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# What is the sum of 3 consecutive integers?

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What is the sum of 3 consecutive integers?  [#permalink]

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21 Sep 2019, 15:36
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55% (hard)

Question Stats:

61% (01:49) correct 39% (01:54) wrong based on 120 sessions

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What is the sum of 3 consecutive integers?

(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

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Re: What is the sum of 3 consecutive integers?  [#permalink]

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21 Sep 2019, 17:21
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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
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Re: What is the sum of 3 consecutive integers?  [#permalink]

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01 Dec 2019, 08:36
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)
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Re: What is the sum of 3 consecutive integers?  [#permalink]

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09 Dec 2019, 11:53
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gmatt1476 wrote:
What is the sum of 3 consecutive integers?

(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.

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

Cheers,
Brent
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Re: What is the sum of 3 consecutive integers?  [#permalink]

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09 Dec 2019, 21:42
gmatt1476 wrote:
What is the sum of 3 consecutive integers?

(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

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.
Re: What is the sum of 3 consecutive integers?   [#permalink] 09 Dec 2019, 21:42
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