sana.noor wrote:If n is a positive integer, is n equal to 100 ?
(1) n^(1/2) > 9
(2) n^(1/2) < 11
Target question:
Does n = 100?
Aside: x^(1/2) is the same as sqrt(x)
Statement 1: n^(1/2) > 9
In other words, sqrt(n) > 9
Square both sides of the inequality to get: n > 81
There are several integer values of n that meet this condition. Here are two:
Case a: n = 99, in which case
n does not equal 100
Case b: n = 100, in which case
n does equal 100
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n^(1/2) < 11
In other words, sqrt(n) < 11
Square both sides of the inequality to get: n < 121
There are several integer values of n that meet this condition. Here are two:
Case a: n = 99, in which case
n does not equal 100
Case b: n = 100, in which case
n does equal 100
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
We know that 9 < sqrt(n) < 11
In other words, 81 < n < 121
There are still several integer values of n that meet this condition. Here are two:
Case a: n = 99, in which case
n does equal 100
Case b: n = 100, in which case
n does equal 100
Since we still cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
