Latest Elitmus Aptitude Question SOLUTION: Z=260*1024+73*512+128*129+81+9 (z in decimal system). now y be the octal representation of z in number system.How many time will the digit 3 be in y options = >2/3/4/5

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(#M40033088) ELITMUS Numerical Ability question Number of 3s Keep an EYE

Z=260*1024+73*512+128*129+81+9 (z in decimal system).
now y be the octal representation of z in number system.How many time will the digit 3 be in y
options = >2/3/4/5

Asked In Elitmus (10 years ago)

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RAKESH  (10 years ago)

Z=260*1024+73*512+128*129+81+9

convert into power of 8
260*1024 = 2*260*8^3= 65*8^4 = 8^4(8^2+1)= 8^6+8^4

73*512 = 8^3*(72+1) = 8^3[8*(8+1)+1] = 8^3(8^2+8^1+1)= 8^5+8^4+8^3

128*129 = 8^2*258 = 8^2(8*32+2)= 8^2(4*8^2+2)= 4*8^4+2*8^2

81= 8^2+16+1 = 8^2+2*8^1+8^0

9= 8^1+8^0

now Z can be written as

z = 8^6 + 8^5 + 6*(8^4) + 8^3 + 3*(8^2) + 3*(8^1) + 2*(8^0)

z= octal(1161332)8

in octal representation of Z = 1161332, no, of 3's are 2

ans: 2

Is this solution Helpfull? Yes (35) | No   

Vivek Jain  (10 years ago)

z can be written in powers of 8(as octalconversion is reqd.)
=> 8^6+8^5+6*8^4+8^3+3*8^2+3*8^1+2*8^0
so no of 3s are 2
Ans: 2

Is this solution Helpfull? Yes (5) | No (5)  

arijit roy  (10 years ago)

260*1024 = 2*260*8^3= 65*8^4 = 8^4(8^2+1)= 8^6+8^4

73*512 = 8^3*(72+1) = 8^3[8*(8+1)+1] = 8^3(8^2+8^1+1)= 8^5+8^4+8^3

128*129 = 8^2*258 = 8^2(8*32+2)= 8^2(4*8^2+2)= 4*8^4+2*8^2

81= 8^2+16+1 = 8^2+2*8^1+8^0

9= 8^1+8^0

now Z can be written as

z = 8^6 + 8^5 + 6*(8^4) + 8^3 + 3*(8^2) + 3*(8^1) + 2*(8^0)

z= octal(1161332)8

in octal representation of Z = 1161332, no, of 3's are 2

ans will be 2

Is this solution Helpfull? Yes (4) | No   

AB  (10 years ago)

260*1024 = 2*260*8^3= 65*8^4 = 8^4(8^2+1)= 8^6+8^4

73*512 = 8^3*(72+1) = 8^3[8*(8+1)+1] = 8^3(8^2+8^1+1)= 8^5+8^4+8^3

128*129 = 8^2*258 = 8^2(8*32+2)= 8^2(4*8^2+2)= 4*8^4+2*8^2

81= 8^2+16+1 = 8^2+2*8^1+8^0

9= 8^1+8^0

now Z can be written as

z = 8^6 + 8^5 + 6*(8^4) + 8^3 + 3*(8^2) + 3*(8^1) + 2*(8^0)

z= octal(1161332)8

in octal representation of Z = 1161332, no, of 3's are 2

Is this solution Helpfull? Yes (1) | No   

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