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# Geometry and Number Problems

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@ManageableMeerkat

Y

50

15

### The second Wednesday of a month occurs ______ days following the first Wednesday

<p>7</p> Signup and view all the answers

### 10 blocks of 26 letters gives a sequence of ______ letters

<p>260</p> Signup and view all the answers

### There are 10 two-digit numbers whose tens digit is a ___

<p>4</p> Signup and view all the answers

### The number of two-digit numbers that have at least one digit that is a ___ is 18

<p>4</p> Signup and view all the answers

### The area of each of the three identical squares is 49 m², therefore the area of W XYZ is 147 m², each square has an area of ___ m²

<p>49</p> Signup and view all the answers

### The perimeter of W XYZ is 56 m and is comprised of 8 such side lengths, thus the length of each side of the three identical squares is 7 m, each square has a side length of ___ m

<p>7</p> Signup and view all the answers

### The first Wednesday of a month must occur on one of the first 7 days of a month, the second Wednesday of a month occurs 7 days following the first Wednesday, and the third Wednesday of a month occurs 14 days following the first ___.

<p>Wednesday</p> Signup and view all the answers

### The forecast wind speed is less than 20 km/h on Monday, Tuesday, Wednesday, and ______.

<p>Sunday</p> Signup and view all the answers

### Since there is no integer n for which 15 × n = 25, then 25 is not a multiple of ______.

<p>15</p> Signup and view all the answers

### Ordering the given list of integers from least to greatest, we get −9, −7, 0, 9, ______.

<p>10</p> Signup and view all the answers

### If 2n = 14, then n = 2. When n = 7, the value of 10n is 10 × 7 = ______.

<p>70</p> Signup and view all the answers

### There are 6 possible outcomes when Tallulah rolls a single standard die once. 1 2 =. ______.

<p>6</p> Signup and view all the answers

### Between 9 a.m. and 10 a.m., Ryan cut ___ of his lawn.

<p>3/8</p> Signup and view all the answers

### Ryan cut ___ of his lawn in 20 minutes.

<p>3/8</p> Signup and view all the answers

### At 10 a.m., Ryan had cut ___ of his lawn.

<p>7/8</p> Signup and view all the answers

### Ryan finished cutting his lawn at ___ a.m.

<p>10:20</p> Signup and view all the answers

### Begin by placing four tiles in the squares of the first ___

<p>row</p> Signup and view all the answers

### The largest possible value of p is 20, when w is equal to ______

<p>1</p> Signup and view all the answers

### Katharina placed the 8 letters in a mixed-up order around the circle. Jaxon begins at position 1 and writes down every third letter that he has not yet written down. The first 3 letters Jaxon writes down are the letters in positions 1, 4 and ______

<p>7</p> Signup and view all the answers

### Continuing to move clockwise around the circle, the next three positions at which letters have not yet been written down are positions 8, 2 and ______, and so Jaxon writes down the letter in position 3

<p>3</p> Signup and view all the answers

### At this point, Jaxon has written the letters in positions 1, 4, 7, 3, and ______

<p>8</p> Signup and view all the answers

### At this point, only the letters in positions 2 and ______ have not been written

<p>5</p> Signup and view all the answers

### A palindrome greater than 10 000 and less than 100 000 is a 5-digit positive integer of the form abcba, where a, b and c are digits and a ≠ 0. The digit a is equal to 2, 4, ______ or 8 (recall a ≠ 0).

<p>6</p> Signup and view all the answers

### A positive integer is a multiple of 9 exactly when the sum of its digits is a multiple of 9, and thus a + b + c + b + a or 2a + 2b + c is a multiple of 9.

<p>4</p> Signup and view all the answers

### When a = 2, we require that 2a + 2b + c = 4 + 2b + c be a multiple of 9. The smallest possible multiple of 9 that 4 + 2b + c can equal is ___

<p>9</p> Signup and view all the answers

### The first Wednesday of a month must occur on one of the first 7 days of a month, the second Wednesday of a month occurs 7 days following the first Wednesday, and the third Wednesday of a month occurs 14 days following the first ___

<p>Wednesday</p> Signup and view all the answers

### 10 blocks of 26 letters gives a sequence of ___ letters

<p>260</p> Signup and view all the answers

### The number of two-digit numbers that have at least one digit that is a ___ is 18

<p>7</p> Signup and view all the answers

### There are 6 possible outcomes when Tallulah rolls a single standard die once. 1 2 =. ___

<p>12</p> Signup and view all the answers

### The forecast wind speed is less than 20 km/h on Monday, Tuesday, Wednesday, and ___

<p>Thursday</p> Signup and view all the answers

### There are 10 two-digit numbers whose tens digit is a ___.

<p>9</p> Signup and view all the answers

### The second Wednesday of a month occurs ___ days following the first Wednesday

<p>7</p> Signup and view all the answers

### If the value of P is less than 9, then QR + P P P + P P P is at most 99 + 888 + 888 = 1875. Since the given sum is 2022, the value of P cannot be less than 9 and thus must equal ___

