A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1> the median of the numbers is greater than the mean
2> the median is 4
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3)Is range > 2
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liferocks
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IMO ans is A
we can reduce the question to whether x >5 or x<3 in which case the range will be >2
now from 1 we get median>(17+x)/5 or median >3+(2+x)/5
if x=3, median is 4 mean 4..does not satisfy the condition
if x=4, median is 4 mean 4.2..does not satisfy the condition
if x=5, median is 4 mean 4.6..does not satisfy the condition
only if x<3 or x>5 the condition is satisfied..condition 1 is sufficient
From option 2 we cannot conclude any thing as when median is 4 the range may or may not be >2
someone please check the approach ..I am very poor in statistics
we can reduce the question to whether x >5 or x<3 in which case the range will be >2
now from 1 we get median>(17+x)/5 or median >3+(2+x)/5
if x=3, median is 4 mean 4..does not satisfy the condition
if x=4, median is 4 mean 4.2..does not satisfy the condition
if x=5, median is 4 mean 4.6..does not satisfy the condition
only if x<3 or x>5 the condition is satisfied..condition 1 is sufficient
From option 2 we cannot conclude any thing as when median is 4 the range may or may not be >2
someone please check the approach ..I am very poor in statistics
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this_time_i_will
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Please have a look at at approach here:ern5231 wrote:Any more answers? This is not the OA
https://www.beatthegmat.com/range-t56935.html
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sandy_online
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from statement 1:ern5231 wrote:A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1> the median of the numbers is greater than the mean
2> the median is 4
the median is greater than mean => x will be either 5, 6 or 7
as if we consider x less then 5 then mean will be more than the median
e.g if x=4, median will be 4 while mean = 21/5 = 4.2
now, values x = 5,6,7 all satisfy the statement 1,
e.g. if x =5, then median =5 but mean will be 22/5 = 4.2 which less than median.
x =6, then median =5 but mean will be 23/5..
so range can be 2,3,4 => not suff.
now, consider statement 2, median 4 this clearly indicated that x=4,
here we can get the range = 5-3 = 2 => sufff .. answer B
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Solution
Range is the difference between the maximum and the minimum value.
Mean of given numbers is (3+4+5+5+x)/5 = (17+x)/5.
(a) If x is less than or equal to 3, then writing in ascending order we have x,3,4,5, 5 and median is 4.
(b) If x is more than 3 but less than or equal to 4, then in AO we have 3,x,4,5,5 and median is 4.
(c) If x is more than 4 and less than 5, then in AO we have 3,4,x,5,5 and median is x.
(d) If x is more than or equal to 5, then in AO we have 3,4,5,5,x and median is 5.
First consider statement (1) alone.
It means (17+x)/5 is less than median. Or x is less than (5*median-17)
So we check for all the cases (a), (b), (c), (d) and verify whether there exists x such that x is less than (5*median - 17).
For (a), we have that x should be less than 5*4 - 17 = 3 which is quite possible. So we say that if x is less than 3 then median is more than mean.
Here then the range will be more than 2.
For (b) we have that x should be less than 5*4 - 17 = 3 which is not possible because x is more than 3 but less than or equal to 4.
For (c) we have that x is less than 5*x - 17 or x is more than 17/4 = 4.25 which is quite possible and so if x is more than 4.25 and less than 5, then median is more than mean.
Here in this case however range is 5 - 3 = 2.
For (d) we have that x is less than 5*5 - 17 = 8, and already x is more than or equal to 5.
So we say that if x is more than or equal to 5 and less than 8, then median is more than mean.
Here again if x is 5, then range is 2 but if x is more than 5, the range is more than 2.
So we conclude that if median is more than mean then range can be either 2 or greater than 2.
So (1) is not enough.
Consider (2) alone.
So either (a) or (b) is possible.
If x is less than 3 then range is more than 2.
If x is equal to 3 then range is 2.
If x is more than 3 but less than or equal to 4, the also range is 2.
So we conclude that if median is 4, then range can be equal to 2 or greater than 2.
So (2) is not enough.
Combining we have that (a) is the only possibility and x is less than 3 and in this case the range is more than 2.
The correct answer is (C).
Range is the difference between the maximum and the minimum value.
Mean of given numbers is (3+4+5+5+x)/5 = (17+x)/5.
(a) If x is less than or equal to 3, then writing in ascending order we have x,3,4,5, 5 and median is 4.
(b) If x is more than 3 but less than or equal to 4, then in AO we have 3,x,4,5,5 and median is 4.
