General Aptitude Test 2

The correct answer is option 4), i.e. If I were the manager, I would try to solve the problems.

Explanation:

• Option 1) is incorrect. It is a second conditional sentence and that is why 'would' should be written here instead of 'will'.
• Option 2) is incorrect. The sentence is expressing a situation that is not true. So, 'were' should be written instead of 'was'. 
• Option 3) is incorrect. 'Would' must be added before the word 'try'.
• Option 4) is the correct sentence.

• In a second conditional sentence two ideas are given and both of these are not true.  It may express something which may not happen in future.
  • Example: If I knew the fact,I would inform you.
  • Simple past tense is used in the first part of the sentence and 'would' is used in the second part.
     
• Use 'were' if the state of being you are describing is in no way the current reality. This is true whenever a hypothetical situation is expressed, for example. 
  • Example: Would you invite me over if I were more polite at the dinner table?

To find the missing number in the sequence, we first need to identify the pattern. Let's analyze the given numbers:

Observe that each ratio decreases by 1 as we move through the sequence: 6, 5, 4, 3, 2. If this pattern continues, the next ratio should be 1. Therefore, the next term should be:

So, the missing term is:

1440

Thus, the correct option is:

Option B 1440

Let’s label the four seats around the square as North, East, South and West, with everyone facing the center.

Place Murali at North.

“Rahul is to the left of Murali.”

Facing inward at North, Murali’s left is West → Rahul sits at West.

The remaining seats are East and South for Arul and Srinivas.

“Srinivas is to the right of Arul.”

If Arul sat at East, his right (facing inward) is South → Srinivas sits at South, Arul at East.

Final seating:

North: Murali

East: Arul

South: Srinivas

West: Rahul

Opposite pairs on a square are North–South and East–West.

Here, North–South is Murali–Srinivas.

Answer: Option C (Srinivas and Murali).

The correct answer is Option 2 i.e Agree with

Explanation:

Let's look at the meaning of the underlined word and the marked option.

• Conform: Comply or agree with(rules, standards.)
• Agree with: To comply with something. 

Thus, it is clear that both words have a similar meaning and are synonyms. 

Let's look at the meanings of other words:

• Understand: Perceive the intended meaning. 
• Accept: Consent to receive or undertake something. 
• Rely on: To depend on something or someone. 

The correct answer is Option 1 i.e Opaque

Explanation:

Let's look at the meaning of the underlined word and the marked option.

• Transparent: Able to see through.
• Opaque: Not able to see through.

Thus, it is clear that both words have the opposite meaning and are antonyms

Let's look at the meanings of other words:

• Hard: Solid, firm, rigid. 
• Thin: With little thickness or depth; slim. 
• Clear: Easy to perceive; transparent. 

Option 2 is the correct solution

Pull its trigger means To make a final decision or commit to a certain course of action (about something).
Example- If we don't pull the trigger on this deal then we might never get the chance again.
Additional information: 'on the card' is another idiom in the sentence which means likely to happen.

Given: f(x) = number of prime numbers less than x

The number of prime numbers less than 100 can be written as:

Prime numbers less than 20 = 2, 3, 5, 7, 11, 13, 17, 19

Prime numbers between 20 and 40 = 23, 29, 31, 37

Prime numbers between 40 and 60 = 41, 43, 47, 53, 59

Prime numbers between 60 and 80 = 61, 67, 71, 73, 79

Prime numbers between 80 and 100 = 83, 89, 97

f(100) = Number of prime numbers less than 100 = 25

Now, f(f(100)) = f(25) = Number of prime numbers less than 25 = 9

Using two fifties: There is only one possibility, 50 + 50 + 7

Using one fifty: We can use at max five tens. So, the number of possibilities = 6

Using no fifties: We can use at max ten tens. So, the number of possibilities = 11

We are given that

holds for all real values of x. To determine when this is true, follow these steps:

Multiply both sides by e^x to eliminate the negative exponent:

Notice that the left-hand side, Pe^2x, depends on x (since e^2x is not a constant function), while the right-hand side, Q, is independent of x.

For the equality to hold true for all real values of x, the only possibility is that the coefficient P must be zero. Otherwise, Pe^2x would take different values as x changes.

Bags x and y are equally likely to be selected.

The probability of selecting a red ball = probability of selecting a red ball from bag x + probability of selecting a red ball from bag y.

