GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2019, 09:44 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If p, r, and s are consecutive integers in ascending order and x is th

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59730
If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

### Show Tags

15 00:00

Difficulty:   55% (hard)

Question Stats: 57% (01:42) correct 43% (01:40) wrong based on 533 sessions

### HideShow timer Statistics

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

_________________
NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1027
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

### Show Tags

4
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.

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4157
If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

### Show Tags

1
Top Contributor
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.

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

RELATED VIDEO FROM MY COURSE

_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

### Show Tags

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

### Show Tags

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.

_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15736
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If p, r, and s are consecutive integers in ascending order and x is th  [#permalink]

### Show Tags

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

GMAT assassins aren't born, they're made,
Rich
_________________ Re: If p, r, and s are consecutive integers in ascending order and x is th   [#permalink] 20 May 2019, 13:30
Display posts from previous: Sort by

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