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Standard VII

Mathematics

Proper Subset

Suppose that ...

Question

Suppose that the number of elements in the set $S$ is $105$ and that $S$ is split into $n$ subsets $11 m + 2$ elements each. If $m$ is an integer, then $m$ is ____ . (No two subsets have common elements)

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Solution

Number of elements in each set $= 11 m + 2$
Number of elements in $n$ subsets $= n (11 m + 2)$
$n (11 m + 2) = 105 = 21 \times 5 = 3 \times 7 \times 5$
$n = 3 \Rightarrow 11 m + 2 = 35$
$\Rightarrow$ $11 m + 2 = 35$
$\Rightarrow$ $11 m = 33$
$\Rightarrow$ $m = 3$

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Suppose that the number of elements in the set S is 105 and that S is split into n subsets 11m+2 elements each. If m is an integer, then m is ____ . (No two subsets have common elements)

Number of elements in each set =11m+2Number of elements in n subsets =n(11m+2)n(11m+2)=105=21×5=3×7×5n=3⇒11m+2=35⇒ 11m+2=35⇒ 11m=33⇒ m=3

Suppose that the number of elements in the set $S$ is $105$ and that $S$ is split into $n$ subsets $11 m + 2$ elements each. If $m$ is an integer, then $m$ is ____ . (No two subsets have common elements)

Number of elements in each set $= 11 m + 2$
Number of elements in $n$ subsets $= n (11 m + 2)$
$n (11 m + 2) = 105 = 21 \times 5 = 3 \times 7 \times 5$
$n = 3 \Rightarrow 11 m + 2 = 35$
$\Rightarrow$ $11 m + 2 = 35$
$\Rightarrow$ $11 m = 33$
$\Rightarrow$ $m = 3$