Probability of selecting a red ball from bag x = probability of selecting bag x × probability of selecting red ball from it = 1/2 × 3/8 = 3/16

Probability of selecting a red ball from bag y = probability of selecting bag y × probability of selecting red ball from it = 1/2 × 4/8 = 4/16

Probability that the ball drawn is red = 3/16 + 4/16 = 7/16

Let's analyze each option one by one.

The product of two primes, where each prime is at least 2, will always have factors other than 1 and itself (namely, the primes themselves).

To determine the number of attempts each wizard makes, we need to calculate the number of possible permutations of the four elements: water, air, fire, and earth. A permutation is an arrangement of all the elements in a specific order. The number of permutations of n elements is given by the factorial of n, which is denoted as n!.

In this case, there are 4 elements. Thus, we need to find 4! (4 factorial):

Therefore, the number of possible permutations of the four elements is 24.

Since the wizards work independently, each wizard will try all 24 permutations by themselves.

Thus, the answer is: Option A: 24

The correct answer is option 2.

Explanation:

Let us look at the relevance of each and every option as per the lines given in the question.

• Option 1 is merely a restatement and not an inference.
• Option 3 is also a restatement.
• Option 4 is not an inference as sufficient data is not provided. The causal AI system was tested in a small, controlled trial where it outperformed real doctors. This doesn't mean that it will be able to outperform doctors in any given scenario.
• Option 2 is the correct answer. It is said in the passage that the new AI system relies on causation and not correlation and it is more accurate than pre-existing AI systems. From this, we can conclude option 2.

Hence, only option 2 can be inferred from the given sentences.

• Option 1 is merely a restatement of what is said in the question. It is not an inference.
• We cannot infer if this is the first time such companies are facing a huge demand for their software. They might have/might not have faced bigger demands before. Hence option 2 is also rejected. 
• Option 4 is also a general observation and restatement of what is said in the question. It has already been mentioned that the hard-line measures adopted by Beijing were met with "little resistance". This means that the citizens couldn't protest much.
• Option 3 is the correct answer. Since it is mentioned that provincial governments, companies, and residential complexes have brought into play/deployed facial recognition software to battle Covid-19, we can arrive at the conclusion that the companies that provide this software are doing well/thriving in this Covid-19 era. 

The correct answer is option 2.

Explanation:

• First is the Federal Reserve’s decision to increase its requirements for money in reserve. 
• This led to a sharp recession.
• Next is the improvement in the economy in 1938.
• Last is the prolonged effects of the Great Depression.

The correct answer is option 3.

Explanation:

• Firstly the terrorists hijack four US planes.
• Next Bush announces that war on terror begins.
• After that Defense Secretary announces the anti-terror campaign.
• Following this, the diplomatic ties between Saudi Arabia and Afghanistan ended

Let's denote the sets as follows:

- Let A be the set of students who like their core branches.

- Let B be the set of students who like other branches.

- Let | A ∩ B | = 500 be the number of students who like both their core and other branches.

- Let | A ∪ B | be the total number of students who like at least one of their core branches or other branches.

- We know the number of students who like neither their core branches nor other branches is 1,500.

- The total number of students is 10,000.

The total can be given by:

So, the number of students who like their core branches is 1,800, which corresponds to Option A.

To find the value of x in the sequence 6, 9, 14, x, 30, 41, let's analyze the differences between consecutive terms. This approach will help us identify any pattern that might exist.

First, let's calculate the differences between the given terms:

For the first pair (6 and 9):

9 - 3 = 3

For the second pair (9 and 14):

14 - 5 - 9

Notice that the differences so far are 3 and 5. Let's assume that the sequences of differences follow an arithmetic pattern with common differences (an increasing pattern of increments). If this trend continues, the next difference should be greater by 2 compared to the previous difference of 5, which makes it:

To verify if this hypothesis holds, we can check the following term differences:

For the pair (21 and 30):

30 - 21 - 9

For the pair (30 and 41):

41 - 30 = 11

Here we observe that the differences (3, 5, 7, 9, and 11) follow an arithmetic pattern of increasing by 2 each time. This confirms our assumption that x should be 21. Therefore, the possible value of x is:

Option B: 21

Scenario: The escalator is moving with its usual speed, addition to which the person steps down.

Analysis:

Let us calculate the speed of the escalator in terms of the number of steps elapsed to get to the bottom.

Let in 1 sec, the number of steps elapsed be x.

In 30 sec, the number of steps elapsed will be 30x.

Similarly, in 18 sec, the number of steps elapsed will be 18x.

In addition to this, the man has stepped down in order to reach earlier as compared to the normal case.

