Newaz111 wrote:For each positive integer n, the integer n* is defined by n* = n² + 1. What is the value of the positive integer k ?
(1) When k is divided by 4, the reminder is 1.
(2) 18 < k* < 36
Target question: What is the value of the positive integer k?
Statement 1: When k is divided by 4, the reminder is 1.
There are MANY MANY possible values of k that satisfy statement 1.
Some possible values of k include 1, 5, 9, 13, etc
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 18 < k* < 36
Let's examine some possible values of k* by testing some positive integers.
1* = 1² + 1 =
2 [not within the range of 18 < k* < 36]
2* = 2² + 1 =
5 [not within the range of 18 < k* < 36]
3* = 3² + 1 =
10 [not within the range of 18 < k* < 36]
4* = 4² + 1 =
17 [not within the range of 18 < k* < 36]
5* = 5² + 1 = 26 [WITHIN the range of 18 < k* < 36]
6* = 6² + 1 =
37 [not within the range of 18 < k* < 36]
7* = 7² + 1 =
50 [not within the range of 18 < k* < 36]
If 18 < k* < 36, then we can see that
k must equal 5
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
