If 10 millimeters equal 1 centimeter, how many square

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1 mm = 0.1 cm

hence 1 mm^2 == 0.1*0.1 == 0.01 cm^2

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10 mm = 1 cm

\(1 mm = \frac{1}{10} cm\)

\(1 mm^2 = \frac{1}{10^2} cm^2\)

\(1 mm^2 = 0.01 cm^2\)

Answer = A

10 mm = 1 cm
1 mm = 1/10 cm

Because is sq:

1 sq mm = 1/100 sq cm
1 sq mm = 0.01 sq cm

what exactly do they mean by square cm and square mm. that's the only part of the problem throwing me off. if they gave concrete numbers id understand

Hi btan219,

This is an example of a 'unit conversion' question. A number of questions on Test Day involve unit conversions (e.g. dollars to cents, hours to minutes, feet to inches, etc.).

Square centimeters and square millimeters are just different ways to measure area.

If you're not a big fan of the metric system, then try the following example:

1) Draw a 1 foot by 1 foot square. This is a "square foot" of area.
2) Since there are 12 inches in 1 foot, you can relabel the two measurements as "12 inches" and "12 inches"
3) 12 x 12 = 144, so this same space = 1 square foot = 144 square inches.

The exact same idea appears here, but we're dealing with metric measurements. Try drawing another picture, but using centimeters and millimeters (instead of feet and inches).

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

im still not understand what they mean by square cm and square mm... how much is a square cm compared to a regular cm?

edit: ok i just kept reading your post until something clicked in my head. let me see if i understand this-

1cm by 1cm = 10mm by 10mm which is 100 square mm. since the area in cm is still 1 square cm, its 1/100=.01?

Square Centimeter is the unit of area, while Centimeter is the unit of length. That's all.

Hi btan219,

YES, that is exactly correct.

Usually, unit conversions on Test Day are simple "unit measurement" conversions (minutes to seconds, for example). Here, we have the extra step of converting the area AFTER we convert the units.

When it comes to area, "square" measurements (square feet, square inches, square centimeters) are basically what they "sound like" - a "square" with sides of THAT measurement. One "square foot" of space is a 1-foot by 1-foot area. In that same way, a 20-foot by 30-foot rectangle is (20)(30) = 600 square feet of area.

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

if the question instead asked, how many square cm does 5 square mm equal?

how would you go about solving it? would it be 5mm by 5mm, or a 5mm by 1mm?
pretty much, when it gives you x square (unit of measurement), is it saying thats the length of each side, or the area?

Hi btan219,

A "square measurement" (square feet, square mm, square miles, etc.) is a measure of area. That measurement does NOT tell you the dimensions of the shape. For example, f you know that the area of a rectangle is 100 square feet, then you do NOT know the dimensions.

In your example, you ask about what 5 square millimeters equals in terms of square centimeters.

We don't know the dimensions that 5 square mm represents (it could be a 1 mm by 5 mm shape, but it could also be 1/2 mm by 10 mm or any other product that equals 5).

Since 1 square cm = 100 square mm, we can convert "backwards"...

1 square mm = 1/100 square cm
5 square mm = 5/100 square cm = 1/20 square cm.

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

Given that 10 mm = 1 cm
So, 1 mm = (1 * 1)/10 = 1/10 cm
Now, we need 1 square mm. So squaring both the sides,
1 square mm = (1/10)^2 square cm
= 1/100 square cm
= 0.01 square cm
Hence option A

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10mm = 1cm

1mm = 0.1 cm

1mm * 1mm = 0.1cm * 0.1cm

=> 1{mm}^2 = 0.01{mm}^2

Answer A

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