21 set 18

[radhika1306]

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.

[kajcha]

IMO E

[radhika1306]

can u explain

[ratindasgupta]

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.

1) K could be 8 or 16. INSUFF

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.

[kajcha]

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