Last visit was: 17 Jul 2024, 07:04 It is currently 17 Jul 2024, 07:04
Toolkit
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.

# Set X consists of seven consecutive integers, and Set Y consists of

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 12 Oct 2011
Posts: 100
Own Kudos [?]: 763 [49]
Given Kudos: 23
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
Math Expert
Joined: 02 Sep 2009
Posts: 94377
Own Kudos [?]: 641641 [31]
Given Kudos: 85693
General Discussion
Manager
Joined: 13 Jun 2011
Status:Do till 740 :)
Posts: 61
Own Kudos [?]: 31 [0]
Given Kudos: 19
Concentration: Strategy, General Management
GMAT 1: 460 Q35 V20
GPA: 3.6
WE:Consulting (Computer Software)
Retired Moderator
Joined: 04 Oct 2009
Status:2000 posts! I don't know whether I should feel great or sad about it! LOL
Posts: 764
Own Kudos [?]: 4028 [0]
Given Kudos: 109
Location: Peru
Concentration: Finance, SMEs, Developing countries, Public sector and non profit organizations
Schools:Harvard, Stanford, Wharton, MIT &amp; HKS (Government)
GPA: 4.0
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: Set X consists of seven consecutive integers, and Set Y consists of [#permalink]
Set X consists of seven consecutive integers, and set Y consists of nine consecutive integers. Is the median of the numbers in set X equal to the median of the numbers in set Y ?
(1) The sum of the numbers in set X is equal to the sum of the numbers in set Y.
(2) The median of the numbers in set Y is 0.

In retaltion to the clue (1), I have the following doubt:
Algebraicaly, we can express the question in this way:
$$X = {x, x+1, x+2,...x+6}$$
$$Y = {y, y+1, y+2,...., y+8}$$
Being x and y integers.

Based on the clue (1) that the sum of the numbers in set X is equal to the sum of the numbers in set Y, we can say:

$$7x + 21 = 9y + 36$$
$$7x - 9y = 15$$

Picking numbers I have found two possible combinations:
x = -3 and y = -4, which means YES to the question.
x = -12 and y = -11, which means NO to the question.

Is there a faster way to solve it?

Source: https://www.gmathacks.com
Manager
Joined: 28 Feb 2012
Posts: 92
Own Kudos [?]: 190 [1]
Given Kudos: 17
GPA: 3.9
WE:Marketing (Other)
Re: Set X consists of seven consecutive integers, and Set Y consists of [#permalink]
1
Kudos
Set X consists of seven consecutive integers, and set Y consists of nine consecutive integers. Is the median of the numbers in set X equal to the median of the numbers in set Y ?
(1) The sum of the numbers in set X is equal to the sum of the numbers in set Y.
(2) The median of the numbers in set Y is 0.

Quite tricky question.
In such questions i try to answer YES or NO precisely by using the info from one of the statements. Lets try YES - two medians are equal, considering that both sets consists of consequtive integers, this to happen all number of set X should be within the set Y and then the mid number will be the same. Since there are no restrictions lets take numbers from 1 to 7 for set X and 1 to 9 for set Y - mid muber is 5.

Statement 1) from the first glance this condition does not fit into our sets from 1 to 9 and 1 to 7. So this statemnt seems sufficient, and i am about to say that possible answer for this question is either A or D. But then i am looking at the statement 2.

Statement 2) sometimes it helps to look at both statements before making any kind of conclusion because in real GMAT questions both statements never contradict each other, and by knowing more information it is easier to make final conclusion. In this qestion i forgot to consider that negative numbers also could be within the sets. This statement tells us about set y only, no info about set X - not sufficient.

Combining both statements: from st.1 we see that sum of set Y is 0, by st.1 we see that the sum of the set X also should be 0. This is only possible if the middle number of the set X is 0.

Manager
Joined: 13 Sep 2015
Posts: 79
Own Kudos [?]: 19 [0]
Given Kudos: 0
Location: United States
GMAT 1: 770 Q50 V45
GPA: 3.84
Re: Set X consists of seven consecutive integers, and Set Y consists of [#permalink]

the first number of set x is x, then the the median is x+4

the first number of set y is y, then the median is y+5

so when x-y=1, the medians are equal

the question is asking: is x-y=1?

