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by ketkoag » Wed Mar 25, 2009 3:22 am
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.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Please let me know a number that is divisible by exactly 4 different prime numbers and that is a perfect square….. or if there is a number which is divisible exactly by 4 prime numbers but not a square of a integer.

OA e??
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by scoobydooby » Wed Mar 25, 2009 3:34 am
stmnt 1) k divisible by 4
if k=8, not square of an integer
if k=16, square pf an integer
not sufficient

stmnt 2) k is divisible by exactly 4 different prime numbers
let k=2*3*5*7=210=> not square of an integer

if k=2^2*3^2*5^2*7^2 =210^2 (divisble by 4 diff primes also square of an integer. (a perfect square has its prime factors raised to even powers)
not sufficient

together
if k=2^2*3*5*7=420, div by 4, not square of an integer
if k=2^2*3^2*5^2*7^2 =210^2 , div by 4, square of an integer

not sufficient and hence E
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