What is the sum of 3 consecutive integers?

Question

(1) The sum of the 3 integers is less than the greatest of the 3 integers.
(2) Of the 3 integers, the ratio of the least to the greatest is 3.

DS51402.01

MahmoudFawzy · Accepted Answer

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

OC2910 · Answer

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)

BrentGMATPrepNow · Answer

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

QuantMadeEasy · Answer

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.

BradyMVP · Answer

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.

palcc · Answer

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

mstepano · Answer

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.

Basshead · Answer

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.

ueh55406 · Answer

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.

Hoozan · 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?

BrentGMATPrepNow · Answer

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

Kudos for you!!!

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What is the sum of 3 consecutive integers?

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What is the sum of 3 consecutive integers?

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