let Q be any no less than 120 such that it leaves a remainder 2 when divided by either 7 or 5 for eg 23,27 qualify as Q sum of such Q as
Answers
Given : Q be any no less than 120 such that it leaves a remainder 2 when divided by either 7 or 5
To Find : sum of such Q
Solution:
Q < 120
leaves a remainder 2 when divided by 7
=> Q = 7k + 2
7k + 2 < 120 => 0 ≤ k ≤ 16 Hence 17 term
2 , 9 , . . 114
Sum = (17/2)(2 + 114) = 986
Q < 120
leaves a remainder 2 when divided by 5
=> Q = 5m + 2
0 ≤ m ≤ 23 Hence 24 term
2 , 7 , . . . , 117
Sum = (24/2)(2 + 117) = 1428
7 * 5 = 35
=> 35n + 2 are common in both
0 ≤ n ≤ 3 Hence 4 term
2 , 37 , 72 , 107
Sum = (4/2)(2 + 107) =218
sum of such Q = 986 + 1428 - 218
= 2,196
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