Question

In the following expression, both A and B are variables that can take positive values.

2\sqrt(A)-(B)/(5)

Which of these actions will cause the expression's value to increase?

Choose 2 answers:

(Choice A)
Keeping A constant and increasing B

(Choice B)
B
Keeping A constant and decreasing B

(Choice C)
C
Increasing A and keeping B constant

(Choice D)
D
Decreasing A and keeping B constant

Answer 1

the acutal solution is B and D

Answer 2

(Choice B) Keeping A constant and decreasing B

(Choice C) Increasing A and keeping B constant

Explanation:

Let us analyze these two options.

2√a - b /5

(Choice B) Keeping A constant and decreasing B

Let a = 100 and b= 30

2√100 - 30/5

= 2(10) - 6

= 20 -6= 14

But if A is kept constant and B is decreased to 20

2√100 - 20/5

= 2(10) - 4

= 20 -4= 16

We see the expression value has increased from 14 to 16.

Similarly analyzing Option C

(Choice C) Increasing A and keeping B constant

Let a = 100 and b= 30

2√100 - 30/5

= 2(10) - 6

= 20 -6= 14

Now increasing A to 121 and keeping B constant would give

Let a = 100 and b= 30

2√121 - 30/5

= 2(11) - 6

= 22 -6= 16

This also increases the expression's value

But the other two choice A and D do not give the same result.

Let a = 100 and b= 30

2√100 - 30/5

= 2(10) - 6

= 20 -6= 14

(Choice A)

Keeping A constant and increasing B

2√100 - 40/5

= 2(10) - 8

= 20 -8= 12

This decreases the value .

Also

(Choice D)

Decreasing A and keeping B constant

2√81 - 40/5

= 2(9) - 8

= 18 -8= 10

This also decreases value

The correct choices are B and C