The sum of 5 consecutive odd numbers of Set-A is 185. What will be the sum of Set-B, containing 4 consecutive odd numbers, if the smallest odd number of Set-B is 14 more than the highest odd number of Set-A ?
Answers
In set A, there are 5 consecutive odd integers as elements.
Let A = {x-4, x-2, x, x+2, x+4}
In set B, there are 4 consecutive odd integers as elements. We've to find the sum of these elements 'if the smallest integer in set B is 14 more than the highest one in set A'.
As it is, we can take the smallest odd integer in set B as x+18 because the highest integer in set A is x+4 and x+4 + 14 = x+18.
Thus B will be {x+18, x+20, x+22, x+24}.
The sum of these elements will be,
x+18 + x+20 + x+22 + x+24
⇒ 4x + 84
⇒ 4(x + 21)
So the value of 4(x + 21) is the answer.
Given that the sum of the integers in set A is 185.
⇒ x-4 + x-2 + x + x+2 + x+4 = 185
⇒ 5x = 185
⇒ x = 185 / 5
⇒ x = 37
⇒ x + 21 = 37 + 21
⇒ x + 21 = 58
⇒ 4(x + 21) = 4 × 58
⇒ 4(x + 21) = 232
Hence the answer is 232.
Answer:
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