Question Bank  Number Theory  Shashank Prabhu, CAT 100 Percentiler


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@shashank_prabhu 26*51=1326

@shashank_prabhu 157

@shashank_prabhu Which of the following divides 144^2 + 169^2 + 144*169?
Not getting answer

@shashank_prabhu
let 2 numbers are 'ab' and 'cd', such that ab>cd.
abcd(abcd)=5481
100 * ab+cdab+cd=5481
99 * ab+2 * cd=548199*ab and 5481 are multiples of 9, hence cd must be a multiple of 9.
At cd=18, we get ab=55
Sum of the two 2digit numbers= 55+18=73

@shashank_prabhu Getting 6 (0,0/0,9/2,7/4,5/6,3/8,1)

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@shashank_prabhu 4 cases.. 9996,9978,9798,7998

@shashank_prabhu Higest number is 432.. Remainder left would be 72

Is the answer 463 with base of the system as 7?

I am getting 504.
Let us first consider the numbers that will divide pow(28,12).Note that 28 can be written as pow(2,2)xpow(7) so we can effectively write pow(28,12) as pow(2,24)xpow(7,12) which gives us the total number of factors as 25*13=325
Similarly for other numbers, we will have 153 and 49 respectively.
Now these factors will have some overlap, we use the inclusionexclusion principle.
Factors that will be common in pairs of =7+7+9. Factors common in pairs of 3=0;
So we need to subtract 7+7+9 from the original answer.
Finally 325+153+49779=504

@shashank_prabhu D21 is the correct answer

@shashank_prabhu Using GM>=HM inequality we get 4 as the answer
sqrt(ab)>=2ab/(a+b). Given ab>(a+b) therefore sqrt(ab)>2 i.e ab>4

@shashank_prabhu 73 is the correct answer x1+x2+x3=12 where we use the binomial theorem to find coeff of X^12 in (1+x+x^2+....x^9)^3

@shashank_prabhu 608. 2^1023 608mod1000