diebeatsthegmat wrote:hi, can you guys please help me solve this problem? the answer is B and i dont understand why the answer is B
i think the answer should be E. Anyways here is the problem and my solution. please take a look and help me find out the mistake in my solution
Is the range of a combined set (S,T) bigger than the sum of ranges of sets S and T ?
1. The largest element of T is bigger than the largest element of S.
2. The smallest element of T is bigger than the largest element of S.[/size]

and here is my solution.
because its about the range and range= highest - lowest so i just take highest and lowest number in the set
1. Largest T> largest S
+set T= ( highest.... lowest)= 5 ...1
set S = ( highest... lowest)=4...0
=> 5-1=4 and 4-0=4 so 4+4=8
set (t,s)= (highest ...lowest) =(5...0) so 5-0=5
thus 5<8
+set T=( 15...9) >>> 15-9=6
set S=(4...-3)>>> 4+3=7
so set (s,t)+(15....-3) 15+3=13
thus rang set(S,T)=18>13
thus 1 is insuff
2. The smallest element of T is bigger than the largest element of S
lowest t> lowest S
+set T= ( highest.... lowest)= 5 ...1
set S = ( highest... lowest)=4...0

-->This is where the mistake come.
Since smallest of t is bigger than larger element of S.

Lowest T>High S

S={0.......4}

T={5........8)

=> 5-1=4 and 4-0=4 so 4+4=8
set (t,s)= (highest ...lowest) =(5...0) so 5-0=5
thus 5<8=range S +rang T
+ set T =( 5...1)>>> range = 4
set S =(18, -2) rang = 20 and also 20 is the range of set (t,s)
rang set t +range set S =(4+20)=24>20=range set (s,t)
+ set T=(19....4)>>>range =15
set S=5...-2) >>> rang=7
range set T+rang set S=22< range (s,t)=(19+2)=21
insuffi
1+2/ largest T > largest S and lowest T> lowest S
+ set T=(19....4)>>>range =15
set S=5...-2) >>> rang=7
range (s,t)=(19+2)=21<range set T+rang set S=22
+set T=( 15...9) >>> 15-9=6
set S=(4...-3)>>> 4+3=7
so set (s,t)+(15....-3) 15+3=13
thus rang set(S,T)=18>13
so insuffi
i dont understand why the OA is B
please give me some explaination

kevincanspain wrote:Is the range of a combined set (S,T) bigger than the sum of ranges of sets S and T ?
1. The largest element of T is bigger than the largest element of S.
2. The smallest element of T is bigger than the largest element of S.


Suppose the ranges of S and T are s and t respectively and the smallest elements of S and T are x and y.
Thus the largest elements of S and T are x + s and y + t

We want to know whether the range of S U T is greater than s + t

(2)

If y > x + s, the greatest element of S U T is y + t and the smallest is x. Thus the range of S U T = y + t - x

Since y - x > s , y + t - x > s + t