SATMathematics Practice Test 1

Question : 47 of 58

Marks: +1, -0

A square field measures 10 meters by 10 meters.Ten students each mark off a randomly selected region of the field; each region is square and has side lengths of 1 meter, and no two regions overlap. The students count the earthworms contained in the soil to a depth of 5 centimeters beneath the ground’s surface in each region. The results are shown in the table below.

Region	Number of earthworms	Region	Number of earth worms
A	107	F	141
B	147	G	150
C	146	H	154
D	135	I	176
E	149	J	166

Which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimetres beneath the ground’s surface in the entire field?

150
1,500
15,000
150,000

Validate

Solution:

The area of the field is 100 square meters. Each 1-meterby-1-meter square has an area of 1 square meter.
Thus, on average, the earthworm counts to a depth of 5 centimeters for each of the regions investigated by the students should be about

1/100

of the total number of earthworms to a depth of 5 centimeters in the entire field.
Since the counts for the smaller regions are from 107 to 176, the estimate for the entire field should be between 10,700 and 17,600.
Therefore, of the given choices, 15,000 is a reasonable estimate for the number of earthworms to a depth of 5 centimeters in the entire field.
Choice A is incorrect; 150 is the approximate number of earthworms in 1 square meter.
Choice B is incorrect; it results from using 10 square meters as the area of the field.
Choice D is incorrect; it results from using 1,000 square meters as the area of the field.

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