Measurement Problems - GMAT Quantitative
Card 1 of 104
A really backward country does not use inches, feet, yards, or meters to measure distance, it uses units called wumps and zumps. These units can also be used to form units of area and volume (i.e. square wumps, cubic zumps).
How many wumps are in one zump?
Statement 1: There are 361 square wumps in one square zump.
Statement 2: There are 6,859 cubic wumps in one cubic zump.
A really backward country does not use inches, feet, yards, or meters to measure distance, it uses units called wumps and zumps. These units can also be used to form units of area and volume (i.e. square wumps, cubic zumps).
How many wumps are in one zump?
Statement 1: There are 361 square wumps in one square zump.
Statement 2: There are 6,859 cubic wumps in one cubic zump.
Tap to reveal answer
If there are 
wumps in a zump, then there are 
square wump in a square zump, and 
cubic wump in a cubic zump. Therefore, given the first statement, you can take the square root of the conversion factor to get the number of wumps in a zump; given the second, you can take the cube root of that conversion factor to the same end. In both cases you get 19.
If there are
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The length of a metal rod can be given by a whole number of inches. How long is the rod?
Statement 1: The length of the rod can be given by a whole number of feet.
Statement 2: The rod is between 40 and 50 inches long, inclusive.
The length of a metal rod can be given by a whole number of inches. How long is the rod?
Statement 1: The length of the rod can be given by a whole number of feet.
Statement 2: The rod is between 40 and 50 inches long, inclusive.
Tap to reveal answer
If Statement 1 alone is assumed, since the length of the rod is given by a whole number of feet, then the length in inches must be a multiple of 12 - 12 inches, 24 inches, etc. However, no other information can be found.
If Statement 2 alone is assumed, there are eleven possible lengths of the rod - 40 inches, 41 inches, and so on up to 50 inches.
Now assume both statements. The length of the rod in inches must be a multiple of 12 between 40 and 50; this narrows it down to one possibility, 48 inches.
If Statement 1 alone is assumed, since the length of the rod is given by a whole number of feet, then the length in inches must be a multiple of 12 - 12 inches, 24 inches, etc. However, no other information can be found.
If Statement 2 alone is assumed, there are eleven possible lengths of the rod - 40 inches, 41 inches, and so on up to 50 inches.
Now assume both statements. The length of the rod in inches must be a multiple of 12 between 40 and 50; this narrows it down to one possibility, 48 inches.
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The weight of a bag of oranges can be given by a whole number of ounces. What is its weight?
Statement 1: The bag of oranges weighs between 110 ounces and 130 ounces inclusive.
Statement 2: The weight of the bag of oranges can be given as a whole number of pounds.
The weight of a bag of oranges can be given by a whole number of ounces. What is its weight?
Statement 1: The bag of oranges weighs between 110 ounces and 130 ounces inclusive.
Statement 2: The weight of the bag of oranges can be given as a whole number of pounds.
Tap to reveal answer
Assume both statements are true. Since, as known from Statement 2, the weight of the bag of oranges is given by a whole number of pounds, then the weight in ounces must be a multiple of 16. From Statement 1, this number is between 110 and 130 inclusive. However, there are two multiples of 16 - 112 and 128 - that fall in this range. Therefore, the question cannot be answered for certain.
Assume both statements are true. Since, as known from Statement 2, the weight of the bag of oranges is given by a whole number of pounds, then the weight in ounces must be a multiple of 16. From Statement 1, this number is between 110 and 130 inclusive. However, there are two multiples of 16 - 112 and 128 - that fall in this range. Therefore, the question cannot be answered for certain.
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The weight of the coffee in a can be given by a whole number of ounces. How many ounces does it weigh?
Statement 1: If eight ounces of coffee are removed, what is left over can be expressed as a whole number of pounds.
Statement 2: There are between 50 and 60 ounces of coffee in the can.
The weight of the coffee in a can be given by a whole number of ounces. How many ounces does it weigh?
Statement 1: If eight ounces of coffee are removed, what is left over can be expressed as a whole number of pounds.
Statement 2: There are between 50 and 60 ounces of coffee in the can.