(1) the sum of set x is 7(x+3) and of set y is 9(y+4)

so 7x-9y=15

insufficient, because

you can solve the equation:

7x-9y=15
x-y=1

then you get:

when x=-3, y=-4, the medians are equal, otherwise not

(2) y=-5

nothing to do with x, insufficient

(1)(2)

from one we know when y=-4, the medians equal, so

sufficient
Intern
Joined: 10 Jun 2016
Posts: 32
Own Kudos [?]: 12 [0]
Given Kudos: 194
Schools: IIM-A"19
Re: Set X consists of seven consecutive integers, and Set Y consists of [#permalink]
My way of solving

X = a, a+1, a+2...a+6
Y = p, p+1, .........p+9

To find Med X = Med Y ?

S-1) a+21 = p+36, So a = p+15.
a = -10 then p =-25
a = -1 then p =14. Many such scenarios leads to nothing. Not sufficient

S-2) -4,-3,-2,-1,0,1,2,3,4. Median = 0 and Sum = 0. Not sufficient as no info for X.

S-T) Since from S-1 sum X = sum Y means X = -3,-2,-1,0, 1,2,3. Yes Median will be same as Sum = Median = 0
VP
Joined: 12 Dec 2016
Posts: 1009
Own Kudos [?]: 1801 [0]
Given Kudos: 2562
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: Set X consists of seven consecutive integers, and Set Y consists of [#permalink]
let's A is the media of X, and B is the median of Y => 7A= 9B => A > B or A=B= 0
Manager
Joined: 06 Apr 2020
Posts: 121
Own Kudos [?]: 64 [0]
Given Kudos: 70
Concentration: Entrepreneurship, Technology
Schools: Wharton '23
WE:Engineering (Energy and Utilities)
Re: Set X consists of seven consecutive integers, and Set Y consists of [#permalink]
Set X consists of seven consecutive integers, and Set Y consists of nine consecutive integers. Is the median of the numbers in set X equal to the median of the numbers in set Y?

(1) The sum of the numbers in set X is equal to the sum of the numbers in set Y.
(2) The median of the numbers in set Y is 0.

Okay so I have a better approach
If sum in set X=sum in set Y
therefore mean of X cannot be equal to mean of Y as total number of elements are different EXCEPT IF THE SUM ITSELF IS 0!
so we dont know that : insufficient
b-> median of Y is zero therefore mean of Y is zero therefore sum of Y is zero and well thats it still not sufficient

A+B
Aaaha so if i know sum of Y is zero and its equal to X
I can be sure as hell that median = mean = 0 and hence they are equal and C is OA
Manager
Joined: 26 Dec 2022
Posts: 123
Own Kudos [?]: 38 [0]
Given Kudos: 48
Location: India
GMAT 1: 710 Q50 V36
Re: Set X consists of seven consecutive integers, and Set Y consists of [#permalink]
Set X consists of seven consecutive integers: m, m+1.....m+6 (median=m+3)
and Set Y consists of nine consecutive integers: n,n+1.....n+8 (median=n+4)

Is the median of the numbers in set X equal to the median of the numbers in set Y? ( So basically question is: Is m+3=n+4 i.e. Is m=n+1?)

(1) The sum of the numbers in set X is equal to the sum of the numbers in set Y. ( 7m+ 1+2...6=9n+1+2...8 => 7m=9n+18 Hence A is not sufficient)
(2) The median of the numbers in set Y is 0. ( Median of Y=0 => n=-4) It doesn't tell us anything about m, so B is not sufficient

Now combining both statements
we get
n=-4
7m=9n+18=> 7m= (-)18 [Clearly we can say that m is not equal to n+1. Hence both statements together are sufficient: C]­
Re: Set X consists of seven consecutive integers, and Set Y consists of [#permalink]
Moderator:
Math Expert
94372 posts