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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
(A) 0.0125
(B) 0.125
(C) 0.25
(D) 1.25
(E) 5
11 Feb 2021, 08:34
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sjuniv32
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
(A) 0.0125
(B) 0.125
(C) 0.25
(D) 1.25
(E) 5
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
Joined: 22 Jun 2020
Last visit: 24 Sep 2022
Posts: 152
Given Kudos: 120
Location: Georgia
Concentration: Finance, General Management
Schools: Booth '25 (WL) Darden '25
GMAT 1: 720 Q51 V38
GPA: 3.71
11 Feb 2021, 09:39
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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
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
