Category: Arithmetic

Question Number 185386 by Rupesh123 last updated on 20/Jan/23 Commented by floor(10²Eta[1]) last updated on 21/Jan/23 $${\mathrm{a}}^2+2\mathrm{ab}+{\mathrm{b}}^2+1990\mathrm{a}+1990\mathrm{b}+36=$$$$={\mathrm{a}}^2+1990\mathrm{a}+36+{\mathrm{b}}^2+1990\mathrm{b}+36$$$$\Rightarrow\mathrm{2ab}=\mathrm{36}\Rightarrow\mathrm{ab}=\mathrm{18}…

Question Number 185270 by Mingma last updated on 19/Jan/23 Answered by mr W last updated on 20/Jan/23 $$2a+1⩽d⩽9\Rightarrow a⩽4\cap a\ne 0$$$$2d=10+a$$$$a=4:d=7\Rightarrow 2\times 4+1=9>7\Rightarrow rejected$$$${a}=\mathrm{2}:\:{d}=\mathrm{6}\:\Rightarrow\mathrm{2}×\mathrm{2}+\mathrm{1}=\mathrm{5}\:<\mathrm{6}\:\Rightarrow{ok} \…

Question Number 185167 by Rupesh123 last updated on 18/Jan/23 Answered by aba last updated on 18/Jan/23 $$\mathrm{P}=(1+2+\dots +9)\mathrm{N}=45\mathrm{N}$$$$\mathrm{if}\mathrm{N}\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{integer},\mathrm{then}\mathrm{P}=45\mathrm{N}\mathrm{will}\mathrm{end}\mathrm{in}0$$$$\mathrm{this}\mathrm{is}\mathrm{not}\mathrm{possible}\mathrm{as}\mathrm{all}\mathrm{the}\mathrm{digits}\mathrm{are}\mathrm{same}$$$$\mathrm{if}\mathrm{N}\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{integer},\mathrm{then}\mathrm{P}=45\mathrm{N}\mathrm{will}\mathrm{end}\mathrm{in}5$$$$\mathrm{P}=\mathrm{45N}=\mathrm{555}…\mathrm{55}…

Question Number 185030 by Engr_Jidda last updated on 15/Jan/23 Commented by Engr_Jidda last updated on 15/Jan/23 $$helpmesolvethesequantitativereasonings$$ Answered by manolex last updated on…

Question Number 119440 by mathocean1 last updated on 24/Oct/20 $$\mathrm{Determine}\mathrm{the}\mathrm{integer}\mathrm{which}\mathrm{can}$$$$\mathrm{be}\mathrm{written}:\mathrm{N}=\overline{\mathrm{xyz}}{}^7=\overline{\mathrm{zyx}}{}^{11}$$ Commented by mathocean1 last updated on 24/Oct/20 $$\mathrm{Please}\:\mathrm{can}\:\mathrm{you}\:\mathrm{detail}\:\mathrm{sir}…