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# If p, r, and s are consecutive integers in ascending order and x is th

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If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

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26 Apr 2019, 02:19
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Question Stats:

60% (01:40) correct 40% (01:27) wrong based on 119 sessions

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If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ?

(1) Twice x is equal to the sum of p, r, and s.
(2) The sum of p, r, and s is zero.

DS43602.01
OG2020 NEW QUESTION

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Re: If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

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26 Apr 2019, 04:15
1
p<r<s

x = (p+r+s)/3

From S1:

2x = p+r+s
2x = 3x
3x-2x = 0
x = 0
Average = 0
Sufficient.

From S2:

p+r+s = 0
Then Average, x = 0
Sufficient.

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If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

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27 Apr 2019, 08:34
Top Contributor
Bunuel wrote:
If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ?

(1) Twice x is equal to the sum of p, r, and s.
(2) The sum of p, r, and s is zero.

Given: p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers
Since p, r and s are EQUALLY spaced, the mean of the 3 numbers = the median of the 3 numbers.
Since p < r < s, we know that r = the mean = the median.

In other words, r = x (since we're told x is the mean)
So, p = x - 1
And s = x + 1 (since p, r, and s are consecutive integers)

Target question: What is the value of x?

Statement 1: Twice x is equal to the sum of p, r, and s.
We can write: 2x = p + r + s
Replace p with x-1, replace r with x, and replace s with x+1 to get: 2x = (x-1) + x + (x+1)
Simplify: 2x =3x
Solve: x = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of p, r, and s is zero.
We can write: p + r + s = 0
Replace p with x-1, replace r with x, and replace s with x+1 to get: (x-1) + x + (x+1) = 0
Simplify: 3x =0
Solve: x = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

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Re: If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

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06 May 2019, 20:14
1
Bunuel wrote:
If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ?

(1) Twice x is equal to the sum of p, r, and s.
(2) The sum of p, r, and s is zero.

DS43602.01
OG2020 NEW QUESTION

If x is the average of three consecutive integers p, r and s, then it’s the value of r, the middle integer.

Statement One Alone:

Twice x is equal to the sum of p, r, and s.

We can create the equation:

2x = p + r + s

2x = (r - 1) + r + (r + 1)

2x = 3r

Since we have concluded x = r in the stem, we have:

2x = 3x

x = 0

Statement one alone is sufficient to answer the question.

Statement Two Alone:

The sum of p, r, and s is zero.

Since x is the average of p, r and s, we have:

x = (p + r + s )/3 = 0/3 = 0

Statement two alone is sufficient to answer the question.

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If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

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14 May 2019, 06:25

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given
• The numbers p, r, and s are consecutive integers in ascending order.
• x is the average (arithmetic mean) of the three integers.

We need to determine
• The value of x.

As x is the average of p, r, and s, we can write x = $$\frac{(p+r+s)}{3}$$

Therefore, to find the value of x, we need to know either the individual values of p, r, and s, or their sum.
With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, twice x is equal to the sum of p, r, and s.
• 2x = p + r + s
We also know that 3x = p + r + s
Therefore, we can write 2x = 3x
• Or, x = 0
As we can determine the value of x, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, the sum of p, r, and s is zero.
• p + r + s = 0
As x = $$\frac{(p+r+s)}{3}$$, we can say
• x = $$\frac{0}{3}$$ = 0
As we can determine the value of x, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)
Since we can determine the answer from either of the statements individually, this step is not required.
Hence, the correct answer choice is option D.

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Re: If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

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20 May 2019, 13:30
Hi All,

We're told that P, R and S are CONSECUTIVE integers in ASCENDING order and X is the AVERAGE (arithmetic mean) of the three integers. We're asked for the value of X.

To start, it's worth noting that since we're dealing with 3 CONSECUTIVE integers, the sum will always be '3 times' the value of the 'middle' numbers, so the average of those 3 numbers will be the value of the "middle" number - in this case, "R" will be the average. This means that X = R, so if we find the value of X or R, then we have answered the question. We can also set up the 'Average Formula': (P + R + S)/3 = X. This can be rewritten into any of the following:

P + R + S = 3X
P + R + S = 3R
P + S = 2R

This question can be approached in a couple of different ways; here's a way to use a mix of Algebra and Number Properties.

(1) Twice X is equal to the sum of P, R and S.

With the information in Fact 1, we can create the following equation:
2X = P + R + S

Comparing this equation to the initial equations we wrote, something interesting should stand out: How can (P + R + S) be equal to 3X AND 2X. Those appear to be 2 different results... and there's only one situation in which they are NOT.... when X = 0. Thus, the 3 values would be -1, 0 and 1 and the average is 0.
Fact 1 is SUFFICIENT

(2) The sum of P, R and S is zero.

Fact 2 gives us the SUM of the three terms, so we can easily calculate the average... X = (0)/3 = 0.
Fact 2 is SUFFICIENT

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Re: If p, r, and s are consecutive integers in ascending order and x is th   [#permalink] 20 May 2019, 13:30
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