1.
This train travels from London ______ Paris.
Correct Answer
B. To
Explanation
The correct answer is "to" because it indicates the destination or endpoint of the train's journey. In this case, the train travels from London to Paris, implying that Paris is the final destination of the train.
2.
We stood at the back ______ the theater.
Correct Answer
A. Of
Explanation
The correct answer is "of" because it is used to indicate a relationship or possession. In this sentence, "of" shows that we are standing at the back that belongs to or is associated with the theater.
3.
I will work _________ five o'clock.
Correct Answer
C. In
Explanation
The correct answer is "in" because when we say "I will work in five o'clock," it means that the person will start working at five o'clock.
4.
The antidote to these problems is hard to find:
Correct Answer
C. Remedy for
Explanation
The phrase "The antidote to these problems is hard to find" suggests that there are certain problems or issues that need to be addressed or resolved. However, finding a solution or remedy for these problems is difficult or challenging. The correct answer "Remedy for" aligns with this context, indicating that the problems mentioned require a solution or remedy, but it is not easily accessible or readily available.
5.
Because of a family feud, he never spoke to his aife's parents
Correct Answer
D. None of these
6.
The article is written in a very lucid style.
Correct Answer
B. Clear
Explanation
The correct answer is "Clear". This is because the statement "The article is written in a very lucid style" suggests that the article is written in a way that is easy to understand and comprehend. "Clear" is the most appropriate word choice to describe this type of writing style.
7.
. _________ man ran into the street. A car hit ____ man.
Correct Answer
C. The, the
Explanation
The correct answer is "the, the" because it is referring to a specific man and a specific car. "The" is used to indicate that the man and the car are known to the speaker and the listener.
8.
Albert Einstein was _____ famous scientist. Einstein won _______ Nobel Prize in Physics in 1921.Einstein left his country and lived in _______ States until he died in 1955.
Correct Answer
B. A, the, the
Explanation
Albert Einstein was a famous scientist. Einstein won the Nobel Prize in Physics in 1921. Einstein left his country and lived in the United States until he died in 1955.
9.
Are you shopping for ________ health club to join so you can get in shape? Shop wisely! You could end up choosing _______ wrong club and losing more money than pounds.
Correct Answer
C. A, the
Explanation
The correct answer is "A, the". The sentence is talking about shopping for a health club, which implies that there are multiple health clubs to choose from. Therefore, "a" is used to indicate that it is one of many options. However, when it comes to losing money, it suggests that there is a specific wrong club that could be chosen, hence "the" is used to specify that particular club.
10.
If f(x) = (x² -50), what is the value of f(-5)?
Correct Answer
B. 25
Explanation
To find the value of f(-5), we substitute -5 into the function f(x) = (x^2 - 50). Therefore, f(-5) = (-5^2 - 50) = (25 - 50) = -25. However, the given answer of 25 is incorrect.
11.
Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
Correct Answer
A. 10
Explanation
To find the number of helpers required, we need to calculate the total number of cakes each helper can make in 3 hours. Since each helper can make 2 large cakes per hour, in 3 hours they can make 6 large cakes. Similarly, each helper can make 35 small cakes per hour, so in 3 hours they can make 105 small cakes.
To meet the requirement of 20 large cakes, we would need 20/6 ≈ 3.33 helpers. Since we cannot have a fraction of a helper, we round up to 4 helpers.
To meet the requirement of 700 small cakes, we would need 700/105 ≈ 6.67 helpers. Again, we round up to 7 helpers.
Therefore, the maximum number of helpers required is 7.
Since the answer given is 10, it is incorrect.
12.
If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?
Correct Answer
D. F(3)
Explanation
Since the function f(x) is undefined for x = 2, we can evaluate the function for all the other given values.
f(-1) = (-1 + 2) / (-1 - 2) = 1/(-3) = -1/3
f(0) = (0 + 2) / (0 - 2) = 2/-2 = -1
f(1) = (1 + 2) / (1 - 2) = 3/-1 = -3
f(3) = (3 + 2) / (3 - 2) = 5/1 = 5
Out of the given values, f(3) has the greatest value of 5.