Tap to reveal answer
From Statement 1 alone, it can be determined that there are eight ounces more that a whole number of pounds; equivalently, the number of ounces in can is 8 greater than a multiple of 16, such as 24, 40, 66, etc. However, we cannot narrow it down further.
From Statement 2 alone, we can narrow the possibilities down to eleven: 50, 51, up to 60 ounces. We cannot narrow it down further.
Assume both statements to be true. We can start with 8 and keep adding 16 to find a number that 8 greater than a multiple of 16 and that is between 50 and 60:
The only possible weight of the coffee is 56 ounces.
From Statement 1 alone, it can be determined that there are eight ounces more that a whole number of pounds; equivalently, the number of ounces in can is 8 greater than a multiple of 16, such as 24, 40, 66, etc. However, we cannot narrow it down further.
From Statement 2 alone, we can narrow the possibilities down to eleven: 50, 51, up to 60 ounces. We cannot narrow it down further.
Assume both statements to be true. We can start with 8 and keep adding 16 to find a number that 8 greater than a multiple of 16 and that is between 50 and 60:
The only possible weight of the coffee is 56 ounces.
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The length of a metal rod can be given by a whole number of inches. How long is the rod?
Statement 1: If four inches are removed from each end, then the length can be given in a whole number of feet.
Statement 2: If twenty inches are removed from one end, then the length can be given in a whole number of yards.
The length of a metal rod can be given by a whole number of inches. How long is the rod?
Statement 1: If four inches are removed from each end, then the length can be given in a whole number of feet.
Statement 2: If twenty inches are removed from one end, then the length can be given in a whole number of yards.
Tap to reveal answer
Assume both statements to be true. Examine these two scenarios.
Case 1: The metal rod is 56 inches long.
If four inches are removed from each end - that is, if eight inches total are removed - the rod will have length 
inches, which is equal to 
feet.
If twenty inches are removed, the rod will have length 
inches, which is equal to one yard.
Case 2: The metal rod is 92 inches long.
If four inches are removed from each end - that is, if eight inches total are removed - the rod will have length 
inches, which is equal to 
feet.
If twenty inches are removed, the rod will have length 
inches, which is equal to 
yards.
Both lengths satisfy the conditions given in both statements, so, together, the statements provide insufficient information.
Assume both statements to be true. Examine these two scenarios.
Case 1: The metal rod is 56 inches long.
If four inches are removed from each end - that is, if eight inches total are removed - the rod will have length
If twenty inches are removed, the rod will have length
Case 2: The metal rod is 92 inches long.
If four inches are removed from each end - that is, if eight inches total are removed - the rod will have length
If twenty inches are removed, the rod will have length
Both lengths satisfy the conditions given in both statements, so, together, the statements provide insufficient information.
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You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?
Statement 1: The area of the sheet is between 3 square yards and 4 square yards inclusive.
Statement 2: Each side of the sheet measures between 60 and 72 inches inclusive.
You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?
Statement 1: The area of the sheet is between 3 square yards and 4 square yards inclusive.
Statement 2: Each side of the sheet measures between 60 and 72 inches inclusive.
Tap to reveal answer
Examine Statement 1. One yard comprises three feet, so one square yard comprises nine square feet. Three square yards is equal to 
square feet, and four square yards is equal to 
square feet. Therefore, the area in feet is one of the whole numbers 
.
Examine Statement 2. 60 inches is equal to 
feet, and 72 inches is equal to 
square feet. The range of areas of the square sheet can be found as follows:
Therefore, the area in feet is one of the whole numbers 
.
Therefore, the two statements together yield ten possible answers - the whole numbers from 27 to 36.
Examine Statement 1. One yard comprises three feet, so one square yard comprises nine square feet. Three square yards is equal to
Examine Statement 2. 60 inches is equal to
Therefore, the area in feet is one of the whole numbers
Therefore, the two statements together yield ten possible answers - the whole numbers from 27 to 36.
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You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?
Statement 1: The length of each side is between 24 and 32 inches, inclusive.
Statement 2: The area of the sheet is no greater than one half of a square yard.
You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?
