If (m + n) = 24, and the product of m and n is equal to 15, then find the value of the sum of the squares of the two variables 'm' and 'n'. Also find the value of (m-n)2.

Thanks for asking question on GMAT Section, Your question was - If (m + n) = 24, and the product of m and n is equal to 15, then find the value of the sum of the squares of the twovariables ‘m‘ and ‘n’.Alsofind the value of (m-n)2. Your correct answer is- C Now read this explanation for more clarifications: According to the data given in the question, (m + n) = 24.....(i) m*n = 15......(ii) We have to find the sum of the squares of the two variables 'm' and 'n' i.e. m2 + n2 According to the standard mathematical formula, (m + n)2 = m2 + 2mn + n2......(iii) ∴ (m + n)2 – 2mn = m2 + n2........(iv) Substituting the value of m + n from equation (i) and (ii), in equation (iv), we get (24)2 – 2(15) = m2 + n2 ∴ 576 – 30 = m2 + n2 ∴ m2 + n2 = 546 We also have to find the value of (m - n)2 Now, according to the standard mathematical formula, (m - n)2 = m2 - 2mn + n2 ∴ (m - n)2 = 546 – 2(15) ∴ (m - n)2 = 546 – 30 = 516 Hence, the correct answer is option c.