13.
A perfect cube is an integer whose cube root is an integer. For example, 27, 64, and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
Correct Answer
C. Pq + 27
Explanation
If p and q are perfect cubes, it means that their cube roots are integers. Multiplying two perfect cubes (pq) will also result in a perfect cube because the product of two integers is always an integer. Similarly, multiplying a perfect cube by 8 (8p) will also result in a perfect cube because 8 is a perfect cube itself. However, adding 27 to pq (pq + 27) will not necessarily result in a perfect cube because the sum of two perfect cubes is not guaranteed to be a perfect cube. Finally, negating a perfect cube (-p) will still result in a perfect cube because negating an integer does not change its perfect cube nature.
14.
A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?
Correct Answer
B. 9
Explanation
Each bow requires 15 inches of ribbon. Since there are 36 inches in a yard, this means each bow requires 15/36 = 5/12 yards of ribbon. Therefore, the maximum number of bows that can be made is 4 / (5/12) = 4 * (12/5) = 48/5 = 9.
15.
If V = 12R / (r + R) , then R =
Correct Answer
A. Vr / (12 -V)
Explanation
The given equation is V = 12R / (r + R). To solve for R, we need to isolate it on one side of the equation. By multiplying both sides of the equation by (r + R), we get V(r + R) = 12R. Expanding the equation, we get Vr + VR = 12R. Rearranging the terms, we have Vr = 12R - VR. Factoring out R on the right side, we get Vr = R(12 - V). Dividing both sides of the equation by (12 - V), we find R = Vr / (12 - V). Therefore, the correct answer is Vr / (12 - V).
16.
The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is?
Correct Answer
C. 75
Explanation
Between noon and 2.30 in the afternoon, the hour hand of a clock moves by an angle of 30 degrees per hour. Since there are 2.5 hours between noon and 2.30, the hour hand would have moved by 30 degrees per hour * 2.5 hours = 75 degrees.
17.
(3x + 2) (2x -5) = ax² + kx + n .What is the value of a -n + k ?
Correct Answer
A. 5
Explanation
The given expression is a product of two binomials. When we expand the expression, we get 6x^2 - 15x + 4x - 10. Simplifying further, we get 6x^2 - 11x - 10. Comparing this with the given expression ax^2 + kx + n, we can see that a = 6, k = -11, and n = -10. Therefore, a - n + k = 6 - (-10) + (-11) = 16 - 11 = 5.
18.
If the radius of a circle is increased by 20% then the area is increased by:
Correct Answer
A. 44%
Explanation
When the radius of a circle is increased by 20%, the area of the circle is increased by a factor of the square of the radius. Since the area is proportional to the square of the radius, a 20% increase in the radius will result in a (1.2)^2 = 1.44 or 44% increase in the area. Therefore, the correct answer is 44%.
19.
If the area of two circles are in the ratio 169 : 196 then the ratio of their radii is
Correct Answer
D. 13 : 14
Explanation
The ratio of the areas of two circles is equal to the square of the ratio of their radii. Therefore, if the area ratio is 169 : 196, the square root of this ratio gives us the ratio of the radii. Taking the square root of both numbers, we get √169 : √196 which simplifies to 13 : 14.
20.
Statement: It is desirable to put the child in school at the age of 5 or so.
Assumptions:
I At that age the child reaches appropriate level of development and is ready to learn.
II The schools do not admit children after six years of age.
Correct Answer
A. If only I is implicit ;
Explanation
The given statement suggests that it is desirable to enroll a child in school at the age of 5 or so. Assumption I states that at this age, the child reaches an appropriate level of development and is ready to learn. This assumption is implicit because it supports the idea that starting school at this age is beneficial for the child's educational development. Assumption II, on the other hand, states that schools do not admit children after six years of age. This assumption is not implicit because the statement does not provide any information about the admission age criteria of schools.