If 10 Millimeters Equal 1 Centimeter, How many Square Centimeters does 1 Square Millimeter Equal?

‘If 10 millimeters equal 1 centimeter, how many square centimeters does 1 square millimeter equal?’ is the topic from the GMAT Quantitative problem set. GMAT quantitative reasoning section tests the candidate's ability to solve mathematical and quantitative problems, interpret graph data, and mathematical reasoning. The quantitative section of the GMAT exam consists of 31 questions. This topic from the GMAT Quant section has five options to answer from. The candidate has to choose the correct option from the given options. GMAT quant section has mainly two sections:

Problem-solving: This question type in GMAT Quantitative analyses candidates' logical and analytical reasoning skills. In this section, candidates indicate the best five answer choices.
Data sufficiency: This question type in GMAT Quantitative analyses candidates’ quantitative problems and identifies relevance with the data given.

Topic: If 10 millimeters equal 1 centimeter, how many square centimeters does 1 square millimeter equal?

0.01
0.1
1
10
100

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Answer: A

Model Answer

There is only one way to solve the problem statement.

Explanation:

Given:

10 millimeters equal 1 centimeter

Find Out:

How many square centimeters does 1 square millimeter equal

Usually, unit conversions 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.

A "square measurement" is a measure of area. That measurement does not inform about the dimensions of the shape. For an example, if the area of a rectangle is 100 square feet, then the dimensions are not known.

In the example, it is asked 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.

Now, if we follow the problem statement, we get:

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 is the correct answer.

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If 10 Millimeters Equal 1 Centimeter, How many Square Centimeters does 1 Square Millimeter Equal?

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