(c) If x is more than 4 and less than 5, then in AO we have 3,4,x,5,5 and median is x.
(d) If x is more than or equal to 5, then in AO we have 3,4,5,5,x and median is 5.
First consider statement (1) alone.
It means (17+x)/5 is less than median. Or x is less than (5*median-17)
So we check for all the cases (a), (b), (c), (d) and verify whether there exists x such that x is less than (5*median - 17).
For (a), we have that x should be less than 5*4 - 17 = 3 which is quite possible. So we say that if x is less than 3 then median is more than mean.
Here then the range will be more than 2.
For (b) we have that x should be less than 5*4 - 17 = 3 which is not possible because x is more than 3 but less than or equal to 4.
For (c) we have that x is less than 5*x - 17 or x is more than 17/4 = 4.25 which is quite possible and so if x is more than 4.25 and less than 5, then median is more than mean.
Here in this case however range is 5 - 3 = 2.
For (d) we have that x is less than 5*5 - 17 = 8, and already x is more than or equal to 5.
So we say that if x is more than or equal to 5 and less than 8, then median is more than mean.
Here again if x is 5, then range is 2 but if x is more than 5, the range is more than 2.
So we conclude that if median is more than mean then range can be either 2 or greater than 2.
So (1) is not enough.
Consider (2) alone.
So either (a) or (b) is possible.
If x is less than 3 then range is more than 2.
If x is equal to 3 then range is 2.
If x is more than 3 but less than or equal to 4, the also range is 2.
So we conclude that if median is 4, then range can be equal to 2 or greater than 2.
So (2) is not enough.
Combining we have that (a) is the only possibility and x is less than 3 and in this case the range is more than 2.
The correct answer is (C).
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anirudhbhalotia
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ern5231 wrote:A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1> the median of the numbers is greater than the mean
2> the median is 4
So as per the question Max - Min > 2 ? Therefore is x>5 or x<3, only then Range > 2.
1. the median of the numbers is greater than the mean
If x>5, say 8, Median = 5, mean = 25/5 = 5 NOT SUFFICIENT
If x>5, say 7, Median = 5, mean = 24/5 = 4.8 SUFFICIENT
If x>5, say 6, Median = 5, mean = 21/5 = 4.5 SUFFICIENT
RANGE > 2
If x<3, say 2, Median = 4, mean = 19/5 = 3.8 SUFFICIENT
RANGE > 2
OVERALL NOT SUFFICIENT
2. the median is 4
So x,3,4,5,5 OR 3,x,4,5,5
If x = 4, Range is not greater than 2.
If x = 3, Range is not greater than 2.
If x = 2, Range is greater than 2.
OVERALL NOT SUFFICIENT
If we combine both
If x = 3, Median = 4, Mean = 20/5 = 4 , we know x cannot be equal to or greater 3 as then condition 1(Median>Mean) wont be satisfied.
If x = 2, Median = 4, Mean = 19/5 = 3.8 SUFFICIENT as range > 2.
If x =1, Median = 4, Mean = 18/5 = 3.6 SUFFICIENT
Answer is C.
2nd explanation makes sense... but after a long time of going over it again and again.
is there possibly a smarter way (not saying any of the methods shown were not smart - they were for sure) to solve this? i don't see how i'd be able to solve this effectively and efficiently during the test...
i'd like to understand to solve smarter, not harder.
is there possibly a smarter way (not saying any of the methods shown were not smart - they were for sure) to solve this? i don't see how i'd be able to solve this effectively and efficiently during the test...
i'd like to understand to solve smarter, not harder.
Hey Gnod...
This is my approach.
Disclaimer: I could not solve the problem at first go and was equally frustrated because none of the explanation seemed to fall within 2 min time-frame that I usually use.
Consider statement 1:
For the series to be within a range of 2, x has to be between 3 and 5
Notice with x= 10 mean of the series becomes 5.4 which contradicts statement 1 that median (which is now 5) is greater than mean.
With x=5, median becomes 5 but Mean becomes 4.4. This satisfies statement 1.
But with x = 3, median becomes 4 and mean becomes 4 as well. This contradicts with statement 1.
So we can see statement 1 is not valid for two values of x that falls within the range.
What I am trying to draw on is that statement 1 cannot set the bar for whether the range will fall within 2 or not.
Therefore, INSUFFICIENT.
Statement 2: Now we know x = 4 or anything less than 4
If x =4 or 3, then the range remains within 2 and median remains 4.
If x = 2, then the range is greater than 2 but the median remains 4.
