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Between-100-and-600-how-many-number-are-such-which-are-totally-divisible-by-11-or-17-




Question Number 58069 by Kunal12588 last updated on 17/Apr/19
Between 100 and 600, how many number  are such which are totally divisible by 11 or 17.
$${Between}\:\mathrm{100}\:{and}\:\mathrm{600},\:{how}\:{many}\:{number} \\ $$$${are}\:{such}\:{which}\:{are}\:{totally}\:{divisible}\:{by}\:\mathrm{11}\:{or}\:\mathrm{17}. \\ $$
Commented by Kunal12588 last updated on 17/Apr/19
Commented by Kunal12588 last updated on 17/Apr/19
Commented by Kunal12588 last updated on 17/Apr/19
Is this correct?
$${Is}\:{this}\:{correct}? \\ $$
Commented by tanmay last updated on 17/Apr/19
yes correct...
$${yes}\:{correct}… \\ $$
Answered by tanmay last updated on 17/Apr/19
N(11)=110,121,...594  110+(x−1)×11=594  x−1=((484)/(11))→x=44+1=45 total 45 nubers←look here    N(17)=102,119...595  102+(y−1)17=595  y=((595−102)/(17))+1  y=((493)/(17))+1=30    now 17×11=187  N(187)=187,374,561  z=3    Aor B=A+B−A∩B  =45+30−3  =72
$${N}\left(\mathrm{11}\right)=\mathrm{110},\mathrm{121},…\mathrm{594} \\ $$$$\mathrm{110}+\left({x}−\mathrm{1}\right)×\mathrm{11}=\mathrm{594} \\ $$$${x}−\mathrm{1}=\frac{\mathrm{484}}{\mathrm{11}}\rightarrow{x}=\mathrm{44}+\mathrm{1}=\mathrm{45}\:{total}\:\mathrm{45}\:{nubers}\leftarrow{look}\:{here} \\ $$$$ \\ $$$${N}\left(\mathrm{17}\right)=\mathrm{102},\mathrm{119}…\mathrm{595} \\ $$$$\mathrm{102}+\left({y}−\mathrm{1}\right)\mathrm{17}=\mathrm{595} \\ $$$${y}=\frac{\mathrm{595}−\mathrm{102}}{\mathrm{17}}+\mathrm{1} \\ $$$${y}=\frac{\mathrm{493}}{\mathrm{17}}+\mathrm{1}=\mathrm{30} \\ $$$$ \\ $$$${now}\:\mathrm{17}×\mathrm{11}=\mathrm{187} \\ $$$${N}\left(\mathrm{187}\right)=\mathrm{187},\mathrm{374},\mathrm{561} \\ $$$${z}=\mathrm{3}\:\: \\ $$$${Aor}\:{B}={A}+{B}−{A}\cap{B} \\ $$$$=\mathrm{45}+\mathrm{30}−\mathrm{3} \\ $$$$=\mathrm{72} \\ $$$$ \\ $$
Commented by Kunal12588 last updated on 17/Apr/19
thank you sir. I answered(image) the question  but there was no reply  and there was another  answer where someone took ′or′ as ′and′. So   I thought my answer(image) is wrong.
$${thank}\:{you}\:{sir}.\:{I}\:{answered}\left({image}\right)\:{the}\:{question} \\ $$$${but}\:{there}\:{was}\:{no}\:{reply}\:\:{and}\:{there}\:{was}\:{another} \\ $$$${answer}\:{where}\:{someone}\:{took}\:'{or}'\:{as}\:'{and}'.\:{So}\: \\ $$$${I}\:{thought}\:{my}\:{answer}\left({image}\right)\:{is}\:{wrong}. \\ $$
Commented by MJS last updated on 18/Apr/19
“or” is not the same as “xor”  divisible by 11 or divisible by 17 includes  divisible by 11 and 17  divisible by 11 xor divisible by 17 excludes  divisible by 11 and 17  so in math language it′s different from spoken  language. we′re on a math forum, so we  should use math language  187 is ((divisible by 11) or (divisible by 17))  187 is not ((divisible by 11) xor (divisible by 17))  btw would you like coffee or tea?
$$“\mathrm{or}''\:\mathrm{is}\:\mathrm{not}\:\mathrm{the}\:\mathrm{same}\:\mathrm{as}\:“\mathrm{xor}'' \\ $$$$\mathrm{divisible}\:\mathrm{by}\:\mathrm{11}\:\mathrm{or}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{17}\:\mathrm{includes} \\ $$$$\mathrm{divisible}\:\mathrm{by}\:\mathrm{11}\:\mathrm{and}\:\mathrm{17} \\ $$$$\mathrm{divisible}\:\mathrm{by}\:\mathrm{11}\:\mathrm{xor}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{17}\:\mathrm{excludes} \\ $$$$\mathrm{divisible}\:\mathrm{by}\:\mathrm{11}\:\mathrm{and}\:\mathrm{17} \\ $$$$\mathrm{so}\:\mathrm{in}\:\mathrm{math}\:\mathrm{language}\:\mathrm{it}'\mathrm{s}\:\mathrm{different}\:\mathrm{from}\:\mathrm{spoken} \\ $$$$\mathrm{language}.\:\mathrm{we}'\mathrm{re}\:\mathrm{on}\:\mathrm{a}\:\mathrm{math}\:\mathrm{forum},\:\mathrm{so}\:\mathrm{we} \\ $$$$\mathrm{should}\:\mathrm{use}\:\mathrm{math}\:\mathrm{language} \\ $$$$\mathrm{187}\:\mathrm{is}\:\left(\left(\mathrm{divisible}\:\mathrm{by}\:\mathrm{11}\right)\:\mathrm{or}\:\left(\mathrm{divisible}\:\mathrm{by}\:\mathrm{17}\right)\right) \\ $$$$\mathrm{187}\:\mathrm{is}\:\mathrm{not}\:\left(\left(\mathrm{divisible}\:\mathrm{by}\:\mathrm{11}\right)\:\mathrm{xor}\:\left(\mathrm{divisible}\:\mathrm{by}\:\mathrm{17}\right)\right) \\ $$$$\mathrm{btw}\:\mathrm{would}\:\mathrm{you}\:\mathrm{like}\:\mathrm{coffee}\:\mathrm{or}\:\mathrm{tea}? \\ $$
Commented by Kunal12588 last updated on 18/Apr/19
yes sir xor is ′Exclusive or′ which excludes  ′and′. would you like coffee or tea − is a eg.  of exclusive or. Am I right sirMJS  btw I like cofee.
$${yes}\:{sir}\:\mathrm{xor}\:{is}\:'{Exclusive}\:{or}'\:{which}\:{excludes} \\ $$$$'{and}'.\:{would}\:{you}\:{like}\:{coffee}\:{or}\:{tea}\:−\:{is}\:{a}\:{eg}. \\ $$$${of}\:{exclusive}\:{or}.\:{Am}\:{I}\:{right}\:{sirMJS} \\ $$$${btw}\:{I}\:{like}\:{cofee}. \\ $$
Commented by MJS last updated on 18/Apr/19
you′re right.
$$\mathrm{you}'\mathrm{re}\:\mathrm{right}. \\ $$

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