VJesus12 wrote: ↑Thu Mar 11, 2021 12:55 pm
A set of 51 different integers has a median of 30 and a range of 60. What is the value of the least possible integer in this set?
a) -10
b) -6
c) -5
d) 5
e) 10
Answer:
C
Source: e-GMAT
The median of a set of \(51\) elements is the \(26\)th element.
So we have \(25\) elements after the median.
When we take one of the answer choices and workout the largest element, we need to see if the largest element is at least \(25\) integers away from \(30\) so as to get distinct elements.
(A) \(-10\)
In this case, the largest element is \(50\) which is only \(20\) integers away from \(30.\) \(\Large{\color{red}\chi}\)
(B) \(-6\)
In this case, the largest element is \(54\) which is only \(24\) integers away from \(30.\) \(\Large{\color{red}\chi}\)
(C) \(-5\)
In this case, the largest element is \(55\) which is \(25\) integers away from \(30.\) \(\Large{\color{green}\checkmark}\)
