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.