NTSE MATHS#4

Algebra Level 2

x and y are 2 non negative numbers such that 2x + y= 10 . The sum of maximum and minimum values of ( x+ y ) is

6 15 9 10

Manish Dash by Manish Dash , 22, India

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3 solutions

Raushan Sharma
Sep 24, 2015

We have this obvious inequality

2 ( x + y ) ≥ 2 x + y ≥ ( x + y ) 2(x+y) \geq 2x+y \geq (x+y)

⇒ 2 ( x + y ) ≥ 10 ≥ ( x + y ) \Rightarrow 2(x+y) \geq 10 \geq (x+y)

So, the maximum value of ( x + y ) (x+y) is 10 and the minimum value is 5. So, sum of maxima and minima = 10+5 = 15

12 Helpful 3 Interesting 4 Brilliant 4 Confused
Karen Black
May 15, 2015

2x+y=10 is a line, and the constraint of x & y being non-negative puts it in quadrant 1. The largest value of y is 10 at x=0, and the largest value of x is 5 at y=0; those are the maximum and minimum values of x+y.

3 Helpful 0 Interesting 1 Brilliant 2 Confused

The maximum value of y given 2x is even is 8 2(1) +8=10 1+8=9 9 is the maximum value for (x+y) The smallest value for y given 2x is even is 2 2(4)+2=10 4+2=6 6 is the smallest value for (a+b) 9+6=15

1 Helpful 0 Interesting 0 Brilliant 1 Confused

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