Again, same principle. Statement 2 fails to specify whether the range is less than 2 or not.
Combine together,
We can assume that x is either 4,3 or 2.
With x =3, mean is 4. But statement 1 says mean has to be less than 4.
Put x =2 and you have a mean that is less than median.
Hence, answer is C.
I am not too sure if I could clarify my approach as much as I wanted to, but I hope this helps.
This is my approach.
Disclaimer: I could not solve the problem at first go and was equally frustrated because none of the explanation seemed to fall within 2 min time-frame that I usually use.
Consider statement 1:
For the series to be within a range of 2, x has to be between 3 and 5
Notice with x= 10 mean of the series becomes 5.4 which contradicts statement 1 that median (which is now 5) is greater than mean.
With x=5, median becomes 5 but Mean becomes 4.4. This satisfies statement 1.
But with x = 3, median becomes 4 and mean becomes 4 as well. This contradicts with statement 1.
So we can see statement 1 is not valid for two values of x that falls within the range.
What I am trying to draw on is that statement 1 cannot set the bar for whether the range will fall within 2 or not.
Therefore, INSUFFICIENT.
Statement 2: Now we know x = 4 or anything less than 4
If x =4 or 3, then the range remains within 2 and median remains 4.
If x = 2, then the range is greater than 2 but the median remains 4.
Again, same principle. Statement 2 fails to specify whether the range is less than 2 or not.
Combine together,
We can assume that x is either 4,3 or 2.
With x =3, mean is 4. But statement 1 says mean has to be less than 4.
Put x =2 and you have a mean that is less than median.
Hence, answer is C.
I am not too sure if I could clarify my approach as much as I wanted to, but I hope this helps.
Range is the difference two extreme numbers in a series...hence for the series to be within range of 2, the value of x has to be between 3 and 5. With any other value, the difference between the smallest and largest number will exceed 2.
As for applying the concept, for each statement I picked 2 numbers within the range and one outside the range.
Ideally you would pick one number inside the range and another outside. I guess this is where the GMAT trick kicks in where you need to double check your assumption. This is more like "Sanity Check" before you jump in.
Both the statements failed to set a limit on how much the number can be.
If an expert looks at my approach, probably they will say its not perfect. But I am willing to settle with this quick cross-check and stay within my time-frame.
As for applying the concept, for each statement I picked 2 numbers within the range and one outside the range.
Ideally you would pick one number inside the range and another outside. I guess this is where the GMAT trick kicks in where you need to double check your assumption. This is more like "Sanity Check" before you jump in.
Both the statements failed to set a limit on how much the number can be.
If an expert looks at my approach, probably they will say its not perfect. But I am willing to settle with this quick cross-check and stay within my time-frame.
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saketk
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My Approach --
STATEMENT 1: -- Median > Mean
3, 4, 5, 5, and x
Case 1: x,3,4,5,5 --- X cannot be equal to or greater than 3.. because Median > Mean -- Range > 2
if 3,4,5,5,x
median = 5
in this case mean should be less than 5.
x can be 5,6,...
So range will be 2,3 .. depending on the value of X..
So, STATEMENT 1 is not sufficient.
STATEMENT- 2
4 is the median.. so the numbers can be arranged in the following way
x,3,4,5,5 -- here X can be anything upto 3.. So the Range will also change accordingly..
STATEMENT 2 is INSUFFICIENT
Combine both statement .. we know that median is 4 and also the value of X cannot be equal to greater than 3 because if we put the value of X=3, then MEDIAN = Mean. So, not possible
So, yes we can find out the range. i.e. Range will be greater than 2.
The correct answer is option C
STATEMENT 1: -- Median > Mean
3, 4, 5, 5, and x
Case 1: x,3,4,5,5 --- X cannot be equal to or greater than 3.. because Median > Mean -- Range > 2
if 3,4,5,5,x
median = 5
in this case mean should be less than 5.
x can be 5,6,...
So range will be 2,3 .. depending on the value of X..
So, STATEMENT 1 is not sufficient.
STATEMENT- 2
4 is the median.. so the numbers can be arranged in the following way
x,3,4,5,5 -- here X can be anything upto 3.. So the Range will also change accordingly..
STATEMENT 2 is INSUFFICIENT
Combine both statement .. we know that median is 4 and also the value of X cannot be equal to greater than 3 because if we put the value of X=3, then MEDIAN = Mean. So, not possible
So, yes we can find out the range. i.e. Range will be greater than 2.
The correct answer is option C
