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X is a set containing 7 different numbers. Y is the set containing 6 different positive numbers all of which are members of set X. Is the mean of X equal to the mean of Y?
(1) Range of X is greater than range of Y
(2) Sum of all the numbers in set X< Sum of all the numbers in set Y
(1) Range of X is greater than range of Y
(2) Sum of all the numbers in set X< Sum of all the numbers in set Y
05 Jul 2017, 10:36
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anurag16
Hi..
If all 7 numbers are different and 6 of them have a certain MEAN, M..
This would be EQUAL to mean of 7 numbers ONLY when 7th number itself is EQUAL to M...
Let's see the statements...
a) Range of X is greater than range of Y
This means the 7th number is either greater than or less than the 6 numbers in set Y..
So the 7 number cannot be EQUAL to mean of 6 numbers..
Ans is NO
Sufficient
b) Sum of all the numbers in set X< Sum of all the numbers in set Y
Clearly a lower number /7 will be less than greater number/6..
Clearly mean of Y>mean of X..
Ans is again NO
Sufficient
D
General Discussion
18 Jun 2023, 04:17
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This is an interesting question which took a lot of my time .
First of all the main thing to notice is that X is a set containing 7 different numbers.
And, Y is a set containing 6 different positive numbers.This tells us that the one extra number in set X can be 0 or negative also.
Now Y is a subset of X.
So lets say that the extra number in set X is k, for sake of ease .
We can note that if sum of numbers of set Y (smaller set) is S then that of set X is S+k.
Now lets jump to answer choices:
a) Range of X is greater than range of Y
Ok. So that means the extra number in set X is either largest or smallest. That's why the range is different .
Example - Consider a set 4,6,8,10 . If I want to change range of this set I have to add a number that is either less than 4 or greater than 10. I can add 5,7,and 9 but that will not change the range .
Also, the question is asking -Is the mean of X equal to the mean of Y?
Think about this small set again 4,6,8,10. the mean is middle value 7 . Now IF we want to add another number in this set AND want to keep the mean same , then what that number would be? It might be easier to understand this via number line:
_________4__6_7_8__10____
If I add a number on the left side of 7 , the mean will shift to the left .Then the mean will be less than 7.
Similarly , if I add a number to the right of 7 , the mean will shift to the right . The mean will then be greater than 7 .
Thus to keep the mean same in an existing set we have to add the number that is equal to mean.
In our question the mean will be somewhere in middle of 6 different numbers but the one extra number in set X is outside this range of 6 number. Hence the mean of X will not be same as that of Y .
SUFFICIENT.
b) Sum of all the numbers in set X< Sum of all the numbers in set Y
The set x contains 7 numbers .
Set Y contains 6 numbers .
Let, Sum of Set Y = S => Mean = \(S/6\) ---(1)
Sum of Set X = S+k => Mean =\( (S + k)/7\) ----(2)
Now (2) can be equal to (1) only if S+k is greater than S.
Eg: 4 = 24/6 = 28/7
Since its given Sum of all the numbers in set X< Sum of all the numbers in set Y , mean of two sets will not be same.
SUFFICIENT
First of all the main thing to notice is that X is a set containing 7 different numbers.
And, Y is a set containing 6 different positive numbers.This tells us that the one extra number in set X can be 0 or negative also.
Now Y is a subset of X.
So lets say that the extra number in set X is k, for sake of ease .
We can note that if sum of numbers of set Y (smaller set) is S then that of set X is S+k.
Now lets jump to answer choices:
a) Range of X is greater than range of Y
Ok. So that means the extra number in set X is either largest or smallest. That's why the range is different .
Example - Consider a set 4,6,8,10 . If I want to change range of this set I have to add a number that is either less than 4 or greater than 10. I can add 5,7,and 9 but that will not change the range .
Also, the question is asking -Is the mean of X equal to the mean of Y?
Think about this small set again 4,6,8,10. the mean is middle value 7 . Now IF we want to add another number in this set AND want to keep the mean same , then what that number would be? It might be easier to understand this via number line:
_________4__6_7_8__10____
If I add a number on the left side of 7 , the mean will shift to the left .Then the mean will be less than 7.
Similarly , if I add a number to the right of 7 , the mean will shift to the right . The mean will then be greater than 7 .
Thus to keep the mean same in an existing set we have to add the number that is equal to mean.
In our question the mean will be somewhere in middle of 6 different numbers but the one extra number in set X is outside this range of 6 number. Hence the mean of X will not be same as that of Y .
SUFFICIENT.
b) Sum of all the numbers in set X< Sum of all the numbers in set Y
The set x contains 7 numbers .
Set Y contains 6 numbers .
Let, Sum of Set Y = S => Mean = \(S/6\) ---(1)
Sum of Set X = S+k => Mean =\( (S + k)/7\) ----(2)
Now (2) can be equal to (1) only if S+k is greater than S.
Eg: 4 = 24/6 = 28/7
Since its given Sum of all the numbers in set X< Sum of all the numbers in set Y , mean of two sets will not be same.
SUFFICIENT
