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Find-the-missing-number-determinant-72-24-6-96-16-12-108-18-A-12-B-16-C-18-D-20-Please-help-




Question Number 206709 by Nimnim111118 last updated on 23/Apr/24
 Find the missing number             determinant ((( 72),(24),(  6)),(( 96),(16),(12)),((108),( ?),(18)))  A.12      B.16    C.18      D.20  Please help...
$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{missing}\:\mathrm{number} \\ $$$$\:\:\:\:\:\:\:\:\:\:\begin{array}{|c|c|c|}{\:\mathrm{72}}&\hline{\mathrm{24}}&\hline{\:\:\mathrm{6}}\\{\:\mathrm{96}}&\hline{\mathrm{16}}&\hline{\mathrm{12}}\\{\mathrm{108}}&\hline{\:?}&\hline{\mathrm{18}}\\\hline\end{array} \\ $$$$\mathrm{A}.\mathrm{12}\:\:\:\:\:\:\mathrm{B}.\mathrm{16}\:\:\:\:\mathrm{C}.\mathrm{18}\:\:\:\:\:\:\mathrm{D}.\mathrm{20} \\ $$$$\mathrm{Please}\:\mathrm{help}… \\ $$
Commented by Frix last updated on 24/Apr/24
E.42  The answer is always 42.
$$\mathrm{E}.\mathrm{42} \\ $$$$\mathrm{The}\:\mathrm{answer}\:\mathrm{is}\:{always}\:\mathrm{42}. \\ $$
Commented by Ghisom last updated on 24/Apr/24
how? ��
Commented by A5T last updated on 24/Apr/24
I guess he′s just joking and trying to point  out these sort of questions are not actually  “objective”.
$${I}\:{guess}\:{he}'{s}\:{just}\:{joking}\:{and}\:{trying}\:{to}\:{point} \\ $$$${out}\:{these}\:{sort}\:{of}\:{questions}\:{are}\:{not}\:{actually} \\ $$$$“{objective}''. \\ $$
Commented by jihamine2301 last updated on 03/May/24
12 cause first line ((72)/6)=12×2=24  ((96)/(12))=8×2=16  ((108)/(18))=6×2=12
$$\mathrm{12}\:{cause}\:{first}\:{line}\:\frac{\mathrm{72}}{\mathrm{6}}=\mathrm{12}×\mathrm{2}=\mathrm{24} \\ $$$$\frac{\mathrm{96}}{\mathrm{12}}=\mathrm{8}×\mathrm{2}=\mathrm{16} \\ $$$$\frac{\mathrm{108}}{\mathrm{18}}=\mathrm{6}×\mathrm{2}=\mathrm{12} \\ $$
Answered by BaliramKumar last updated on 23/Apr/24
72 = ((24)/2)×6  96 = ((16)/2)×12  108 = (x/2)×18       ⇒   108 = 9x   ⇒ x = 12
$$\mathrm{72}\:=\:\frac{\mathrm{24}}{\mathrm{2}}×\mathrm{6} \\ $$$$\mathrm{96}\:=\:\frac{\mathrm{16}}{\mathrm{2}}×\mathrm{12} \\ $$$$\mathrm{108}\:=\:\frac{{x}}{\mathrm{2}}×\mathrm{18}\:\:\:\:\:\:\:\Rightarrow\:\:\:\mathrm{108}\:=\:\mathrm{9}{x}\:\:\:\Rightarrow\:{x}\:=\:\mathrm{12}\:\:\:\:\:\:\:\: \\ $$
Commented by Nimnim111118 last updated on 23/Apr/24
Thank you Sir
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{Sir} \\ $$
Answered by Ghisom last updated on 24/Apr/24
72+24+6=102  96+16+12=102+22  108+x+18=102+22+22 ⇒ x=20
$$\mathrm{72}+\mathrm{24}+\mathrm{6}=\mathrm{102} \\ $$$$\mathrm{96}+\mathrm{16}+\mathrm{12}=\mathrm{102}+\mathrm{22} \\ $$$$\mathrm{108}+{x}+\mathrm{18}=\mathrm{102}+\mathrm{22}+\mathrm{22}\:\Rightarrow\:{x}=\mathrm{20} \\ $$
Answered by Frix last updated on 24/Apr/24
l=number of line, λ:=9−((l(l+5))/6)  l=1⇒ λ=8; 72−24=6λ=48  l=2 ⇒ λ=((20)/3); 96−16=12λ=80  l=3 ⇒ λ=5; 108−x=18λ=90 ⇒ x=18 ★    ...wait, now where′s 42???       72+24=96+12=108+6=114       6+6=12+6=18+6=24  ⇒  Line 4:     ∣114∣  ?  ∣ 24 ∣  l=4 ⇒ λ=3; 114−y=24λ=72 ⇒ y=42  Ha! I knew it!
$${l}=\mathrm{number}\:\mathrm{of}\:\mathrm{line},\:\lambda:=\mathrm{9}−\frac{{l}\left({l}+\mathrm{5}\right)}{\mathrm{6}} \\ $$$${l}=\mathrm{1}\Rightarrow\:\lambda=\mathrm{8};\:\mathrm{72}−\mathrm{24}=\mathrm{6}\lambda=\mathrm{48} \\ $$$${l}=\mathrm{2}\:\Rightarrow\:\lambda=\frac{\mathrm{20}}{\mathrm{3}};\:\mathrm{96}−\mathrm{16}=\mathrm{12}\lambda=\mathrm{80} \\ $$$${l}=\mathrm{3}\:\Rightarrow\:\lambda=\mathrm{5};\:\mathrm{108}−{x}=\mathrm{18}\lambda=\mathrm{90}\:\Rightarrow\:{x}=\mathrm{18}\:\bigstar \\ $$$$ \\ $$$$…\mathrm{wait},\:\mathrm{now}\:\mathrm{where}'\mathrm{s}\:\mathrm{42}??? \\ $$$$\:\:\:\:\:\mathrm{72}+\mathrm{24}=\mathrm{96}+\mathrm{12}=\mathrm{108}+\mathrm{6}=\mathrm{114} \\ $$$$\:\:\:\:\:\mathrm{6}+\mathrm{6}=\mathrm{12}+\mathrm{6}=\mathrm{18}+\mathrm{6}=\mathrm{24} \\ $$$$\Rightarrow \\ $$$$\mathrm{Line}\:\mathrm{4}:\:\:\:\:\:\mid\mathrm{114}\mid\:\:?\:\:\mid\:\mathrm{24}\:\mid \\ $$$${l}=\mathrm{4}\:\Rightarrow\:\lambda=\mathrm{3};\:\mathrm{114}−{y}=\mathrm{24}\lambda=\mathrm{72}\:\Rightarrow\:{y}=\mathrm{42} \\ $$$$\mathrm{Ha}!\:\mathrm{I}\:\mathrm{knew}\:\mathrm{it}! \\ $$
Commented by Ghisom last updated on 24/Apr/24
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