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The adjoining figure contains three squares with areas of 100, 16 and 49 lying side by side as shown. By how much should the area of the middle square be reduced in order that the total length PQ of the resulting three squares is 19 ?<br><img src="/images/question-image/arithmetic-ability/area/1574318436-53.png" title="Area mcq question image" alt="Area mcq question image">

Correct Answer: 12
PQ = $$\sqrt {100} $$  + $$\sqrt {16} $$ + $$\sqrt {49} $$  = (10 + 4 + 7) = 21
Side of middle square = $$\sqrt {16} $$  = 4
Reduction in PQ = (21 - 19) = 2
New side of middle square = (4 - 2) = 2
∴ Reduction in area of middle square = (42 - 22) = 12

A university library budget committee must reduce exactly five of eight areas of expenditure—I, J, K, L, M, N, O and P—in accordance with the following conditions: If both I and O are reduced, P is also reduced.
If L is reduced, neither N nor O is reduced.
If M is reduced, J is not reduced.
Of the three areas J, K, and N exactly two are reduced. Question : If both K and N are reduced, which one of the following is a pair of areas neither of which could be reduced?

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