The concentration of a certain chemical in a full water...

[AAPL]

The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is $$3+\frac{4}{\sqrt{5-x}}$$
parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

The OA is E.

Experts, to solve this PS question, I just need to isolate the x and get it value, right?

I appreciate if any expert explains it to me. Thank you so much.

[regor60]

The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is $$3+\frac{4}{\sqrt{5-x}}$$
parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

The OA is E.

Experts, to solve this PS question, I just need to isolate the x and get it value, right?

I appreciate if any expert explains it to me. Thank you so much.

yes, just solve for X

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Hi AAPL,

While the given question might 'look scary', it's essentially asking us to find the value of X that will make the given calculation equal 6. With a little logic and TESTing THE ANSWERS, we can get the solution.

Since we're dealing with 3 + (some fraction) = 6, we need the fraction to equal 3....

4/(something) = 3

Thus we need the denominator of the fraction to equal about 1.333. There's a great shortcut here if you know your 'perfect squares':

13^2 = 169 so...
(1.3)^2 = 1.69
14^2 = 196 so...
(1.4)^2 = 1.96

IF we plug X=3 into the equation, then we end up with a denominator that's a little bigger than 1.4
IF we plug X=3.2 into the equation, then we end up with a denominator that's closer to 1.333

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is $$3+\frac{4}{\sqrt{5-x}}$$
parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

6 = 3 + 4/√(5 - x)

3 = 4/√(5 - x)

Squaring both sides, we have:

9 = 16/(5 - x)

45 - 9x = 16

29 = 9x

3.2 ≈ x

Answer: E