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5 in S?

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by sanju09 » Thu Mar 22, 2012 2:25 am
If S is a set of ten consecutive integers, is the integer 5 in S?
(1) The integer -3 is in S.
(2) The integer 4 is in S.
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by killer1387 » Thu Mar 22, 2012 3:28 am
sanju09 wrote:If S is a set of ten consecutive integers, is the integer 5 in S?
(1) The integer -3 is in S.
(2) The integer 4 is in S.
IMO E.
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by Brent@GMATPrepNow » Thu Mar 22, 2012 8:32 am
sanju09 wrote:If S is a set of ten consecutive integers, is the integer 5 in S?
(1) The integer -3 is in S.
(2) The integer 4 is in S.
Statement 1: The integer -3 is in S.
case a: S = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} --> 5 is not in S
case b: S = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5} --> 5 is in S
INSUFFICIENT

Statement 2: The integer 4 is in S
case a: S = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} --> 5 is not in S
case b: S = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5} --> 5 is in S
INSUFFICIENT

Statements 1 & 2: -3 and 4 are both in S
case a: S = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} --> 5 is not in S
case b: S = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5} --> 5 is in S
INSUFFICIENT

The answer is E

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by Whitney Garner » Thu Mar 22, 2012 9:51 am
sanju09 wrote:If S is a set of ten consecutive integers, is the integer 5 in S?
(1) The integer -3 is in S.
(2) The integer 4 is in S.
A quick way to test is to go with extremes:

(1)
  • - Let -3 be the largest integer...we don't even have to count up, 5 CANNOT be in the set because it is bigger than -3 (the biggest number).
    - Let -3 be the smallest integer...now count up 9 more...6 would be the greatest so 5 WOULD be in the SET.
2 different answers: NOT Sufficient

(2)
Same plan:
  • - Let 4 be the largest integer, then 5 CANNOT be in the set.
    - Let 4 be the smallest, then the next number in the set is 5, so 5 WOULD be in the set.
2 different answers: NOT Sufficient

(1+2)
Same plan:
  • - Let 4 be the largest integer and check to make sure -3 is in the set {4, 3, 2, 1, 0, -1, -2, -3, ...] yep, and in this scenario 5 CANNOT be in the set.
    - Let -3 be the smallest integer and check to make sure that 4 is in the set {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6], it is AND so is 5...so 5 WOULD be in the set.
2 different answers: NOT Sufficient

The answer is E

Hope this helps!
:)
Whit
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