Wednesday, February 28, 2024
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Thursday, February 29, 2024
(outside of North American and South America)
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Calculating,
Answer: (E)
When
Alternatively, when
Answer: (B)
Since
Therefore,
Since the sum of the angles in
Answer: (A)
On Friday, the Cayley Comets scored
This is equal to
Alternatively, since
Answer: (B)
The volume of a prism is equal to the area of its base times its
depth.
Here, the prism has identical bases with area
Answer: (C)
The percentage of cookies that Lloyd ate that were chocolate chip
or oatmeal was
This leaves
Since Lloyd ate two times as many gingerbread cookies as sugar cookies,
then
Answer: (C)
Simplifying,
Answer: (D)
Since
We can check, for example using a calculator, that the square root of
each of the other four choices is not an integer, and so each of these
four choices cannot be expressed as the square of an integer.
Answer: (C)
Suppose that the smallest of the five odd integers is
Since consecutive odd integers differ by
Therefore,
From this, we obtain
Thus, the smallest of the five integers is
Answer: (C)
When two standard six-sided dice are rolled, there are
Of these, the pairs
Since there are
Answer: (B)
Since Arturo has an equal number of
The value of the bills in each group is
Since the total value of Arturo’s bills is
Thus, Arturo has
Answer: (D)
Since the mass of
In other words, the mass of
Since the mass of
Answer: (C)
Draw a perpendicular from
Since quadrilateral
This means that
Further,
Now,
By the Pythagorean Theorem,
Since
Thus, the perimeter of
Answer: (E)
Since
When the numbers
The average of these
Answer: (A)
The sum of the lengths of the horizontal line segments in Figure
2 is
Similarly, the sum of the lengths of the vertical line segments in
Figure 2 is
In other words, the sum of the perimeters of the four rectangles in
Figure 2 is
Since the sum of the perimeters also equals
Answer: (A)
Since
Answer: (B)
The integers between
We want each of
There are
There are 5 choices for each of
The choice of each digit is independent, and so the total number of such
integers is
Answer: (A)
The line with equation
Since the line has
When the line is translated
A line with slope
Alternatively, we could note that when the graph of
Answer: (B)
Since squares
Since
Since
Since the area of
Since the area of
Since
Therefore,
Since
Since
Therefore, the area of square
Answer: (D)
Suppose that the length of the race was
Suppose further that Jiwei finished the first race in
Since Hari finished in
Since speed equals distance divided by time, then Jiwei’s average speed
was
For Jiwei to finish in the same time as Hari, Jiwei must increase his
average speed from
This is an increase of one-quarter over the original speed, or an
increase of
Answer: (B)
Since the second column includes the number
To generate the
This gives:
We cannot use step (i) any more times, otherwise the entries in
column
To obtain the final grid from this current grid using only step (ii), we
must increase each entry in column
Therefore,
Answer:
Let
The slope of
The line with equation
If
If
If
For integers
There are
Answer:
To calculate the shaded area, we add the area of the rectangle
and the areas of the four semi-circles, and subtract the area of the
larger circle.
Since the rectangle is
The two semi-circles of diameter
The two semi-circles of diameter
Since the larger circle passes through the four vertices of the
rectangle, the diagonal of the rectangle is its diameter. (This is
because the diagonal subtends an angle of
The length of the diagonal is
Finally, this means that the area of the shaded region is
The closest integer to
Answer:
If Rasheeqa walks directly from
We note that Rasheeqa cannot walk from
Rasheeqa can add increments of
This means that Rasheeqa’s total time, in minutes, can be each of
Rasheeqa can also walk from
Any walk that uses the path from
Rasheeqa can again add increments of
This means that Rasheeqa’s total time, in minutes, can be each of
Rasheeqa can also walk from
Any walk that uses the path from
Rasheeqa can again add increments of
This means that Rasheeqa’s total time, in minutes, can be each of
Examining these lists, we see that
Of the positive integers
Since there are
Answer:
The patterns that Erin can construct can include
A pattern cannot include fewer than
We consider the following cases which are determined by the number of
X’s in each pattern.
Case 1:
Using O’s to represent empty squares, there are
XXXOOOO, OXXXOOO, OOXXXOO, OOOXXXO, OOOOXXX
Case 2:
There are
XXXXOOO, OXXXXOO, OOXXXXO, OOOXXXX
(It is possible to have
We can also place
XXXOXOO, XXXOOXO, XXXOOOX, OXXXOXO, OXXXOOX, OOXXXOX, XOXXXOO, XOOXXXO, XOOOXXX, OXOXXXO, OXOOXXX, OOXOXXX
Case 3:
There are
XXXXXOO, OXXXXXO, OOXXXXX
(We can place
We can also place
XXXOXXO, XXXOOXX, OXXXOXX, XXOXXXO, XXOOXXX, OXXOXXX, XXXXOXO, XXXXOOX, OXXXXOX, XOXXXXO, XOOXXXX, OXOXXXX, XXXOXOX, XOXXXOX, XOXOXXX
Case 4:
We cannot place
We can, however, have
There are
XXXXXOX, XXXXOXX, XOXXXXX, XXOXXXX
In total, there are
Answer: