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The length of an edge of cube A is 5% greater than the length of an ed

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The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post 03 Oct 2019, 21:05
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

56% (02:12) correct 44% (01:41) wrong based on 43 sessions

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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post 03 Oct 2019, 21:23
1
Given La=1.05Lb; and Vb=27, we are to determine Va.

We can eliminate A, B, and C because there is no way the Volume of cube A will be less than the Volume of cube B.
1.05x27=28.25 and this corresponds to answer choice B. we can eliminate it as well, because we know that the volume of cube A = 1.05^3 * 27.

Only E is left, hence E must be the answer.
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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post 03 Oct 2019, 22:04
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let length of cube B be a
then length of cube A will be 1.05a

so volume of cube A will be (1.05a)^3 = 1.157* a^3( here volume of cube B = a^3 is 27)
= 31.25

oa:E
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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post Updated on: 04 Oct 2019, 21:15
1
1
Let the length of cube B = x
--> Length of cube A = x(1 + 5/100) = 21/20x

Given, Volume of cube B = 27 cm^3
--> (x)^3 = 27

Volume of A = (21/20x)^3 = 31.25

IMO E

Originally posted by Dillesh4096 on 03 Oct 2019, 22:25.
Last edited by Dillesh4096 on 04 Oct 2019, 21:15, edited 1 time in total.
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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post Updated on: 04 Oct 2019, 21:20
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The length of an edge of cube A is 5% greater than the length of an edge of cube B. If the volume of cube B is 27 cubic centimetres, then which of the following is nearest to the volume of cube A ?

A. 23.1
B. 24.33
C. 27.0125
D. 28.35
E. 31.25

Since 27 \(cm^3\) means side of cube B = 3 cm.

Side of cube A > 3. Hence volume of Cube A > 27

Only 'C', 'D' and 'E' are left.

Side of cube A = 3*1.05 = 3.15
Volume of Cube A = 3.15^3 = (3 + 0.15)^3


Answer E.
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Originally posted by lnm87 on 03 Oct 2019, 22:36.
Last edited by lnm87 on 04 Oct 2019, 21:20, edited 1 time in total.
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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post 04 Oct 2019, 01:33
1
The length of an edge:
—> Cube A = 1.05x
—> Cube B= x
The volume of Cube B =27
\(x^{3}\)=27
x=3
—> 1.05x=3.15 (the length of the edge of cube A)

Volume of the cube A= \((3.15)^{3}\)

A,B is out. Because they are less than 27.

Calculating the \((3.15)^{3}\) takes a time.
So, let’s take 3.1 instead of 3.15
—> 3.1*3.1=9.61
Again, multiply 9.61 by 3 = 28.83
—> Check the answer, just one answer is greater than 28.83.

E is the answer

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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post 04 Oct 2019, 03:47
1
Quote:
The length of an edge of cube A is 5% greater than the length of an edge of cube B. If the volume of cube B is 27 cubic centimetres, then which of the following is nearest to the volume of cube A ?

A. 23.1
B. 24.33
C. 27.0125
D. 28.35
E. 31.25


\(a=1.05b…b^3=27…b=3…a^3=[1.05(3)]^3=(3.15)^3=31.25\)

Answer (E)

\(a=1.05b…b^3=27…\)
\(direct.proportion:(1.05b)^3/b^3=x^3/27…\)
\(x^3=27(1.05)^3=27(1+5(10^{-2}))^3…27[1^3+(5(10^{-2}))^3+3(1)(5(10^{-2})^2+3(5(10^{-2}))(1)^2]…\)
\(x^3=27[1+(125*10^{-6})+3(25*10^{-4})+3(5*10^{-2})…x^3=27[1+0.000125+0.0075+0.15]…\)
\(x^3=27[1.157625]…x^3=27[~1.16]…x^3=27+2.7+1.6=27+4.1=~31.3…\)

Answer (E)
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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post 04 Oct 2019, 08:07
Sides of cube B is 3

So, Length of Cube A is 105% of 3 = 3.15

Volume of Cube A is 3.15^3 ~ 31.25 , Hence Answer must be (E)
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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post 04 Oct 2019, 10:01
Can anyone teach me the short technique of multiplying 2.85*2. 85*2.85? How can I do this within 2 min?
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Re: The length of an edge of cube A is 5% greater than the length of an ed  [#permalink]

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New post 04 Oct 2019, 10:27
For this Question its important to note that

Volume of a Cube = S^3

Volume of Cube B = 27 ==> So one side must equal 3(3x3x3)

If the edge of a cube A is greater by 5%.

That means each side of cube A = 3 * 1.05

3 * 1.05 can be broken down into

(3 * 1) + (3 * 5/100) ==> 3.15^3 ==> Estimate that 3.2*3.2 is about 10 * 3.2 is about 32 to so answer has to be a little less than 32.

So E
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Re: The length of an edge of cube A is 5% greater than the length of an ed   [#permalink] 04 Oct 2019, 10:27
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