If (0.000125^(1/2) + 0.005)(0.25x^(1/2) - 0.5) = 0.01, what is the val

Question

If  (\sqrt{0.000125} + 0.005)(\sqrt{0.25x} - 0.5) = 0.01 , what is the value of x?

(A) 0.0125

(B) 0.125

(C) 0.25

(D) 1.25

(E) 5

chetan2u · Answer

One should realize from the terms that we may be looking at  (a+b)(a-b)=a^2-b^2

(\sqrt{0.000125} + 0.005)(\sqrt{0.25x} - 0.5) = 0.01

Multiply both sides by 100,

100*(\sqrt{0.000125} + 0.005)(\sqrt{0.25x} - 0.5) =100* 0.01=1

(\sqrt{100^2*0.000125} + 100*0.005)(\sqrt{0.25x} - 0.5) = 1

(\sqrt{1.25} + 0.5)(\sqrt{0.25x} - 0.5) = 1

Multiply both sides by  \sqrt{1.25}-0.5

(\sqrt{1.25}-0.5)(\sqrt{1.25} + 0.5)(\sqrt{0.25x} - 0.5) = 1*(\sqrt{1.25}-0.5)

(\sqrt{1.25}^2-0.5^2)(\sqrt{0.25x} - 0.5) = (\sqrt{1.25}-0.5)

(1.25-0.25)(\sqrt{0.25x} - 0.5) = (\sqrt{1.25}-0.5)

(1)(\sqrt{0.25x} - 0.5) = (\sqrt{1.25}-0.5)

(1)(\sqrt{0.25x} ) = (\sqrt{1.25})

Square both sides

0.25x=1.25

x=\frac{1.25}{0.25}=5

E

Foreheadson · Answer

First I tried to do ugly multiplications. after 5 minutes, I realized that whatever I was doing was not thr Gmat way. than I looked at thr answer choices. I tried x=1, to reduce the possible answer choices. 
first i simplified. 0.000125 is an ugly number, so I used approximation to 0.0001. bcs sqrt is easy, it's 0.01. 0.015*(0.5sqrt(x)-0.5)=0.01. if x=1 the answer is 0. it must be higher. leaves with D and E.
tried x=4. 0.015*(0.5*2-0.5)=0.015*0.5=0.0075. less than the actual answer of 0.01. so answer is clearly E.
this way I did the task in 2 mins. Hope it helps.

Posted from my mobile device

udaypratapsingh99 · Answer

That's a good way for this question. I solved it by equating the number of digits count - before & after the decimal - for LHS & RHS. This helped me solve it in 15 seconds (after wasting 3 minutes in complete calculation).
I acknowledge, your way is better as it is more general and error proof.

udaypratapsingh99 · Answer

Took me  15 seconds  to solve.

(\sqrt{0.000125}+0.005)(\sqrt{0.25x}−0.5)=0.01

Let's approximate the number for digits.
=> \sqrt{0.000125} = a (say) has 3 digits after decimal
=> (\sqrt{0.000125}+0.005) = a + 0.005 again will have 3 digits after decimal.
=> Therefore, for LHS in given expression to be equal to RHS, ie 0.01, (\sqrt{0.25x}−0.5) should have 1 to 2 digits before decimal.
=> x must have at least 1 digit before decimal. E is the only answer that satisfies this condition.

Therefore,  E is the Correct Answer

**took me 15 seconds but after wasting 3 minutes on manual calculations. LoL!

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If (0.000125^(1/2) + 0.005)(0.25x^(1/2) - 0.5) = 0.01, what is the val

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If (0.000125^(1/2) + 0.005)(0.25x^(1/2) - 0.5) = 0.01, what is the val

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards