Its not given that K is positive integer. It just asks that if K has 3 distinct positive prime factors. We cannot assume K to be positive.

OG Diag Test Q doubt OA (0 also an integer)

I tried searching in the forum with little success. If its already discussed can you plz point me to that thread. Does the integer k have at least three different positive prime factors ? (1) k/15 is an integer (2) k/10 is an integer OA : C I understand why the answer is so. But it ignores the case ...

Sum of GP= a * (r^n - 1) / (r - 1)

here the ratio of sum of 6 terms by sum of 3 terms

=> (r^6 - 1) / (r^3 -1 ) = 9
=> r^6 - 9r^3 + 8 = 0
=> (r^3 - 1)(r^3 - 8) = 0

So IMO Ans = 2 i.e. C

another possible approach...

its a GP series excluding the first 2.

Sn = a(r^n - 1)/r-1

here a = 2
r = 2
n = 8

ans = 2 +2(2^8 - 1) = 2^9

I x?y = xy so commutator = xy - yx so always 0 II x?y = (x-y)^2 so commutator = (x-y)^2 - (y-x)^2 taking -1 in one and squaring again makes it 1 so always 0 III x?y = (x+y)^3 so commutator = (x+y)^3 - (y-x)^3 its cube so -1 common wont help so not always 0 so IMO ans = C OA Plz. can u pl. explain h...

I x?y = xy

so commutator = xy - yx so always 0

II x?y = (x-y)^2

so commutator = (x-y)^2 - (y-x)^2 taking -1 in one and squaring again makes it 1 so always 0

III x?y = (x+y)^3

so commutator = (x+y)^3 - (y-x)^3 its cube so -1 common wont help so not always 0

so IMO ans = C

OA Plz.

Q 1: The equation can be reduced to 12/100 .. i.e 3/25 .. Now since denominator is higher numerator itself will be the remainder. The numerator has to be multiple of 3 so ans = 45 E Q2: If there is a shortcut would love to know... One guess : Answer choices may help in this particular case. But for ...

Don't know a quick way to find.. It took me almost 10 min to reach to the solution... The two points are (6,2) and (0,6) The length of diagonal = sqrt(52) Length of the side = sqrt(26) Now the two points we know and the length we know so using the formula sqrt( sqr(x1-x2) + sqr(y1-y2)) we can get tw...