# 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.

**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.**

a . 500, 550

b. 516, 546

c. 546, 516

d. 600, 500

e. None of the above

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**.