Average height of six students is 172 cm. Four new students, whose heights are (k + 2), (k - 2), (k + 5) and 2k cm more than the original average, join the group. If the average of the group is now 174 cm, find the value of k.

The total required increase in the overall sum of heights to raise the average of 10 students from 172 to 174 is 10 multiplied by 2, which equals 20. The sum of the added heights over the original average is (k + 2) plus (k - 2) plus (k + 5) plus 2k, which simplifies to 5k + 5. Setting this equal to the required increase gives the equation 5k + 5 = 20, meaning 5k = 15 and k = 3.

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