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

Question

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 (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

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

Q. 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

1

2

3

4

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

Q. 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

1

2

3

4

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

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