Using reasoning to solve problems
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HiSET › Using reasoning to solve problems
Rewrite the sum of 16 gallons and pints as a number of quarts.
quarts
quarts
quarts
quarts
None of the other choices gives the correct response.
Explanation
One gallon is equivalent to 4 quarts, so 16 gallons can be converted to quarts by multiplying by conversion factor 4:
One quart is equivalent to 2 pints, so pints can be converted to quarts by dividing by conversion factor 2:
Added together:
,
the correct response.
Rewrite the sum of 16 gallons and pints as a number of quarts.
quarts
quarts
quarts
quarts
None of the other choices gives the correct response.
Explanation
One gallon is equivalent to 4 quarts, so 16 gallons can be converted to quarts by multiplying by conversion factor 4:
One quart is equivalent to 2 pints, so pints can be converted to quarts by dividing by conversion factor 2:
Added together:
,
the correct response.
Rewrite the sum of 2 feet and inches as a number of yards.
yards
yards
yards
yards
yards
Explanation
One yard is equivalent to 3 feet, so 2 feet can be converted to yards by dividing by the conversion factor 3:
Also, one yard is equal to 36 inches, so inches can be converted to yards by dividing by the conversion factor 36;
Add these quantities:
Rewriting with the least common denominator, which is 36:
,
the correct choice.
Rewrite the sum of meters and 50 millimeters as a number of centimeters.
centimeters
centimeters
centimeters
centimeters
centimeters
Explanation
One meter is equivalent to 100 centimeters, so meters can be converted to centimeters by multiplying by conversion factor 100:
One centimeter is equivalent to 10 millimeters, so 50 millimeters can be converted to centimeters by dividing by conversion factor 10:
Add these quantities:
,
the correct response.
Rewrite the sum of 2 meters and millimeters as a number of centimeters.
centimeters
centimeters
centimeters
centimeters
centimeters
Explanation
One meter is equivalent to 100 centimeters, so 2 meters can be converted to centimeters by multiplying by conversion factor 100:
One centimeter is equivalent to 10 millimeters, so millimeters can be converted to centimeters by dividing by conversion factor 10:
Add these quantities:
,
the correct answer.
Give the missing term in the sequence:
Explanation
The sequence is one of sets. Note that in each term, the final element in each subsequent set increases by 1. Also note that each set comprises the set of all factors of its greatest element. Therefore, the missing set is the set that includes 7 and all of its other factors. Since 7 is a prime number, its set of factors is simply , making this the correct response.
Rewrite the sum of gallons and 10 pints as a number of quarts.
quarts
quarts
quarts
quarts
quarts
Explanation
One gallon is equivalent to 4 quarts, so gallons can be converted to quarts by multiplying by conversion factor 4:
One quart is equivalent to 2 pints, so 10 pints can be converted to quarts by dividing by conversion factor 2:
Added together:
,
the correct response.
Rewrite the sum of feet and 18 inches as a number of yards.
yards
yards
yards
yards
Explanation
One yard is equivalent to 3 feet, so feet can be converted to yards by dividing by the conversion factor 3:
Also, one yard is equal to 36 inches, so 18 inches can be converted to yards by dividing by the conversion factor 36;
Add these quantities:
Rewriting with the least common denominator, which is 6:
,
the correct choice.
In acres, give the area of a square plot of land three and one half miles in sidelength.
7,840 acres
3,920 acres
15,680 acres
4,480 acres
2,240 acres
Explanation
A square plot of land has as its area the square of the length of a side, so the land in question has area
square miles.
One square mile is equal to 640 acres, so multiply this by the conversion factor 640:
Give the missing term in the sequence:
Explanation
The sequence is one of sets. Note that in each term, the final element in each subsequent set increases by 1. Also note that each set comprises the set of all factors of its greatest element. Therefore, the missing set is the set that includes 7 and all of its other factors. Since 7 is a prime number, its set of factors is simply , making this the correct response.