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IMO A

we need to find b - a >= 2* 3^n - 2*2^n

from I - we get, b - a = 3*3^n - 2*2^n which is more than 2* 3^n - 2*2^n given that n > 0 and an int.

from II - no info abt a or b. Hence insuff.

whats the OA and OE?

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IMO C here's why.... "rivaliing .... achievement" is modifying "the army of..." part of sentence to really focus starts from "the army of..." here, ||ilsm comes into picture.. the army of... created .... and took ..... {eliminate option D and E} for the remaining answer...

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here's my take ... sum of 11, 13, ...,19 = no of terms * avg no of terms = 5 avg = 15 sum = 75 note that sum of 31, 33.... each term is 20 more than prev series so add 20 * 5 to prev addition = 75 + 100 next series each term is 40 more... add 200 to 75 next series 60 more, add 300 to 75 next series ...

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(1) A2 - 5A - 6 = 0

i understand it's a quadratic and you mean A^2
but

2A+4, root(2A+9)

does this mean 2^A?

pls use ^ symbol to represent powers. thanks

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For 8 x 8 chess board, you can select two columns in 2* 8c2 ways (since order doesnt matter). in these 2 columns, you can have 8 * 7 squares selection so IMO the answer should be 2 * 8c2 * 8 * 7 = 112 * (8! / (6!*2!)) = 112 * 28 = 3136 ways can you please post the answer here? hope this helps.. Than...

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you have almost solved the problem I solved the eqn like a regular quadratic equation until I reach (x+3)(x+4)>0 At which point I figure that either both terms are +ve or both are -ve as you know +ve * +ve = +ve or -ve * -ve = +ve so both (x+3) and (x+4) should have same sign (either +ve or -ve) cas...

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Interesting question. a,b,c,d are int. m = avg s = std dev Is s > 0? std dev = sq rt [ (sum of (mean - term)^2) / no of terms ] which means std dev is always positive and std dev can be 0 if and only if all terms in the set are zero. std dev is greater than 0 even if avg of the set is 0. so essentia...