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