Since the total number of steps elapsed in both cases will be the same, we can write:

26 + 30x = 34 + 18x

\(x=\frac{2}{3}~steps\)

∴ The number of steps in the escalator will be:

\(x =26+30\times (\frac{2}{3})\)

x = 46

From the given data, we can conclude:

1) Prem scored 1 run in Prashant's over, i.e. Prashant conceded 1 run to Prem.

2) Prashant scored 2 runs in Prabhu's over, i.e. Prabhi conceded 2 runs to Prashant.

3) Prabhu scored 5 runs in Prince's over, i.e. Prince conceded 5 runs to Prabhi

Given: Prince neither scored 3 runs nor conceded 3 runs. Prem did not bowl to Prince. From this, we can conclude that:

4) Prnce scored 4 runs in Piyush's over, i.e. Piyush conceded 4 runs to Prince.

5) Piyush scored 3 runs in Prem's over, i.e. Prem conceded 3 runs to Piyush

∴ Statement in Option (3) is not correct.

Scenario:

We observe that each letter is written the times as the letter’s serial number in alphabets.

The series consists of alphabets in the following manner:

A (1^st in series), 2 times B (2^nd, 3^rd), 3 times C (4^th,5^th, 6^th), 4 times D (7^th, 8^th, 9^th, 10^th) and so on….…

Each letter is written the times as the letter’s serial number in alphabets. Also, If the serial number of letters in alphabets is n, after writing n times the number of letters in the series follows the pattern \(\frac{n(n+1)}{2}\).

Example: After writing last D which is 10^th number in the series and 4^th number in alphabets written 4 times, the pattern satisfies, i.e.

\(10=\frac{4(4+1)}{2}\)

Analysis:

Now, the 240^th number may be the end of a letter, or may be repetition of a letter at any position, but still, the following equality will hold true:

\(\frac{n(n+1)}{2}≤ 240\)

n (n + 1) ≤ 480

The maximum value of n for which this equality holds true is n = 21, i.e.

\(\frac{21(21+1)}{2} = 231\)

∴ The 21^st number in alphabets after writing 21 times will give 231^st number in the series which is U. V is 22^nd number in the alphabets which is written 22 times.

But since 240 - 231 = 9, after “U”, the 9^th letter in series will be “V” as “V” is written 22 times.

∴ The 240^th letter is “V”.

The rectangular sheet is transformed into curved surface of a right circular cylinder in two ways either by rolling along its length or along its breadth.

Case 1: The sheet is rolling along its length

In this case, it forms a cylinder having height h₁ = 18 cm and the circumference of its base equal to 30 cm.

Let the radius of its base is r₁

Circumference = 2πr₁ = 30

⇒ r₁ = 15/π

Volume of cylinder \({V_1} = \pi r_1^2{h_1}\)

\( = \pi {\left( {\frac{{15}}{\pi }} \right)^2} \times 18 = \frac{{4050}}{\pi }c{m^3}\)

Case 2: The sheet is rolling along its length

In this case, it forms a cylinder having height h₁ = 30 cm and the circumference of its base equal to 18 cm.

Let the radius of its base is r₂

Circumference = 2πr₂ = 18

⇒ r₂ = 9/π

Volume of cylinder \({V_2} = \pi r_2^2{h_2}\)

\( = \pi {\left( {\frac{9}{\pi }} \right)^2} \times 30 = \frac{{2430}}{\pi }c{m^3}\)

Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle.

Let the radius of the circular track = r

When A reaches the point diametrically opposite to his starting point, he meets B.

The length covered by A = πr

Since B was initially ahead of A by 30°, for 180° movement of A, B covered 150°.

For a 180° movement, the length covered is πr.

For 1° movement, the length covered is: πr/180

For 150° movement, the length covered will be:

\(\frac{\pi r}{180^o}\times 150^o=\frac{5\pi r}{6}\)

Let the speed of A is S_A and the speed of B is S_B

As both A and B traveled for the same time,

\(\frac{{π r}}{{{S_A}}} = \frac{{\frac{5}{6}π r}}{{{S_B}}}\)

\( \Rightarrow \frac{{{S_B}}}{{{S_A}}} = \frac{6}{5}\)

The correct answer is option 2 i.e. only (ii).

Explanation:

• For statement (i), we need to relate oceans and ponds. The common link between the two is the connection with a lake.
• Since no ocean is a lake, we cannot say that all oceans are ponds.
• For statement (ii), we need to relate water body and lake. The common link between the two is the connection with an ocean. 
• Since every water body is an ocean and no ocean can be a lake, no water body can be a lake.

Clearly, only statement (ii) can be inferred.