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?

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

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

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.

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,

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

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