Statement 1: The length of each side is between 24 and 32 inches, inclusive.
Statement 2: The area of the sheet is no greater than one half of a square yard.
Tap to reveal answer
Assume Statement 1 alone.
24 inches is equal to 
feet, and 32 inches is equal to 
feet. If, as given in Statement 1, the length of each side of a square falls between these measures, the range of the area is as follows:
This gives us four possible whole numbers of square feet for the area - 4, 5, 6, and 7.
Assume Statement 2 alone. One yard comprises three feet, so one square yard comprises nine square feet. One half of a square yard is equal to half of nine, or four and a half, square feet. This allows us to narrow down the area to four whole numbers of square feet - 1, 2, 3, or 4.
Neither statement alone is sufficient, but both are - since 4 square feet is the only possibility that satisfies both statements, it can be found to be the answer to the question if both are assumed.
Assume Statement 1 alone.
24 inches is equal to
This gives us four possible whole numbers of square feet for the area - 4, 5, 6, and 7.
Assume Statement 2 alone. One yard comprises three feet, so one square yard comprises nine square feet. One half of a square yard is equal to half of nine, or four and a half, square feet. This allows us to narrow down the area to four whole numbers of square feet - 1, 2, 3, or 4.
Neither statement alone is sufficient, but both are - since 4 square feet is the only possibility that satisfies both statements, it can be found to be the answer to the question if both are assumed.
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You are given a square metal sheet whose area can be given by a whole number of square meters. What is the length of each side?
Statement 1: The length of each side is between 250 and 280 centimeters, inclusive.
Statement 2: The length of each side is between 2,500 millimeters and 2,800 millimeters inclusive.
You are given a square metal sheet whose area can be given by a whole number of square meters. What is the length of each side?
Statement 1: The length of each side is between 250 and 280 centimeters, inclusive.
Statement 2: The length of each side is between 2,500 millimeters and 2,800 millimeters inclusive.
Tap to reveal answer
Assume Statement 1 alone. Since one meter is equal to 100 centimeters, the minimum and maximum lengths in meters are 
meters and 
meters. The squares of these lengths provide the minimum and maximum areas of the sheet:
From the main body of the problem, the area in square meters must be a whole number, so its area must be seven meters.
Assume Statement 2 alone. One meter is equal to 1,000 millimeters, so the minumum and maximum lengths are 
meters and 
meters. These are the same boundaries derived from Statement 1, so again, the area can be determined to be seven meters.
Assume Statement 1 alone. Since one meter is equal to 100 centimeters, the minimum and maximum lengths in meters are
From the main body of the problem, the area in square meters must be a whole number, so its area must be seven meters.
Assume Statement 2 alone. One meter is equal to 1,000 millimeters, so the minumum and maximum lengths are
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You are given a square metal sheet whose area can be given by a whole number of square yards. What is the length of each side?
Statement 1: The area of the sheet is less than 3,000 square inches.
Statement 2: The area of the sheet is less than 15 square feet.
You are given a square metal sheet whose area can be given by a whole number of square yards. What is the length of each side?
Statement 1: The area of the sheet is less than 3,000 square inches.
Statement 2: The area of the sheet is less than 15 square feet.
Tap to reveal answer
Assume Statement 1 alone. One yard is equal to 36 inches, so one square yard is equal to 
square inches. The maximum area of 3,000 square inches is equal to 
square yards; since the area is a whole number of square yards less than this, we can narrow the area down to 1 or 2 square yards. Without further information, we cannot narrow this down further.
Assume Statement 2 alone. One yard is equal to 3 feet, so one square yard is equal to 
square feet. The maximum area of 15 square feet is equivalent to 
square yards; since the area is a whole number of square yards less than this, the only possible area is one square yard.
Assume Statement 1 alone. One yard is equal to 36 inches, so one square yard is equal to
Assume Statement 2 alone. One yard is equal to 3 feet, so one square yard is equal to
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You are given a square metal sheet whose area can be given by a whole number of square yards. What is the length of each side?
Statement 1: Each side has length between 4 and 6 feet inclusive.
Statement 2: Each side has length between 44 and 54 inches inclusive.
