
\(2x < 1\)
\(x< \frac{1}{2}\) ---. so no definite value for x (insufficient)

from statement (2), \(\frac{x-1}{x+1} = 3\), so \(x = -2\) and the three numbers are \(-1,-2,-3\) and the sum = \(-6\) --> sufficient

What is the sum of 3 consecutive integers?

we need a unique set to find the sum

(1) The sum of the 3 integers is less than the greatest of the 3 integers.: Insufficient
as we need sum is less than greatest: therefore the series is of negative numbers -3,-2,-1 or -4,-3,-2 but no unique set to find the sum hence insufficient

(2) Of the 3 integers, the ratio of the least to the greatest is 3.
ratio of least/greatest = 3 therefore >1 only possible if it is a negative series : ( positive series will always give ratio <1) . the statement also provides ratio of 3 therefore -3,-2,-1 is only possible set : hence sufficient

(B)

Target question: What is the sum of 3 consecutive integers?

Statement 1: The sum of the 3 integers is less than the greatest of the 3 integers.
There are several sets of three consecutive integers that satisfy statement 1. Here are two:
Case a: The numbers are {-1, 0, 1}. In this case the sum is 0, and 0 is less than the biggest number in the set (1). The answer to the target question is the sum of the integers is 0
Case b: The numbers are {-2, -1, 0}. In this case the sum is -3, and -3 is less than the biggest number in the set (0). The answer to the target question is the sum of the integers is -3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Of the 3 integers, the ratio of the least to the greatest is 3.
Let x = the smallest integer
So, x + 1 = the middle integer
And, x + 2 = the greatest integer

From statement to we can write: x/(x+2) = 3
Multiply both sides of the equation by x + 2 to get: x = 3x + 6
Subtract 3x from both sides to get: -2x = 6
Solve: x = -3
Since x is the smallest integer, we now know that the three consecutive integers are {-3, -2, -1}
The answer to the target question is the sum of the integers = (-3) + (-2) + (-1) = -6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Three integers are a, a+1, a+2
Sum is 3*(a+1)

(1) a can be any non positive integer. Insufficient

(2) a / (a+2) = 3
a = -3. Sufficient

B is correct.

Brent, how come statement 2 cannot be -3,-2,-1? Is the ratio not 3:1 ? If so what is the ratio of the least to greatest? This question has me stumped. Thanks.

I think he made a little mistake by putting the greatest to the least instead of the least to the greatest

Yes, he made a little mistake by reversing the ratio.
Also, from statement (1) which has to be true, you can see that "The sum of the 3 integers is less than the greatest of the 3 integers", and this is not the case for the set {1, 2, 3}.

Sum should have been -6, for the set {-3, -2, -1}, but the answer is still (luckily) B.

What is the sum of 3 consecutive integers?

(1) The sum of the 3 integers is less than the greatest of the 3 integers.

x + x + 1 + x +2 < x +2
3x + 3 < x + 2
2x < -1
x < -1/2

INSUFFICIENT.

(2) Of the 3 integers, the ratio of the least to the greatest is 3.

X/X+2 = 3
X = -3
Sum = -6

SUFFICIENT.

Answer is B.
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Our integers: n, n+1 ,n+2

(1) The sum of the 3 integers is less than the greatest of the 3 integers.

\(n+n+1+n+2\) < \(n+2\)

\(3n+3 < n+2\)
\(3n < n-1\)

plug values for n. (clearly +ve integers are out of question, so let's start with -ve values)

if \(n= -1\)

\(-3 < -2\) (yes)

if \(n= -2\)
\(-6 < -3\) (yes)

Two possibilities. insufficient.

(2) Of the 3 integers, the ratio of the least to the greatest is 3.

\(n/n+2 = 3\)
\(n=3(n+2)\)
\(n=3n+6\)
\(-2n=6\)
\(n=-3\)

Done. we got the first integer; we can get the rest as this is a consecutive series.

B is the Answer.

Hey BrentGMATPrepNow, in statement (2) we are told that the ratio of least to the greatest is 3. So shouldn't it be (x)/(x+2) = 3?

Thanks for the heads up! I have edited my response accordingly.

Kudos for you!!!

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