It is currently 29 Sep 2020, 09:54

### 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

# A set has exactly five consecutive positive integers.

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 13406
Followers: 292

Kudos [?]: 3406 [2] , given: 12285

A set has exactly five consecutive positive integers. [#permalink]  17 Sep 2018, 20:34
2
KUDOS
Expert's post
00:00

Question Stats:

44% (01:29) correct 55% (01:25) wrong based on 88 sessions

A set has exactly five consecutive positive integers.

 Quantity A Quantity B The percentage decrease in the average of the numbers when one of the numbers is dropped from the set 20%

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

VP
Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1312 [3] , given: 251

Re: A set has exactly five consecutive positive integers. [#permalink]  18 Sep 2018, 03:37
3
KUDOS
Carcass wrote:
A set has exactly five consecutive positive integers.

 Quantity A Quantity B The percentage decrease in theaverage of the numbers whenone of the numbers is droppedfrom the set 20%

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Here

let's take the numbers from 1 to 5

So the average of the numbers = $$\frac{15}{5} =3$$

Now if we remove a number what will be the average? to get that we need to take the greatest number from the series

So in this case , 5 is the greatest

So average of 1 ,2 ,3 ,4 =$$\frac{10}{4}= 2.5$$

Therefore the percentage decrease = $$\frac{{3 - 2.5}}{3} * 100 = 16.66%$$, this the maximum value we can get if we remove from the set.

Hence QTY A < QTY B

*** it can be any 5 consecutive positive numbers the maximum value will be 16.66%****
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Manager
Joined: 08 Dec 2018
Posts: 94
Followers: 0

Kudos [?]: 44 [0], given: 30

Re: A set has exactly five consecutive positive integers. [#permalink]  09 Mar 2019, 08:54
tricky wording. Only the decreases are issues .
Intern
Joined: 13 Oct 2018
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 3

Re: A set has exactly five consecutive positive integers. [#permalink]  28 Jan 2020, 02:23
How do we know which number is to be excluded ? Ans can change depending on the number we exclude

@GreenlightTestPrep
GRE Instructor
Joined: 10 Apr 2015
Posts: 3840
Followers: 149

Kudos [?]: 4506 [2] , given: 69

Re: A set has exactly five consecutive positive integers. [#permalink]  28 Jan 2020, 06:31
2
KUDOS
Expert's post
Carcass wrote:

A set has exactly five consecutive positive integers.

 Quantity A Quantity B The percentage decrease in the average of the numbers when one of the numbers is dropped from the set 20%

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Here is an algebraic solution that allows us to examine all possible cases.

Let x = the smallest integer in the set
So, x + 1 = the next consecutive integer
x + 2 = the next integer
x + 3 = the next integer
x + 4 = the greatest integer

Average $$= \frac{x+(x+1)+(x+2)+(x+3)+(x+4)}{5}=\frac{5x+10}{5}=x+2$$

Key concept: In order to get the greatest DECREASE in the average, we must remove the biggest number in the set.
So we'll remove (x+4) from the set
The new average $$= \frac{x+(x+1)+(x+2)+(x+3)}{4}=\frac{4x+6}{4}=x+1.5$$

Percent decrease = (100)(old - new)/old

We get: percent decrease $$= \frac{(100)[(x+2)-(x+1.5)]}{x+2}$$

$$= \frac{(100)[0.5]}{x+2}$$

$$= \frac{50}{x+2}$$

Notice that the percent increase depends on the value of x.
For example, if $$x=8$$, then the percent decrease $$= \frac{50}{8+2}= \frac{50}{10}=5%$$, which is LESS THAN 20%

Also notice that, in order to maximize the percent decrease, we must minimize the value of x.
Since we're told x is a positive integer, the smallest possible value of x is 1.
When $$x=1$$, then the percent decrease $$= \frac{50}{1+2}= \frac{50}{3}≈16.666...%$$
This means 16.666...% is the GREATEST possible value of Quantity A.

This means Quantity B will always be greater than Quantity A

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

GRE Instructor
Joined: 10 Apr 2015
Posts: 3840
Followers: 149

Kudos [?]: 4506 [2] , given: 69

Re: A set has exactly five consecutive positive integers. [#permalink]  28 Jan 2020, 06:36
2
KUDOS
Expert's post
Alpha14 wrote:
How do we know which number is to be excluded ? Ans can change depending on the number we exclude

@GreenlightTestPrep

Great question!
Notice that, if we remove the middle number, then the percent decrease in the average is zero.
So, in this case, Quantity B will be greater.
At this point our goal should be to MAXIMIZE the percent decrease. This is achieved by removing the biggest number in the set.
As I show in my post above, removing the biggest number in the set will always yield a percent decrease that is less than 20%.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

GRE Instructor
Status: Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Joined: 19 Jan 2020
Posts: 112
GMAT 1: 740 Q51 V39
GPA: 3.72
Followers: 5

Kudos [?]: 130 [1] , given: 1

Re: A set has exactly five consecutive positive integers. [#permalink]  28 Jan 2020, 09:55
1
KUDOS
Carcass wrote:

A set has exactly five consecutive positive integers.

 Quantity A Quantity B The percentage decrease in the average of the numbers when one of the numbers is dropped from the set 20%

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Let the 5 numbers be: $$x, x+1, x+2, x+3, x+4$$

Since the numbers are in Arithmetic Progression (i.e. consecutive numbers have a constant gap), we have:
Mean = Median = 3rd term = $$x+2$$

(Note: You can always add up the terms and check the average)

One of the 5 numbers will be dropped

Maximum change in mean will occur if either of the 2 extreme terms, i.e. $$x$$ or $$x+4$$ is dropped. The average will decrease if $$x+4$$ is dropped (Note: if $$x$$ is dropped, the average would actually increase. Also, if the middle number, i.e. $$x+2$$ is dropped, there will be no change in the mean)

If $$x+4$$ is dropped: The 4 terms are: $$x, x+1, x+2, x+3$$

=> New Mean = Median = $$[(x+1)+(x+2)]/2 = x+1.5$$

=> Percent decrease in mean = $$[{(x+2)-(x+1.5)}/(x+2)] * 100$$ = $$[50/(x+2)]%$$

The above percent will be maximum if the value of $$x$$ is minimum, i.e. $$x=1$$

=> Maximum percent decrease = $$[50/(1+2)]% = 16.67%$$

Thus, Quantity B is greater than Quantity A

Note: Some important results that come up here:

In an Arithmetic Progression i.e. consecutive terms having a constant difference of $$d$$:

#1. Mean = Median
#2. The average remains unchanged if the middle term (or both middle terms) are removed
#3. The maximum change in mean occurs when one of the extreme terms is removed

#4. The maximum change in mean (when one of the extreme terms is removed) = $$d/2$$, where $$d$$ is the constant difference between consecutive terms
_________________

Sujoy Kumar Datta | GMAT - Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA
IIT Kharagpur, TUD Germany

Ping me for GRE & GMAT - Concepts & Strategy

Director - CUBIX (https://www.cubixprep.com) | OneClick (http://www.oneclickprep.com)
_________

Re: A set has exactly five consecutive positive integers.   [#permalink] 28 Jan 2020, 09:55
Display posts from previous: Sort by