You are given a square metal sheet whose area can be given by a whole number of square yards. What is the length of each side?
Statement 1: Each side has length between 4 and 6 feet inclusive.
Statement 2: Each side has length between 44 and 54 inches inclusive.
Tap to reveal answer
Assume Statement 1 alone. Since the length of one side is at minimum 4 feet, or equivalently, 
yards, its area is at least the square of this, or 
square yards. Since the length of one side is at most 6 feet, or, equivalently, 
yards, its area is at most the square of this, or 4 square yards. Since the area must be equal to a whole number of yards, we can only narrow the area down to 2, 3, or 4 square yards.
Assume Statement 2 alone. Since the length of one side is at minimum 44 inches, or equivalently, 
yards, its area is at least the square of this, or 
square yards. Since the length of one side is at most 54 inches, or, equivalently, 
yards, its area is at most the square of this, or 
square yards. Since the area must be equal to a whole number of yards, the only possible area for the sheet is 2 square yards.
Assume Statement 1 alone. Since the length of one side is at minimum 4 feet, or equivalently,
Assume Statement 2 alone. Since the length of one side is at minimum 44 inches, or equivalently,
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You are given a square metal sheet whose area can be given by a whole number of square meters. What is the length of each side?
Statement 1: The length of each side of the sheet is between 7 and 8 feet, inclusive.
Statement 2: The area of the sheet is between 40 and 60 square feet, inclusive.
NOTE: 1 meter = about 3.3 feet.
You are given a square metal sheet whose area can be given by a whole number of square meters. What is the length of each side?
Statement 1: The length of each side of the sheet is between 7 and 8 feet, inclusive.
Statement 2: The area of the sheet is between 40 and 60 square feet, inclusive.
NOTE: 1 meter = about 3.3 feet.
Tap to reveal answer
Assume Statement 1 alone. Since one meter is equal to about 3.3 feet, we can divide the minimum and maximum lengths in feet by 3.3 to get these lengths in meters:
Minimum length: 7 feet
meters
Maximum length: 8 feet
meters
The minimum and maximum areas of the sheet in square meters are the squares of these:
Since the area of the sheet must be a whole number of square meters, the only possble area is 5 square meters.
Assume Statement 2 alone. Since one meter is equal to about 3.3 feet, we square this to get the conversion factor from square meters to square feet:
One square meter is equal to 
square feet.
Divide the minimum and maximum areas in square feet by 10.89 to convert them to square meters:
Minimum area: 40 square feet
square meters:
Maximum area: 60 square feet
square meters:
The area in square meters is a whole number between 3.7 and 5.5, so the area in square meters is either 4 or 5 . Without additional information, however, we cannot narrow it down further.
Assume Statement 1 alone. Since one meter is equal to about 3.3 feet, we can divide the minimum and maximum lengths in feet by 3.3 to get these lengths in meters:
Minimum length: 7 feet
Maximum length: 8 feet
The minimum and maximum areas of the sheet in square meters are the squares of these:
Since the area of the sheet must be a whole number of square meters, the only possble area is 5 square meters.
Assume Statement 2 alone. Since one meter is equal to about 3.3 feet, we square this to get the conversion factor from square meters to square feet:
One square meter is equal to
Divide the minimum and maximum areas in square feet by 10.89 to convert them to square meters:
Minimum area: 40 square feet
Maximum area: 60 square feet
The area in square meters is a whole number between 3.7 and 5.5, so the area in square meters is either 4 or 5 . Without additional information, however, we cannot narrow it down further.
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You are given a metal cube whose volume can be given as a whole number of cubic yards. What is its volume?
Statement 1: Each edge has length between 6 feet and 7 feet, inclusive.
Statement 2: The area of each face of the cube is between 
square feet and 
square feet, inclusive.
You are given a metal cube whose volume can be given as a whole number of cubic yards. What is its volume?
Statement 1: Each edge has length between 6 feet and 7 feet, inclusive.
