Question 1

Find the temperature after a rise of 10 ºС from - 11 ºС . ​
A) 21 ºС
B) -21 ºС
C) -20 ºС
D) -22 ºС
E) -1 ºС

Accepted Answer

When the temperature rises by 10 ºС from -11 ºС, it reaches -1 ºС (-11 ºС + 10 ºС = -1 ºС).

Question 2

A temperature measurement from the Earth's stratosphere is taken as - 68 ° F . The temperature on the Earth's surface below is found to be 40 ° F . Find the difference between the surface temperature reading and the stratosphere temperature reading. ​
A) 108 ° F
B) -28 ° F
C) -29 ° F
D) 29 ° F
E) 28 °F

Accepted Answer

The difference is calculated by subtracting the stratosphere temperature from the surface temperature: 40 °F - (-68 °F) = 40 °F + 68 °F = 108 °F.

Question 3

Subtract: ​  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Subtract: ​  ​
A) 
B) 
C) 
D)...

Question 4

The GCF of two numbers m and n is 32 , their LCM is 64 , and both m and n are less than 79 . Find m and n. ​
A) m = 32 and n = 64
B) m = 37 and n = 128
C) m = 32 and n = 128
D) m = 64 and n = 59
E) m = 64 and n = 64

Accepted Answer

The GCF (Greatest Common Factor) of m and n is 32, and their LCM (Least Common Multiple) is 64. The product of the GCF and LCM of two numbers is equal to the product of the numbers themselves. Therefore, $m \times n = 32 \times 64$. The only pair that satisfies this condition and where both numbers are less than 79 is m = 32 and n = 64.

Question 5

The Crabby Apple restaurant lost $2000 in the month of January. If their net worth at the end of the month is -$200, what was their net worth at the beginning of the month? ​
A) $2200
B) -$2200
C) -$2000
D) $200
E) $1800

Accepted Answer

The answer of The Crabby Apple restaurant lost $2000 in...

Question 6

The GCF of 114 and x is 38; the LCM of 114 and x is 228. Find x . ​
A) x = 71
B) x = 152
C) x = 722
D) x = 76
E) x = 80

Accepted Answer

The GCF (Greatest Common Factor) of 114 and x is 38, which means 38 is the highest number that divides both 114 and x without leaving a remainder. Since 114 is divisible by 38, we can find that 114 = 38 * 3. For the LCM (Least Common Multiple) of 114 and x to be 228 and the GCF to be 38, x must be a number that when multiplied by 114 through their lowest common multiple gives 228, and when divided by their greatest common factor gives 38. The LCM of two numbers a and b is given by (a*b)/GCF(a,b). Here, we know the LCM (228), and we know the GCF (38), so we can solve for x in the equation (114*x)/38 = 228. Simplifying this gives x = 76.

Question 7

Two mechanical shafts are joined together at their ends. Together, their total length is  ft. If one shaft is  ft long, how long must the other shaft be? ​
A)  ft
B)  ft
C)  ft
D)  ft
E)  ft

Accepted Answer

The answer of Two mechanical shafts are joined together at...

Question 8

Using Pattern Blocks, if hexagon + triangle =  , then what is the value of trapezoid? ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Accepted Answer

The answer of Using Pattern Blocks, if hexagon + triangle...

Question 9

The GCF of two numbers is 21 . Their LCM is 357 . What are the two numbers? ​
A) 21 and 357
B) 19 and 355
C) 42 and 355
D) 22 and 358
E) 42 and 714

Accepted Answer

The answer of The GCF of two numbers is 21...

Question 10

Fred has 6-gallon tanks and George has 5-gallon tanks. They both purchased the same amount of gasoline to fill their tanks. What is the smallest amount of gasoline they could have purchased? ​
A) 12 gallons
B) 60 gallons
C) 90 gallons
D) 30 gallons
E) 10 gallons

Accepted Answer

To find the smallest amount of gas they could have purchased, we need to find the greatest common divisor (GCD) of 6 and 5, which is 1. This means that they would need to purchase enough gasoline to fill both tanks to a multiple of 1 gallon. The smallest such multiple that is greater than or equal to both tank sizes is 30 gallons. Therefore, the smallest amount of gasoline they could have purchased is 30 gallons.