<p>9</p> Signup and view all the answers

### When a standard fair coin is tossed three times, there are 8 possible outcomes. If H represents head and T represents tail, these 8 outcomes are: HHH, HHT, HTH, THH, HTT, THT, TTH, and ___. Of these 8 outcomes, there are exactly 2 whose outcomes are all the same (HHH and TTT). Therefore, the probability that the three outcomes are all the same is ___

<p>TTT, 1/4 or 0.25</p> Signup and view all the answers

### Adding 14 days to each of the possible dates for the first Wednesday of the month, we get that the third Wednesday of a month must occur on the 15th, 16th, 17th, 18th, 19th, 20th, or 21st of that month. Of the given answers, the public holiday cannot occur on the 22nd of that month. Therefore, the third Wednesday of the month cannot be on the ___

<p>22nd</p> Signup and view all the answers

### If the 2022 Gauss Contest Solutions state that the probability that the three outcomes of coin tossing are all the same is 1/4 or 0.25, then the answer given must be ___

<p>(C) 17</p> Signup and view all the answers

### The number of two-digit numbers that have at least one digit that is a 9 is ___.

<p>18</p> Signup and view all the answers

### The circumference of Bindu's bike tires is 60π cm.

<p>True</p> Signup and view all the answers

### The sum of all 8 numbers in the list is 216.

<p>True</p> Signup and view all the answers

### The largest number in the list is paired with the third smallest number.

<p>False</p> Signup and view all the answers

### The mean (average) temperature recorded was 20°C.

<p>True</p> Signup and view all the answers

### The area of polygon WXYZ is 147 m².

<p>False</p> Signup and view all the answers

### If a number has two equal digits, it will satisfy the given property.

<p>True</p> Signup and view all the answers

### The number of numbers that satisfy the given property is 126.

<p>True</p> Signup and view all the answers

### Student A reports correctly on 90% of the samples that contain blueberry.

<p>True</p> Signup and view all the answers

### The area of each of the three identical squares is 49 m².

<p>False</p> Signup and view all the answers

### The sum of values for a in the table is 42.

<p>False</p> Signup and view all the answers

### A two-digit number with two equal digits cannot have the sum of its digits greater than 9.

<p>True</p> Signup and view all the answers

### The number of two-digit numbers with two equal digits and the third digit as 0 is 18.

<p>True</p> Signup and view all the answers

### A two-digit number with two equal digits and the third digit as the sum of the two equal digits can have 6 as one of the equal digits.

<p>False</p> Signup and view all the answers

### The area of each of the three identical squares is 49 m², therefore the area of WXYZ is 147 m².

<p>True</p> Signup and view all the answers

### The product of the digits in a two-digit number with two equal digits and the third digit as 0 is always 0.

<p>True</p> Signup and view all the answers

### The sum of the increases (or decreases) in the sale of bobbleheads between 2016 and 2017, and 2018 and 2019 is 55.

<p>False</p> Signup and view all the answers

### The difference between the perimeter of the regular pentagon and the total number of dots labelled on the faces shown is 2 cm.

