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07 Jul 2021, 08:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
46% (02:44) correct
54%
(02:37)
wrong
based on 82
sessions
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If x is a positive integer less than 10, is z less than the average (arithmetic mean) of x and 10 ?
(1) The positive difference between z and x is greater than the positive difference between z and 10.
(2) z = 5x
(1) The positive difference between z and x is greater than the positive difference between z and 10.
(2) z = 5x
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
https://gmatclub.com/forum/data-sufficiency-ds-141/
https://gmatclub.com/forum/data-sufficiency-ds-141/
07 Jul 2021, 11:38
Kudos
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If x is a positive integer less than 10, is z less than the average (arithmetic mean) of x and 10 ?
We are looking for: Is 2z<x+10
(1) The positive difference between z and x is greater than the positive difference between z and 10.
So |z-x|>|z-10|
Square both sides
\(z^2-2xz+x^2>z^2+100-20z……..x^2-100+20z-2xz>0…..(x-10)(x+10)-2z(x-10)>0\)
\((x-10)(x+10-2z)>0\)
We know that x<10 or x-10<0, so x+10-2z<0 or 2z>x+10…..
Answer is NO.
We can also analyse \(|z-x|>|z-10|\).
This means z is farther from x than from 10.
Thus z will always be closer to z as compared to x and as x is less than 10, z is more than the mean of x and 10.
Sufficient
(2) z = 5x
If x=1, then z=5 but mean =(1+10)/2 or 5.5……answer is Yes
If x=3, then z=15….mean =9. Answer is no
Insufficient
A
We are looking for: Is 2z<x+10
(1) The positive difference between z and x is greater than the positive difference between z and 10.
So |z-x|>|z-10|
Square both sides
\(z^2-2xz+x^2>z^2+100-20z……..x^2-100+20z-2xz>0…..(x-10)(x+10)-2z(x-10)>0\)
\((x-10)(x+10-2z)>0\)
We know that x<10 or x-10<0, so x+10-2z<0 or 2z>x+10…..
Answer is NO.
We can also analyse \(|z-x|>|z-10|\).
This means z is farther from x than from 10.
Thus z will always be closer to z as compared to x and as x is less than 10, z is more than the mean of x and 10.
Sufficient
(2) z = 5x
If x=1, then z=5 but mean =(1+10)/2 or 5.5……answer is Yes
If x=3, then z=15….mean =9. Answer is no
Insufficient
A
07 Jul 2021, 11:58
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Bunuel
Given that x is less than 10.
Statment 1:-
For this statement to be true, z must be greater than avg of x & 10. This can be under stood from number line.
If we draw a number line, we can see that if z is less than x, then (X-Z) <(10-Z) , so not possible.
If z is between x and avg of x&10, then X-Z<10-Z, so not possible.
If Z is between avg(x&10) and 10,
Then, Z-X >10-Z, hence possible.
Similarly for Z>10, Z-X>10-X
HENCE Possible.
From this we can say that Option A is sufficient.
Statment 2:-
If x=1, z=5 but Z will bw less than avg of x&10
Now, if x>=2, Z=5x>=10
So, Z will be greater than 10.
Hence, No solution.
Hence Answer should be A.
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