Statement 2: The area of each face of the cube is between
Tap to reveal answer
Assume both statements are true. If we let 
be the length of one side in yards, then from Statement 1, we can divide maximum and minimum lengths by 3 to obtain
From Statement 2 alone, We can take the square root of the maximum and minmum areas to obtain the maximum and minimum areas in feet, then divide by three to convert these to yards:
(NOTE: 
is being used for sidelength in feet).
From the two statements together, we obtain
The maximum and minimum values of the volume are the cubes of those of the sidelengths:
The volume must be a whole number of cubic yards, so it must be 8, 9, or 10 - but without additional information, we cannot narrow it down further.
Assume both statements are true. If we let
From Statement 2 alone, We can take the square root of the maximum and minmum areas to obtain the maximum and minimum areas in feet, then divide by three to convert these to yards:
(NOTE:
From the two statements together, we obtain
The maximum and minimum values of the volume are the cubes of those of the sidelengths:
The volume must be a whole number of cubic yards, so it must be 8, 9, or 10 - but without additional information, we cannot narrow it down further.
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You are given a metal cube whose volume can be given by a whole number of cubic meters. What is its volume?
Statement 1: Each edge of the cube has length between 160 and 180 centimeters, inclusive.
Statement 2: The surface area of the cube is between 1,350 square decimeters and 1,944 square decimeters, inclusive.
You are given a metal cube whose volume can be given by a whole number of cubic meters. What is its volume?
Statement 1: Each edge of the cube has length between 160 and 180 centimeters, inclusive.
Statement 2: The surface area of the cube is between 1,350 square decimeters and 1,944 square decimeters, inclusive.
Tap to reveal answer
Assume Statement 1 alone. Each edge of the cube has length between 160 centimeters and 180 centimeters; since one meter is equal to 100 centimeters, the length of one edge falls between 1.6 meters and 1.8 meters. Its volume therefore falls between
cubic meters
and
cubic meters.
The only whole number of meters that falls between these boundaries is 5 meters, so the question is answered.
Assume Statement 2 alone. The minimum surface area of the cube is 1,350 square decimeters, so, to find the minumum length of an edge, use the surface area formula, setting 
:
decimeters; divide by 10 (decimeters per meter) to convert to 1.5 meters.
Similarly, to get the maximum edge length, set 
:
decimeters; divide by 10 to get 1.8 meters.
The volume of the cube therefore falls between
cubic meters
and
cubic meters.
This leaves us with two possible whole number answers, 4 and 5, so the question is not answered.
Assume Statement 1 alone. Each edge of the cube has length between 160 centimeters and 180 centimeters; since one meter is equal to 100 centimeters, the length of one edge falls between 1.6 meters and 1.8 meters. Its volume therefore falls between
and
The only whole number of meters that falls between these boundaries is 5 meters, so the question is answered.
Assume Statement 2 alone. The minimum surface area of the cube is 1,350 square decimeters, so, to find the minumum length of an edge, use the surface area formula, setting
Similarly, to get the maximum edge length, set
The volume of the cube therefore falls between
and
This leaves us with two possible whole number answers, 4 and 5, so the question is not answered.
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A really backward country does not use inches, feet, yards, or meters to measure distance, it uses units called wumps and zumps. These units can also be used to form units of area and volume (i.e. square wumps, cubic zumps).
How many wumps are in one zump?
Statement 1: There are 361 square wumps in one square zump.
Statement 2: There are 6,859 cubic wumps in one cubic zump.
A really backward country does not use inches, feet, yards, or meters to measure distance, it uses units called wumps and zumps. These units can also be used to form units of area and volume (i.e. square wumps, cubic zumps).
How many wumps are in one zump?
Statement 1: There are 361 square wumps in one square zump.
Statement 2: There are 6,859 cubic wumps in one cubic zump.
Tap to reveal answer
If there are wumps in a zump, then there are square wump in a square zump, and cubic wump in a cubic zump. Therefore, given the first statement, you can take the square root of the conversion factor to get the number of wumps in a zump; given the second, you can take the cube root of that conversion factor to the same end. In both cases you get 19.
If there are
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The length of a metal rod can be given by a whole number of inches. How long is the rod?
Statement 1: The length of the rod can be given by a whole number of feet.
Statement 2: The rod is between 40 and 50 inches long, inclusive.