<p>True</p> Signup and view all the answers

### The area of each identical square, given that the area of WXYZ is 147 m², is 49 m².

<p>True</p> Signup and view all the answers

### The product of the individual probabilities of choosing each of the 3 balls G, Y, or V is 50.

<p>False</p> Signup and view all the answers

### The average number of bobbleheads sold in 2016, 2017, 2018, 2019, 2020, and 2021 is 45.

<p>True</p> Signup and view all the answers

### The sum of all numbers from 6 to 10 is greater than the sum of all numbers from 11 to 15.

<p>True</p> Signup and view all the answers

### The difference between 25 and 17 is less than the difference between 40 and 28.

<p>False</p> Signup and view all the answers

### The area of a polygon with sides WX, XY, YZ, and WZ is 196 m².

<p>False</p> Signup and view all the answers

### The product of 12 and 9 is equal to the product of 6 and 18.

<p>True</p> Signup and view all the answers

### The average of 5, 8, and 12 is greater than the average of 3, 7, and 10.

<p>True</p> Signup and view all the answers

### The sum of all values of m from 6 to 20 inclusive having a units digit of 7 or 2 is 36.

<p>True</p> Signup and view all the answers

### The difference between the values of 7679 + 63m when m is equal to 7 and 12 is 315.

<p>False</p> Signup and view all the answers

### The area of polygon WXYZ is 196 m².

<p>False</p> Signup and view all the answers

### The product of the three students' reported numbers of blueberry samples between 8000 and 9000 is a multiple of 5.

<p>False</p> Signup and view all the answers

### The average value of the three numbers reported by the students as containing blueberry is 12.

<p>True</p> Signup and view all the answers

### When n = 20, the value of x is 0.

<p>True</p> Signup and view all the answers

### For n = 20, the value of y can be either -10 or 2.

<p>False</p> Signup and view all the answers

### When n = 20, the value of z is 8.

<p>True</p> Signup and view all the answers

### When n = 30, the percentage of students who participated in at least canoeing and swimming is 40%.

<p>False</p> Signup and view all the answers

### For n = 40, the sum of all positive integers k is 56.7.

<p>True</p> Signup and view all the answers

### The area of polygon WXYZ is 147 m².

<p>True</p> Signup and view all the answers

### The mean (average) temperature recorded was 25°C.

<p>False</p> Signup and view all the answers

### The sum of all positive integers k for values of n greater than 100 is less than 200.

<p>True</p> Signup and view all the answers

### When n = 80, the value of x is greater than y.

<p>False</p> Signup and view all the answers

### The product of k and n for n = 100 is approximately 99.

<p>True</p> Signup and view all the answers

### Match the following operations with their results:

<p>41 + 35 = 76 19 - 9 = 10 26 * 2 = 52 45 / 3 = 15</p> Signup and view all the answers

### Match the following pairs with their sum:

<p>13 + 28 = 41 35 + 19 = 54 26 + 28 = 54 45 + 9 = 54</p> Signup and view all the answers

### Match the following numbers with their product:

<p>7 * 8 = 56 12 * 5 = 60 9 * 4 = 36 11 * 3 = 33</p> Signup and view all the answers

### Match the following shapes with their areas:

<p>Square WXYZ (one side) = $7 m^2$ Three identical squares combined (total area) = $147 m^2$ Triangle PQR (area) = $30 cm^2$ Circle with radius 5 cm (area) = $25π cm^2$</p> Signup and view all the answers

### Match the following sets of temperatures with their averages:

<p>First 25 days (sum) = $525°C$ Last 5 days (sum) = $75°C$ Total recorded temperatures (mean) = $20°C$ Average of 5, 8, and 12 = $8.3°C$</p> Signup and view all the answers

### Match the following mathematical operations with their results:

<p>$5 + 7$ = 12 $10 - 3$ = 7 $4 \times 6$ = 24 $20 \div 5$ = 4</p> Signup and view all the answers

### Match the following geometric shapes with their areas:

<p>Square with side length 3 = 9 sq units Circle with radius 5 = 78.5 sq units Triangle with base 6 and height 4 = 12 sq units Rectangle with length 8 and width 2 = 16 sq units</p> Signup and view all the answers

### Match the following pairs of numbers with their product:

<p>$9 \times 6$ = 54 $4 \times 10$ = 40 $7 \times 3$ = 21 $11 \times 2$ = 22</p> Signup and view all the answers

### Match the following sets of numbers with their sum:

<p>3, 8, 12 = 23 5, 14, 6 = 25 10, 17, 8 = 35 4, 9, 15 = 28</p> Signup and view all the answers

### Match the following groups of numbers with their average:

<p>20, 30, 40 = 30 15, 25, 35 = 25 12, 18, 24 = 18 7, 14, 21 = 14</p> Signup and view all the answers

### Match the following operations with their results:

<p>$12 + 18$ = 30 $25 - 15$ = 10 $7 \times 4$ = 28 $36 \div 6$ = 6</p> Signup and view all the answers

### Match the following pairs with their differences:

<p>$50 - 22$ = 28 $39 - 17$ = 22 $64 - 29$ = 35 $81 - 45$ = 36</p> Signup and view all the answers

### Match the following polygons with their areas:

<p>Square with side length 10 = 100 sq units Rectangle with length 12 and width 8 = 96 sq units Triangle with base 6 and height 5 = 15 sq units Circle with radius 4 = ~50.27 sq units</p> Signup and view all the answers

### Match the following pairs with their products:

<p>$9 \times 7$ = 63 $5 \times 11$ = 55 $3 \times 9$ = 27 $8 \times 4$ = 32</p> Signup and view all the answers

### Match the following sets of numbers with their averages:

<p>3, 7, 9 = 6.33 12, 16, 20 = 16 5, 5, 10 = 6.67 18, 22, 28 = 22.67</p> Signup and view all the answers

