Note figure not to scale
Twice area of triangle ABC | Area of triangle DBC |
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Solution
Note that the figure is not to scale so do not assume anything about the heights of the triangles. They both have a common base, but without knowing the heights we cannot compare the areas. For this reason, it is a D answer choice.
The number of integers between 50 and100 which are multiples of 3 | The number of integers between 10 and 81 which are multiples of 4 |
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Solution
In column A the first member of the series of multiples of 3 will be 51 and the last will be 99. Take the difference and divide by 3 and add one to get the number of multiples of 3. (17).
In column B, the first member of the series of multiples of 4 will be 12, and the last will be 80. Take the difference and divide by 4 and add one to get the number of multiples of 4. (18).
(You could, of course, simply count them on your fingers....it would not take much longer.)
45 per cent of n = 60
90 per cent of n | 120 |
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Solution
If 45 per cent of a number is 60; then 90 percent of the same number is twice as much (i.e. 120).
1/3 4/5 6/7 2/9 3/11
The smallest fraction shown | The product of the greatest fraction shown and 2/3 |
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Solution
If you are not too happy with fractions, convert to decimals. (Divide the top number by the bottom).
In order from left to right we have 0.333, 0.8, 0.857, 0.222, 0.272
The smallest is 0.222; the greatest is 0.857 (6/7), which when multiplied by 2/3 = 4/7
(0.571). Thus the right side is greater.
The time it would take to drive 80 miles at an average speed of 60 miles per hour | The time it would take to drive 60 miles at an average speed of 45 mile an hour |
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Solution
Speed = distance / time; time = distance / speed.
Time taken on the left = 80/60 = 1.33 hours
Time on the right = 60/45 = 1.33 hours
x, y and z are consecutive integers
and
xyz = 0
z | 0 |
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Solution
If the product of the three consecutive integers is 0, then one of the numbers must be zero. But which one? The numbers could be -2, -1, 0, in which case z = 0, but we could also have -1, 0, 1 or 0,1,2
Also the question did not state that x,y,z were in that order. In any case, it is a D answer.
Twice the volume of a cube of side 1 | Volume of a cube of side 2 |
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Solution
A cube of side 1 has volume of 1 cubic unit.
A cube of side two has volume 2 x 2 x 2 = 8 cubic units. This is greater than twice the volume of the cube of side 1.
ABCD is a rectangle
The length of the curved path from A to C | 5 |
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Solution
The curved path must be longer than the straight-line distance between A and C.
The straight-line distance is the hypotenuse of a 3-4-5 triangle, and is therefore 5.
75,410 rounded to the nearest hundred | 75,410 rounded to the nearest thousand |
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Solution
To the nearest hundred, 75410 becomes 75400
To the nearest thousand 75410 becomes 75000
-1 (-1) | -1 +(-1) |
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Solution
On the left we have +1
On the right we have -2 (which is obviously less).