The length of a metal rod can be given by a whole number of inches. How long is the rod?
Statement 1: The length of the rod can be given by a whole number of feet.
Statement 2: The rod is between 40 and 50 inches long, inclusive.
Tap to reveal answer
If Statement 1 alone is assumed, since the length of the rod is given by a whole number of feet, then the length in inches must be a multiple of 12 - 12 inches, 24 inches, etc. However, no other information can be found.
If Statement 2 alone is assumed, there are eleven possible lengths of the rod - 40 inches, 41 inches, and so on up to 50 inches.
Now assume both statements. The length of the rod in inches must be a multiple of 12 between 40 and 50; this narrows it down to one possibility, 48 inches.
If Statement 1 alone is assumed, since the length of the rod is given by a whole number of feet, then the length in inches must be a multiple of 12 - 12 inches, 24 inches, etc. However, no other information can be found.
If Statement 2 alone is assumed, there are eleven possible lengths of the rod - 40 inches, 41 inches, and so on up to 50 inches.
Now assume both statements. The length of the rod in inches must be a multiple of 12 between 40 and 50; this narrows it down to one possibility, 48 inches.
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The weight of a bag of oranges can be given by a whole number of ounces. What is its weight?
Statement 1: The bag of oranges weighs between 110 ounces and 130 ounces inclusive.
Statement 2: The weight of the bag of oranges can be given as a whole number of pounds.
The weight of a bag of oranges can be given by a whole number of ounces. What is its weight?
Statement 1: The bag of oranges weighs between 110 ounces and 130 ounces inclusive.
Statement 2: The weight of the bag of oranges can be given as a whole number of pounds.
Tap to reveal answer
Assume both statements are true. Since, as known from Statement 2, the weight of the bag of oranges is given by a whole number of pounds, then the weight in ounces must be a multiple of 16. From Statement 1, this number is between 110 and 130 inclusive. However, there are two multiples of 16 - 112 and 128 - that fall in this range. Therefore, the question cannot be answered for certain.
Assume both statements are true. Since, as known from Statement 2, the weight of the bag of oranges is given by a whole number of pounds, then the weight in ounces must be a multiple of 16. From Statement 1, this number is between 110 and 130 inclusive. However, there are two multiples of 16 - 112 and 128 - that fall in this range. Therefore, the question cannot be answered for certain.
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The weight of the coffee in a can be given by a whole number of ounces. How many ounces does it weigh?
Statement 1: If eight ounces of coffee are removed, what is left over can be expressed as a whole number of pounds.
Statement 2: There are between 50 and 60 ounces of coffee in the can.
The weight of the coffee in a can be given by a whole number of ounces. How many ounces does it weigh?
Statement 1: If eight ounces of coffee are removed, what is left over can be expressed as a whole number of pounds.
Statement 2: There are between 50 and 60 ounces of coffee in the can.
Tap to reveal answer
From Statement 1 alone, it can be determined that there are eight ounces more that a whole number of pounds; equivalently, the number of ounces in can is 8 greater than a multiple of 16, such as 24, 40, 66, etc. However, we cannot narrow it down further.
From Statement 2 alone, we can narrow the possibilities down to eleven: 50, 51, up to 60 ounces. We cannot narrow it down further.
Assume both statements to be true. We can start with 8 and keep adding 16 to find a number that 8 greater than a multiple of 16 and that is between 50 and 60:
The only possible weight of the coffee is 56 ounces.
From Statement 1 alone, it can be determined that there are eight ounces more that a whole number of pounds; equivalently, the number of ounces in can is 8 greater than a multiple of 16, such as 24, 40, 66, etc. However, we cannot narrow it down further.
From Statement 2 alone, we can narrow the possibilities down to eleven: 50, 51, up to 60 ounces. We cannot narrow it down further.
Assume both statements to be true. We can start with 8 and keep adding 16 to find a number that 8 greater than a multiple of 16 and that is between 50 and 60:
The only possible weight of the coffee is 56 ounces.
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The length of a metal rod can be given by a whole number of inches. How long is the rod?
Statement 1: If four inches are removed from each end, then the length can be given in a whole number of feet.
