1.
If #x = x/4, what is the product of #5 and #8?
Correct Answer
B. 2.5
Explanation
To find the product of #5 and #8, we need to substitute the values of #5 and #8 into the equation #x = x/4.
#5 = 5/4 = 1.25
#8 = 8/4 = 2
Now, we can multiply #5 and #8: 1.25 * 2 = 2.5. Therefore, the product of #5 and #8 is 2.5.
2.
Cody has a box of cereal. On Monday, he ate 1/7 of the cereal. On Tuesday, he ate 1/6 of the remaining cereal. What fraction of the cereal is now left in the box?
Correct Answer
C. 5/7
Explanation
Cody ate 1/7 of the cereal on Monday, which means that 6/7 of the cereal is still left. On Tuesday, he ate 1/6 of the remaining cereal, which is 1/6 * 6/7 = 1/7 of the total cereal. Therefore, after Tuesday, there is 6/7 - 1/7 = 5/7 of the cereal left in the box.
3.
Julie is half as old as Benita. If Benita will be 24 years old in 8 years, how old was Julie 3 years ago?
Correct Answer
B. 5
Explanation
If Benita will be 24 years old in 8 years, it means that currently Benita is 24 - 8 = 16 years old. Since Julie is half as old as Benita, Julie is 16 / 2 = 8 years old. Therefore, 3 years ago, Julie was 8 - 3 = 5 years old.
4.
Tia has a box containing 15 blue marbles, 12 green marbles, 7 red marbles, and 1 white marble. Tia removed 8 marbles, 6 of which were blue. If she removes one more marble at random, what is the probability that it will be blue?
Correct Answer
A. 1/3
Explanation
Tia initially had a total of 15 + 12 + 7 + 1 = 35 marbles in the box. She removed 8 marbles, 6 of which were blue. After removing 8 marbles, there are now 35 - 8 = 27 marbles left in the box. Out of these 27 marbles, there are still 15 blue marbles remaining. Therefore, the probability of randomly selecting a blue marble is 15/27, which simplifies to 5/9.
5.
Lance is 39 years old. Ted is 22 years old. Rose is 45 years old. How old is Eric if the mean age of the four friends is 33.5?
Correct Answer
B. 28
Explanation
The mean age of the four friends is calculated by adding up their ages and dividing by the number of friends. In this case, the sum of their ages is 39 + 22 + 45 + Eric's age. Since the mean age is given as 33.5, we can set up the equation (39 + 22 + 45 + Eric's age) / 4 = 33.5. Solving this equation, we find that Eric's age is 28.
6.
Melissa uses 3/5 as much water as Neil to water her plants. If Melissa uses 4 and 1/3 gallons of water, how much does Neil use?
Correct Answer
E. 7 and 2/9 gallons
Explanation
If Melissa uses 3/5 as much water as Neil, and Melissa uses 4 and 1/3 gallons of water, we can set up a proportion to find out how much Neil uses. Let's call Neil's water usage "x". The proportion would be (3/5)x = 4 and 1/3. To solve for x, we can multiply both sides of the equation by the reciprocal of 3/5, which is 5/3. This gives us x = (4 and 1/3) * (5/3) = 21/3 = 7. Therefore, Neil uses 7 gallons of water. Since Neil uses 7 gallons and 2/9 gallons is less than 1 gallon, the correct answer is 7 and 2/9 gallons.
7.
What is product of the square root of 9 and the square root of 49?
Correct Answer
A. 21
Explanation
The product of the square root of 9 and the square root of 49 can be calculated by multiplying the two square roots together. The square root of 9 is 3, and the square root of 49 is 7. Therefore, the product of the two square roots is 3 * 7 = 21.
8.
What is the greatest common factor of 135 and 210?
Correct Answer
D. 15
Explanation
The greatest common factor (GCF) is the largest number that divides evenly into both numbers. To find the GCF of 135 and 210, we can list the factors of each number and find the largest one they have in common. The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. The largest factor they have in common is 15, so the GCF of 135 and 210 is 15.
9.
A group of tourists is being led through a famous cathedral by a guide. One family of four is Japanese, but at least three other tourists in the group are not. All but five of the group are Americans. What is the least number of tourists that can be in this group?
Correct Answer
C. 7
Explanation
The least number of tourists that can be in this group is 7. This is because there are at least three tourists who are not Japanese, which means there are at least three non-Japanese tourists in addition to the Japanese family of four. Additionally, all but five of the group are Americans, which means there are at least two non-American tourists in the group. Therefore, the minimum number of tourists in the group is 7.
10.
In a foreign language, "nyeer cog joch" means "big yellow taxi," "shaw joch" means "big house," and "nyeer deniro" means "taxi driver."Which word means yellow?
Correct Answer
D. Cog
Explanation
Based on the given information, "nyeer cog joch" means "big yellow taxi" and "shaw joch" means "big house." Since "cog" is the only word that appears in the phrase "nyeer cog joch" and does not appear in any other phrases, it can be inferred that "cog" means "yellow."
11.
All actors are friendly.Some writers are actors.No doctor is a writer.If all of the above statements are true, which of the following must also be true?
Correct Answer
E. Some friendly people are writers.
Explanation
The given statements imply that all actors are friendly and some writers are actors. Therefore, it can be concluded that some friendly people are writers, as the actors who are friendly can be considered as friendly people, and some of them are also writers according to the given information.