Question 11

During a card game of Hearts, Nick had a score of 25 points before his opponent "shot the moon," subtracting a score of 26 from Nick's total. What was Nick's score after his opponent "shot the moon"? ​
A) -51
B) 51
C) -1
D) 50
E) 1

Accepted Answer

The answer of During a card game of Hearts, Nick...

Question 12

Use each of these numbers exactly once to make the following equation true: 1, 2, 3, 5, 44 , 60 . Answers may vary. ​  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

One possible equation that can be created using these numbers is 60/5 + 2 x 44 - 3 = 87. This equation uses each of the given numbers exactly once and solves to be true. Choice D is the only option that includes the number sequence used in this equation.

Question 13

Find the least common multiple (LCM) of the numbers 12, 16, 14. ​
A) 168
B) 12
C) 2
D) 1
E) 336

Accepted Answer

To find the LCM of 12, 16, and 14, we need to factor each number into its prime factors:
12 = 2^2 * 3
16 = 2^4
14 = 2 * 7

Now, we first need to identify the highest power of each prime factor that occurs in any of the given numbers. In this case, the highest power of 2 is 2^4, the highest power of 3 is 3^1, and the highest power of 7 is 7^1.

Next, we multiply these highest powers of prime factors:
2^4 * 3^1 * 7^1 = 336

Therefore, the least common multiple of 12, 16, and 14 is 336, which is option E.

Question 14

Sam was told by the doctor that he had to lose about 40 pounds. Six weeks ago he weighed 190 pounds. Below is a weekly record of his progress. How much does he weigh now? ​  ​ ​
A) 179 pounds
B) 181 pounds
C) 173 pounds
D) 150 pounds
E) 170 pounds

Accepted Answer

The answer of Sam was told by the doctor that...

Question 15

A plane flying at its maximum speed can go 220 miles per hour with a tailwind or 160 miles per hour into a headwind. What is the wind speed? ​
A) 30 miles per hour
B) 35 miles per hour
C) 160 miles per hour
D) 60 miles per hour
E) 25 miles per hour

Accepted Answer

Let's represent the speed of the plane as "p" and the speed of the wind as "w".

With the tailwind, the speed of the plane is p+w=220. 
With the headwind, the speed of the plane is p-w=160.

We can set up a system of equations:
p+w=220
p-w=160

We can solve for p by adding the two equations:
2p=380
p=190

Now we can substitute p=190 into one of the equations to solve for w:
190+w=220
w=30

Therefore, the wind speed is 30 miles per hour.

Question 16

Find the least common multiple (LCM) of the numbers 12 , 16 . ​
A) 48
B) 4
C) 1
D) 12
E) 192

Accepted Answer

The least common multiple (LCM) of 12 and 16 is found by identifying the highest power of prime factors in each number (12 = 2^2 * 3, 16 = 2^4), then multiplying these highest powers together. The LCM is 2^4 * 3 = 16 * 3 = 48.

Question 17

The elevation, or height, of places on Earth is measured in relation to sea level, or the average level of the ocean's surface. The table below shows heights above sea level as a positive number and depth below sea level as a negative number. Find the difference in elevation between Mt. Everest and the the Dead Sea . 
A) -9360 m
B) -9260 m
C) 9360 m
D) 9261 m
E) 9258 m

Accepted Answer

According to the table, the elevation of Mt. Everest is 8,848 meters and the depth of the Dead Sea is -422 meters. To find the difference in elevation, we subtract the two values: 8,848 - (-422) = 9,270 meters. Therefore, the answer is D) 9261 m, which is the closest to 9,270.

Question 18

A plane flying at its maximum speed can go 250 miles per hour with a tailwind or 160 miles per hour into a headwind. What is the plane's maximum speed with no wind? ​
A) 160 miles per hour
B) 125 miles per hour
C) 45 miles per hour
D) 250 miles per hour
E) 205 miles per hour

Accepted Answer

We can solve this problem by using the formula:

Speed with no wind = (Speed with tailwind + Speed with headwind) / 2

Plugging in the given values, we get:

Speed with no wind = (250 + 160) / 2
Speed with no wind = 205 miles per hour

Therefore, the plane's maximum speed with no wind is 205 miles per hour, which is option E.

Question 19

Add: - 20 + (- 8 ) ​
A) 12
B) -12
C) 28
D) -29
E) -28

Accepted Answer

To add a negative integer, we can think of it as subtracting the absolute value of that integer. 
-20 + (-8) becomes -20 -8 = -28. Therefore, the answer is E) -28.

