7Number 7ExplanationThe sum of three consecutive odd numbers is 100510051005. Which of the following relationships is correct between quantities PPP and QQQ based on the information provided? PPPQQQThe largest number401401401P<QP < QP<QP>QP > QP>QP=QP = QP=QP=2QP = 2QP=2QThe information provided is not sufficient to decide on one of the four options aboveExplanationLet the smallest odd number be aaa. Since consecutive odd numbers have a difference of 222, the three numbers are a,a+2,a+4a, a + 2, a + 4a,a+2,a+4. The sum of these three numbers is given as 100510051005. a+(a+2)+(a+4)=1005a + (a + 2) + (a + 4) = 1005a+(a+2)+(a+4)=10053a+6=10053a + 6 = 10053a+6=10053a=1005−63a = 1005 - 63a=1005−63a=9993a = 9993a=999a=333a = 333a=333 The largest number is a+4a + 4a+4. The largest number=333+4=337\text{The largest number} = 333 + 4 = 337The largest number=333+4=337 Thus, the value of P=337P = 337P=337. Given the value of Q=401Q = 401Q=401. Therefore, the relationship between PPP and QQQ is: 337<401⇒P<Q337 < 401 \Rightarrow P < Q337<401⇒P<Q
