Data Sufficiency

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.

the answer to this DS is B,
let's denote V set of all elements of S, and T.
the the range of V is : max(S,T)-min(S,T)
the question can be written as follow:
max(S,T)-min(S,T)?max(S)+max(T)-(min(T)+min(S)).[1]
(1)alone tells us max(T)>max(S)
then[1] become
max(T)-min(S,T)-max(S)-max(T)+(min(T)+min(S))
canceling max(T)
-min(S,T)-max(S)+min(T)+min(S), Insufficient to see that pick numbers:
min(T)=8, min(S)=2, max(S)=7 the result will be
-2-7+8+2=1 > 0
min(T)=1, min(S)=2, max(S)=7
-1-7+2+1=-5<0
Insufficient.
(2)alons tells us max(T)>min(T)>max(s)>min(T)
[1] becomes:
max(T)-min(S)-max(S)-max(T)+min(T)+min(S)
cancel out equal term yields:
min(T)-max(S)>0
Sufficient

very well explained by adam...answer shud be B

adam15 wrote:the answer to this DS is B,
let's denote V set of all elements of S, and T.
the the range of V is : max(S,T)-min(S,T)
the question can be written as follow:
max(S,T)-min(S,T)?max(S)+max(T)-(min(T)+min(S)).[1]
(1)alone tells us max(T)>max(S)
then[1] become
max(T)-min(S,T)-max(S)-max(T)+(min(T)+min(S))
canceling max(T)
-min(S,T)-max(S)+min(T)+min(S), Insufficient to see that pick numbers:
min(T)=8, min(S)=2, max(S)=7 the result will be
-2-7+8+2=1 > 0
min(T)=1, min(S)=2, max(S)=7
-1-7+2+1=-5<0
Insufficient.
(2)alons tells us max(T)>min(T)>max(s)>min(T)
[1] becomes:
max(T)-min(S)-max(S)-max(T)+min(T)+min(S)
cancel out equal term yields:
min(T)-max(S)>0
Sufficient

this looks like too much work for 2 mins!

anyone else have any different approaches? this question is hard!

it seems like too much work...because adam has explained it in great detail....you can use this approach and solve it in under 2 mins

crackgmat007 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.

Hi crackgmat 007,

For this kind of question, you are way better off using your reasoning skills (maybe picking some numbers along the way just to facilitate your thinking) than you are setting up a bunch of equations.

Step one of the Kaplan method is to focus on the question stem. This becomes more important with toughter questions.
Ask yourself: When will the combined range of the sets be larger than the range of one of the sets?

Then answer yourself: Well, if one set was entirely contained within another, then the combined range WOULD NOT be bigger (instead, it would be equal to the range of the larger set).

So, the moment one set is NOT contained within one another, the combined range of the two sets will be larger than the ranges of at least one of the two sets.

But what about the sum of the ranges of the two sets? For the combined range to be larger than the sum of the two sets, there would have to be absolutely no overlap at all between the two sets.

...now (and only now), do we go to the statements.

1. The largest element of T is bigger than the largest element of S.
Well, we don't know anything about the small elements . If T's smallest element were larger than S's largest element, then the combined range of the sets is larger, as there is no overlap:

T: 6........9

S: 2.....4
Here, the answer to the question is "yes."

But if T's smallest element were smaller than S's smallest element, the range of the combined sets is smaller, as T would contain S:

T: 1................7

S: 2.......5

Here, the answer to the question is "no."

Because we get both a "yes" and a "no" answer, the first statement is insufficient, and the correct answer will be B, C, or E.

2. The smallest element of T is bigger than the largest element of S.
This necessitates no overlap:

T: |10.....

S: .........9|

Because there is no overlap, the range of the combined sets is larger than the sum of the ranges of the two sets, the second statement is independently sufficient, and the answer to the question is definitely "yes."

Choose B

Takeaway: A lot of times in harder DS questions, you need to make one big important deduction. This deduction will then allow you to rephrase the question and handle the statements effectively.

(Nuts. I can't separate out the numbers visually in the sets to illustrate what I meant. I am separating them out in the textbox that I write in, but it is not displaying that way. Hopefully, it's still clear enough).