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# A square of side x has the length of each of its sides doubled. Its ne

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Math Expert
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A square of side x has the length of each of its sides doubled. Its ne [#permalink]

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10 Apr 2018, 00:01
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35% (medium)

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65% (00:30) correct 35% (00:24) wrong based on 63 sessions

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A square of side x has the length of each of its sides doubled. Its new area is what percent of its original area?

A. 100
B. 200
C. 300
D. 400
E. 500
[Reveal] Spoiler: OA

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Re: A square of side x has the length of each of its sides doubled. Its ne [#permalink]

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10 Apr 2018, 00:16
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Expert's post

Solution

Given:
• The initial side length of the square is x.
• The side of square is doubled i.e. new side length is 2x.

To find:
• We need to find that new area of the square is what percentage of the initial area.

Approach and Working:

• Initial area of the square=$$x^2$$
• New area of the square= $$(2x)^2$$= $$4x^2$$

Now, we need to find $$4x^2$$is what percentage of $$x^2$$.
• $$\frac{4x^2}{x^2}$$*100
• =4*100= 400
Thus, the new area of the square is 400% of the initial area.

Hence, the correct answer is option D.

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Re: A square of side x has the length of each of its sides doubled. Its ne [#permalink]

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10 Apr 2018, 02:10
Bunuel wrote:
A square of side x has the length of each of its sides doubled. Its new area is what percent of its original area?

A. 100
B. 200
C. 300
D. 400
E. 500

Small Square, Side = x
Area = x^2

Big Square, Side = 2x
Area = (2x)^2 = 4x^2

New area as percentage of previous area = (New Area / Old Area)*100 = (4x^2 / x^2)*100 = 400%

Alternative:

The area is square of side so ratio of area grows by sqaure of ratio of sides

Since ratio of sides = 1/2
therefore ratio of areas = (1/2)^2 = 1/4
Hence new area = 400% of old area
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A square of side x has the length of each of its sides doubled. Its ne [#permalink]

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10 Apr 2018, 06:16
Bunuel wrote:
A square of side x has the length of each of its sides doubled. Its new area is what percent of its original area?

A. 100
B. 200
C. 300
D. 400
E. 500

Let side length = 2
Area of small square = 4

Length of sides doubles, new side = 4
New area = 16

New area = what percent OF old?
That's the potential trap. "Of" implies multiplication (division).*

Percent of = $$(\frac{Part}{Whole}*100)$$

$$(\frac{16}{4}*100)=4*100=400$$
percent

*"Percent greater than" implies addition (subtraction): $$\frac{New-Old}{Old}*100$$
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Re: A square of side x has the length of each of its sides doubled. Its ne [#permalink]

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10 Apr 2018, 08:58
Bunuel wrote:
A square of side x has the length of each of its sides doubled. Its new area is what percent of its original area?

A. 100
B. 200
C. 300
D. 400
E. 500

Let x = 1 , So 2x = 2

Initial area is 1 sq units and Increased area is 4 sq units

So, New area is $$\frac{4}{1} *100$$ = $$400$$ % of original area, Answer must be (D)
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Re: A square of side x has the length of each of its sides doubled. Its ne [#permalink]

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11 Apr 2018, 16:15
Bunuel wrote:
A square of side x has the length of each of its sides doubled. Its new area is what percent of its original area?

A. 100
B. 200
C. 300
D. 400
E. 500

We can let the original side of the square be 2, so the area of the square is 4.

The new (doubled) side is 4, so the new area is16.

The new area is 16/4 x 100 = 400 percent of the original area.

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Re: A square of side x has the length of each of its sides doubled. Its ne   [#permalink] 11 Apr 2018, 16:15
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