18. If K is a positive integer, is K the square of an integer?
(1) K is divisible by 4
(2) K is divisible by exactly 4 different prime numbers
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
21 set 18
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 144
- Joined: Fri Apr 13, 2007 2:25 am
-
- Master | Next Rank: 500 Posts
- Posts: 144
- Joined: Fri Apr 13, 2007 2:25 am
-
- Senior | Next Rank: 100 Posts
- Posts: 98
- Joined: Mon Jun 11, 2007 10:32 pm
- Location: Mumbai
1) K could be 8 or 16. INSUFFradhika1306 wrote:18. If K is a positive integer, is K the square of an integer?
(1) K is divisible by 4
(2) K is divisible by exactly 4 different prime numbers.
2) Irrelevant info. INSUFF
Combining, we know that K is divisible by 4 and three other prime numbers at least. Cant say if it is a square of an integer though.
Hence E.
Stmt 1 - K is divisble by 4.. so nos can be 4, 8, 12... not all numbers are sq of an int - NOT SUFF
Stmt 2 - k is divisble be 4 prime nos - so if we choose no as 2*3*5*7 = 210.. this is divisble be 4 prime nos but not a square of an int.. however, we can have a no 210^2 - divisible by 2,3, 5, 7 but also square.. NOT SUFF
Together - NOT SUFF
So E
Stmt 2 - k is divisble be 4 prime nos - so if we choose no as 2*3*5*7 = 210.. this is divisble be 4 prime nos but not a square of an int.. however, we can have a no 210^2 - divisible by 2,3, 5, 7 but also square.. NOT SUFF
Together - NOT SUFF
So E