Quiz 3: Understanding Addition and Subtraction

Find the temperature after a rise of 10 ºС from - 11 ºС . ​

A temperature measurement from the Earth's stratosphere is taken as - 68 ° F . The temperature on the Earth's surface below is found to be 40 ° F . Find the difference between the surface temperature reading and the stratosphere temperature reading. ​

Subtract: ​ ​

The GCF of two numbers m and n is 32 , their LCM is 64 , and both m and n are less than 79 . Find m and n. ​

The Crabby Apple restaurant lost $2000 in the month of January. If their net worth at the end of the month is -$200, what was their net worth at the beginning of the month? ​

The GCF of 114 and x is 38; the LCM of 114 and x is 228. Find x . ​

Two mechanical shafts are joined together at their ends. Together, their total length is ft. If one shaft is ft long, how long must the other shaft be? ​

Using Pattern Blocks, if hexagon + triangle = , then what is the value of trapezoid? ​

The GCF of two numbers is 21 . Their LCM is 357 . What are the two numbers? ​

Fred has 6-gallon tanks and George has 5-gallon tanks. They both purchased the same amount of gasoline to fill their tanks. What is the smallest amount of gasoline they could have purchased? ​

During a card game of Hearts, Nick had a score of 25 points before his opponent "shot the moon," subtracting a score of 26 from Nick's total. What was Nick's score after his opponent "shot the moon"? ​

Use each of these numbers exactly once to make the following equation true: 1, 2, 3, 5, 44 , 60 . Answers may vary. ​ ​

Find the least common multiple (LCM) of the numbers 12, 16, 14. ​

Sam was told by the doctor that he had to lose about 40 pounds. Six weeks ago he weighed 190 pounds. Below is a weekly record of his progress. How much does he weigh now? ​ ​ ​

A plane flying at its maximum speed can go 220 miles per hour with a tailwind or 160 miles per hour into a headwind. What is the wind speed? ​

Find the least common multiple (LCM) of the numbers 12 , 16 . ​

A plane flying at its maximum speed can go 250 miles per hour with a tailwind or 160 miles per hour into a headwind. What is the plane's maximum speed with no wind? ​

Add: - 20 + (- 8 ) ​

Find the temperature after a rise of 10 ºС from - 11 ºС .

A temperature measurement from the Earth's stratosphere is taken as - 68 ° F . The temperature on the Earth's surface below is found to be 40 ° F . Find the difference between the surface temperature reading and the stratosphere temperature reading.

Subtract:

The GCF of two numbers m and n is 32 , their LCM is 64 , and both m and n are less than 79 . Find m and n.

The Crabby Apple restaurant lost $2000 in the month of January. If their net worth at the end of the month is -$200, what was their net worth at the beginning of the month?

The GCF of 114 and x is 38; the LCM of 114 and x is 228. Find x .

Two mechanical shafts are joined together at their ends. Together, their total length is ft. If one shaft is ft long, how long must the other shaft be?

Using Pattern Blocks, if hexagon + triangle = , then what is the value of trapezoid?

The GCF of two numbers is 21 . Their LCM is 357 . What are the two numbers?

Fred has 6-gallon tanks and George has 5-gallon tanks. They both purchased the same amount of gasoline to fill their tanks. What is the smallest amount of gasoline they could have purchased?

During a card game of Hearts, Nick had a score of 25 points before his opponent "shot the moon," subtracting a score of 26 from Nick's total. What was Nick's score after his opponent "shot the moon"?

Use each of these numbers exactly once to make the following equation true: 1, 2, 3, 5, 44 , 60 . Answers may vary.

Find the least common multiple (LCM) of the numbers 12, 16, 14.

Sam was told by the doctor that he had to lose about 40 pounds. Six weeks ago he weighed 190 pounds. Below is a weekly record of his progress. How much does he weigh now?

A plane flying at its maximum speed can go 220 miles per hour with a tailwind or 160 miles per hour into a headwind. What is the wind speed?

Find the least common multiple (LCM) of the numbers 12 , 16 .

A plane flying at its maximum speed can go 250 miles per hour with a tailwind or 160 miles per hour into a headwind. What is the plane's maximum speed with no wind?

Add: - 20 + (- 8 )