### Match the following numbers with their sum:

<p>5 and 7 = 12 8 and 3 = 11 10 and 4 = 14 6 and 9 = 15</p> Signup and view all the answers

### Match the following numbers with their difference:

<p>15 and 8 = 7 12 and 4 = 8 20 and 10 = 10 18 and 6 = 12</p> Signup and view all the answers

### Match the following pairs with the area of a polygon:

<p>Square with side length of 7 units = 49 square units Equilateral triangle with side length of 5 units = 10.83 square units Rectangle with length of 8 units and width of 3 units = 24 square units Regular hexagon with side length of 6 units = 93.53 square units</p> Signup and view all the answers

### Match the following numbers with their product:

<p>9 and 7 = 63 12 and 5 = 60 8 and 4 = 32 11 and 6 = 66</p> Signup and view all the answers

### Match the following sets of numbers with their average:

<p>3, 6, 9 = 6 5, 10, 15 = 10 8, 12, 16 = 12 7, 14, 21 = 14</p> Signup and view all the answers

### Match the following pairs of numbers with their sum:

<p>5 and 8 = 13 12 and 15 = 27 20 and 25 = 45 30 and 40 = 70</p> Signup and view all the answers

### Match the following pairs of numbers with their difference:

<p>10 and 6 = 4 18 and 12 = 6 27 and 15 = 12 35 and 20 = 15</p> Signup and view all the answers

### Match the following pairs of numbers with their product:

<p>4 and 7 = 28 10 and 10 = 100 15 and 8 = 120 20 and 5 = 100</p> Signup and view all the answers

### Match the following pairs of numbers with their average:

<p>6 and 12 = 9 18 and 24 = 21 30 and 40 = 35 45 and 55 = 50</p> Signup and view all the answers

### Match the following pairs of numbers with their sum:

<p>3 and 6 = 9 11 and 14 = 25 22 and 18 = 40 31 and 39 = 70</p> Signup and view all the answers

### Match the following pairs of numbers with their difference:

<p>17 and 9 = 8 26 and 13 = 13 35 and 22 = 13 48 and 32 = 16</p> Signup and view all the answers

### Match the following pairs of numbers with their product:

<p>2 and 8 = 16 10 and 5 = 50 12 and 7 = 84 15 and 3 = 45</p> Signup and view all the answers

### Match the following pairs of numbers with their average:

<p>7 and 14 = 10.5 19 and 27 = 23 29 and 41 = 35 48 and 56 = 52</p> Signup and view all the answers

### Match the following numbers with their sum:

<p>7 and 9 = 16 12 and 15 = 27 20 and 25 = 45 30 and 35 = 65</p> Signup and view all the answers

### Match the following numbers with their difference:

<p>25 and 17 = 8 40 and 28 = 12 50 and 36 = 14 60 and 42 = 18</p> Signup and view all the answers

### Match the following pairs with their sum:

<p>2 and 5 = 7 10 and 15 = 25 18 and 22 = 40 30 and 33 = 63</p> Signup and view all the answers

### Match the following numbers with their product:

<p>3 and 7 = 21 5 and 10 = 50 8 and 12 = 96 15 and 20 = 300</p> Signup and view all the answers

### Match the following numbers with their sum:

<p>6, 7, 12, 17 = 42 8, 13, 18, 19 = 68 9, 14, 15, 20 = 58 10, 11, 16, 20 = 57</p> Signup and view all the answers

### Match the following numbers with their average:

<p>10, 15, and 20 = 15 18, 22, and 26 = 22 30, 35, and 40 = 35 45, 50, and 55 = 50</p> Signup and view all the answers

### Match the following pairs of numbers with their difference:

<p>8 and 3 = 5 15 and 7 = 8 19 and 12 = 7 16 and 9 = 7</p> Signup and view all the answers

### Match the following numbers with their product:

<p>4, 6, 8, 10 = 240 3, 5, 7, 9 = 945 2, 6, 12, 18 = 2592 1, 5, 9, 13 = 585</p> Signup and view all the answers

### Match the following polygons with their area:

<p>Triangle XYZ with sides of length 10m each = 43.3 m² Square WXYZ with side length of 8m = 64 m² Rectangle PQRS with length of 12m and width of 6m = 72 m² Circle O with radius of 5m = ~78.5 m²</p> Signup and view all the answers

### Match the following numbers with their average:

<p>15, 18, 21, 24 = 19.5 9, 11.5, 14.2, 17.8 = 13.125 3.4, 6.7, 9.1, 12.3 = ~7.875 22.7, 25.1, 28.6, 31.2 = ~26.65</p> Signup and view all the answers

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