Statement 2: If twenty inches are removed from one end, then the length can be given in a whole number of yards.
The length of a metal rod can be given by a whole number of inches. How long is the rod?
Statement 1: If four inches are removed from each end, then the length can be given in a whole number of feet.
Statement 2: If twenty inches are removed from one end, then the length can be given in a whole number of yards.
Tap to reveal answer
Assume both statements to be true. Examine these two scenarios.
Case 1: The metal rod is 56 inches long.
If four inches are removed from each end - that is, if eight inches total are removed - the rod will have length inches, which is equal to feet.
If twenty inches are removed, the rod will have length inches, which is equal to one yard.
Case 2: The metal rod is 92 inches long.
If four inches are removed from each end - that is, if eight inches total are removed - the rod will have length inches, which is equal to feet.
If twenty inches are removed, the rod will have length inches, which is equal to yards.
Both lengths satisfy the conditions given in both statements, so, together, the statements provide insufficient information.
Assume both statements to be true. Examine these two scenarios.
Case 1: The metal rod is 56 inches long.
If four inches are removed from each end - that is, if eight inches total are removed - the rod will have length
If twenty inches are removed, the rod will have length
Case 2: The metal rod is 92 inches long.
If four inches are removed from each end - that is, if eight inches total are removed - the rod will have length
If twenty inches are removed, the rod will have length
Both lengths satisfy the conditions given in both statements, so, together, the statements provide insufficient information.
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You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?
Statement 1: The area of the sheet is between 3 square yards and 4 square yards inclusive.
Statement 2: Each side of the sheet measures between 60 and 72 inches inclusive.
You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?
Statement 1: The area of the sheet is between 3 square yards and 4 square yards inclusive.
Statement 2: Each side of the sheet measures between 60 and 72 inches inclusive.
Tap to reveal answer
Examine Statement 1. One yard comprises three feet, so one square yard comprises nine square feet. Three square yards is equal to square feet, and four square yards is equal to square feet. Therefore, the area in feet is one of the whole numbers .
Examine Statement 2. 60 inches is equal to feet, and 72 inches is equal to square feet. The range of areas of the square sheet can be found as follows:
Therefore, the area in feet is one of the whole numbers .
Therefore, the two statements together yield ten possible answers - the whole numbers from 27 to 36.
Examine Statement 1. One yard comprises three feet, so one square yard comprises nine square feet. Three square yards is equal to
Examine Statement 2. 60 inches is equal to
Therefore, the area in feet is one of the whole numbers
Therefore, the two statements together yield ten possible answers - the whole numbers from 27 to 36.
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You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?
Statement 1: The length of each side is between 24 and 32 inches, inclusive.
Statement 2: The area of the sheet is no greater than one half of a square yard.
You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?
Statement 1: The length of each side is between 24 and 32 inches, inclusive.
Statement 2: The area of the sheet is no greater than one half of a square yard.
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Assume Statement 1 alone.
24 inches is equal to feet, and 32 inches is equal to feet. If, as given in Statement 1, the length of each side of a square falls between these measures, the range of the area is as follows:
This gives us four possible whole numbers of square feet for the area - 4, 5, 6, and 7.
Assume Statement 2 alone. One yard comprises three feet, so one square yard comprises nine square feet. One half of a square yard is equal to half of nine, or four and a half, square feet. This allows us to narrow down the area to four whole numbers of square feet - 1, 2, 3, or 4.
Neither statement alone is sufficient, but both are - since 4 square feet is the only possibility that satisfies both statements, it can be found to be the answer to the question if both are assumed.
Assume Statement 1 alone.
24 inches is equal to
This gives us four possible whole numbers of square feet for the area - 4, 5, 6, and 7.
Assume Statement 2 alone. One yard comprises three feet, so one square yard comprises nine square feet. One half of a square yard is equal to half of nine, or four and a half, square feet. This allows us to narrow down the area to four whole numbers of square feet - 1, 2, 3, or 4.
Neither statement alone is sufficient, but both are - since 4 square feet is the only possibility that satisfies both statements, it can be found to be the answer to the question if both are assumed.
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