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Manager  Joined: 12 Oct 2011
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GMAT 1: 700 Q48 V37 GMAT 2: 720 Q48 V40 Set X consists of seven consecutive integers, and Set Y  [#permalink]

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5
25 00:00

Difficulty:   95% (hard)

Question Stats: 43% (02:02) correct 57% (01:53) wrong based on 580 sessions

### HideShow timer Statistics 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.

Isn't there really just one possibility for both sets, the one in which the median is 0? I can't think of two sets with those properties that have the same sum other than the one with median 0.
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Re: Set X consists of seven consecutive integers...  [#permalink]

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15
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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?

Sets X and Y are evenly spaced. In any evenly spaced set (aka arithmetic progression):
(mean) = (median) = (the average of the first and the last terms) and (the sum of the elements) = (the mean) * (# of elements).

So the question asks whether (mean of X) = (mean of Y)?

(1) The sum of the numbers in set X is equal to the sum of the numbers in set Y --> 7*(mean of X) = 9* (mean of Y) --> answer to the question will be YES in case (mean of X) = (mean of Y) = 0 and will be NO in all other cases (for example (mean of X) =9 and (mean of Y) = 7). Not sufficient.
For example consider following two sets:
Set X: {6, 7, 8, 9, 10, 11, 12} --> sum 63;
Set Y: {3, 4, 5, 6, 7, 8, 9, 10, 11} --> sum 63.

(2) The median of the numbers in set Y is 0 --> (mean of Y) = 0, insufficient as we know nothing about the mean of X, which may or may not be zero.

(1)+(2) Since from (2) (mean of Y) = 0 and from (2) 7*(mean of X) = 9* (mean of Y) then (mean of X) = 0. Sufficient.

Hope it's clear.
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Since the numbers are in A.P
mean = Median .
mx= Sum /6
my= Sum /9.

Qt is mx=my?

#1 Sum is same. If sum is same and divided by 6 or 9. it will be different.
hence in sufficient.

#2 Median is zero. We do not anything about set X hence in sufficient

#1 + #2 ..

Median(Y) is zero and Sum is same

this would mean mean is also Zero since they are in A.P

since sum is same mean .median of x is also zero
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Set X consists of seven consecutive integers  [#permalink]

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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: http://www.gmathacks.com
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Joined: 02 Sep 2009
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Re: Set X consists of seven consecutive integers  [#permalink]

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metallicafan wrote:
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: http://www.gmathacks.com

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Re: Set X consists of seven consecutive integers, and Set Y  [#permalink]

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Re: Set X consists of seven consecutive integers, and Set Y  [#permalink]

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1
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.

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Set X consists of seven consecutive integers, and Set Y  [#permalink]

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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
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Re: Set X consists of seven consecutive integers, and Set Y  [#permalink]

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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
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Re: Set X consists of seven consecutive integers, and Set Y  [#permalink]

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let's A is the media of X, and B is the median of Y => 7A= 9B => A > B or A=B= 0
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Re: Set X consists of seven consecutive integers, and Set Y  [#permalink]

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_________________ Re: Set X consists of seven consecutive integers, and Set Y   [#permalink] 22 Aug 2018, 10:26
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