Geometry and Number Problems

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In the sequence, the 259th letter is a ______

Y

The probability that the arrow stops on the largest section is ______%

50

The 2022 Gauss Contest Solutions are found on Page ______

15

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

7 Signup and view all the answers

10 blocks of 26 letters gives a sequence of ______ letters

260 Signup and view all the answers

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

4 Signup and view all the answers

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

4 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

49 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

7 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 ___.

Wednesday Signup and view all the answers

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

Sunday Signup and view all the answers

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

15 Signup and view all the answers

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

10 Signup and view all the answers

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

70 Signup and view all the answers

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

6 Signup and view all the answers

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

3/8 Signup and view all the answers

Ryan cut ___ of his lawn in 20 minutes.

3/8 Signup and view all the answers

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

7/8 Signup and view all the answers

Ryan finished cutting his lawn at ___ a.m.

10:20 Signup and view all the answers

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

row Signup and view all the answers

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

1 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 ______

7 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

3 Signup and view all the answers

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

8 Signup and view all the answers

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

5 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).

6 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.

4 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 ___

9 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 ___

Wednesday Signup and view all the answers

10 blocks of 26 letters gives a sequence of ___ letters

260 Signup and view all the answers

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

7 Signup and view all the answers

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

12 Signup and view all the answers

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

Thursday Signup and view all the answers

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

9 Signup and view all the answers

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

7 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 ___

9 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 _

TTT, 1/4 or 0.25 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 ___

22nd 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 ___

(C) 17 Signup and view all the answers

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

18 Signup and view all the answers

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

True Signup and view all the answers

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

True Signup and view all the answers

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

False Signup and view all the answers

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

True Signup and view all the answers

The area of polygon WXYZ is 147 m².

False Signup and view all the answers

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

True Signup and view all the answers

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

True Signup and view all the answers

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

True Signup and view all the answers

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

False Signup and view all the answers

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

False Signup and view all the answers

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

True Signup and view all the answers

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

True 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.

False 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.

True 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.

True 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.

False 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.

True Signup and view all the answers

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

True 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.

False Signup and view all the answers

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

True 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.

True Signup and view all the answers

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

False Signup and view all the answers

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

False Signup and view all the answers

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

True Signup and view all the answers

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

True 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.

True Signup and view all the answers

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

False Signup and view all the answers

The area of polygon WXYZ is 196 m².

False 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.

False Signup and view all the answers

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

True Signup and view all the answers

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

True Signup and view all the answers

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

False Signup and view all the answers

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

True Signup and view all the answers

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

False Signup and view all the answers

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

True Signup and view all the answers

The area of polygon WXYZ is 147 m².

True Signup and view all the answers

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

False Signup and view all the answers

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

True Signup and view all the answers

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

False Signup and view all the answers

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

True Signup and view all the answers

Match the following operations with their results:

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

Match the following pairs with their sum:

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

Match the following numbers with their product:

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

Match the following shapes with their areas:

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) = $25π cm^2$ Signup and view all the answers

Match the following sets of temperatures with their averages:

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

Match the following mathematical operations with their results:

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

Match the following geometric shapes with their areas:

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 Signup and view all the answers

Match the following pairs of numbers with their product:

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

Match the following sets of numbers with their sum:

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

Match the following groups of numbers with their average:

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

Match the following operations with their results:

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

Match the following pairs with their differences:

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

Match the following polygons with their areas:

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 Signup and view all the answers

Match the following pairs with their products:

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

Match the following sets of numbers with their averages:

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

Match the following numbers with their sum:

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

Match the following numbers with their difference:

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

Match the following pairs with the area of a polygon:

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 Signup and view all the answers

Match the following numbers with their product:

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

Match the following sets of numbers with their average:

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

Match the following pairs of numbers with their sum:

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

Match the following pairs of numbers with their difference:

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

Match the following pairs of numbers with their product:

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

Match the following pairs of numbers with their average:

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

Match the following pairs of numbers with their sum:

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

Match the following pairs of numbers with their difference:

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

Match the following pairs of numbers with their product:

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

Match the following pairs of numbers with their average:

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

Match the following numbers with their sum:

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

Match the following numbers with their difference:

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

Match the following pairs with their sum:

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

Match the following numbers with their product:

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

Match the following numbers with their sum:

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

Match the following numbers with their average:

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

Match the following pairs of numbers with their difference:

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

Match the following numbers with their product:

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

Match the following polygons with their area:

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 Signup and view all the answers

Match the following numbers with their average:

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 Signup and view all the answers

Geometry and Number Problems

Podcast Beta

Questions and Answers

In the sequence, the 259th letter is a ______

The probability that the arrow stops on the largest section is ______%

The 2022 Gauss Contest Solutions are found on Page ______

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

10 blocks of 26 letters gives a sequence of ______ letters

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

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

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

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

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 ___.

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

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

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

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

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

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

Ryan cut ___ of his lawn in 20 minutes.

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

Ryan finished cutting his lawn at ___ a.m.

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

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

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 ______

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

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

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

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).

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.

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 ___

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 ___

10 blocks of 26 letters gives a sequence of ___ letters

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

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

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

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

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

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 ___

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 ___

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

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

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

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

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

The area of polygon WXYZ is 147 m².

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The area of polygon WXYZ is 196 m².

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

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

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

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

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

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

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

The area of polygon WXYZ is 147 m².

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

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

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