Is xy a multiple of 48?

STATEMENT 1--x is a multiple of 4.
we don't know the value of y
if y = 2 then --NO
if y = 24 then-- YES
so INSUFFICIENT

STATEMENT 2--y is a multiple of 6.
we don't know the value of x
if x = 2 then --NO
if x = 16 then ---YES
so INSUFFICIENT

combining (1)&(2)
x is a multiple of 4 and y is a multiple of 6

then xy = 12,24,....,48
if xy =12 then NO
if xy = 48 then YES
so INSUFFICIENT

E

XY should be of the form 2^4.3.p where p is a natural number.

Statement 1: X is multiple of 4 => x = 2^2.q where q is a natural number; we are not sure about Y.........Not Sufficient

Statement 2: Y is multiple of 6 => y = 2.3.r where r is a natural number; we are not sure about the value of X ......Not Sufficient.

Taking both the statements together:
XY = 2^2.q.2.3.r => 2^3.3.q.r = 24.q.r => XY is a multiple of 24 but we can not say it's a multiple of 48 because q and r are variables here.

Hence both statements are not sufficient. The answer should be E

st1 > x is multiple of 4, so that would be: 4,8,12, 16, 20. we don't know anything about y. Not suff.

St2> y is multiple of 6, so that would be: 6,12,18,24. we don't know anything about x. Not suff.

1 + 2:

if x=4 and y= 12 (it's just one example you can pick any combo) then yes, xy = 48, multiple of 48. BUT x & y can be any multiple of 4 and 6 respectively.

what if x= 4 and y=6, then xy=24 << this is not a multiple of 48. hence, Not suff.

E.

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