Instructions

For the following questions answer them individually

Question 21

An encryption system operates as follows:

Step 1. Fix a number k $$(k \leq 26)$$.

Step 2. For each word, swap the first k letters from the front with the last k letters from the end in reverse order. If a word contains less than 2k letters, write the entire word in reverse order.

Step 3. Replace each letter by a letter k spaces ahead in the alphabet. If you cross Z in the process to move k steps ahead, start again from A.

Example: k = 2: zebra --> arbez --> ctdgb.

If the word “flight” becomes “znmorl” after encryption, then the value of k:

Video Solution

Solution

Flight become znmorl

Let's assume $$k>3$$

So flight will become thgilf -> znmrol. Hence the value of k will be 6

Instructions

Read the following scenario and answer the three questions that follow.
The following plot describes the height (in cm), weight (in kg), age (in years) and gender (F for female, M for male) of 20 patients visiting a hospital.

A person’s body mass index (BMI) is calculated as weight (in kg) divided by squared height (measured in square metres). For example, a person weighing 100 kg and of height 100 cm (1m) will have a BMI of 100. A person with BMI less than or equal to 18.5 is considered as underweight, above 18.5 but less than or equal to 25 as normal weight, above 25 but less than or equal to 30 as overweight, and above 30 as obese.

Question 22

The average age of the female patients who weigh 50 kg or above is approximately

Video Solution

Solution

There are 5 ladies whose weights are 50 or above

There ages are 50,50, 70,60 and 80

Average = 310/5 = 62

Question 23

The highest BMI among all patients is approximately

Video Solution

Solution

For the highest BMI, weight should be as high as possible and height as little as possible.

Hence it is possible with the person with a weight of 69 kg and a height of 1.6m

His BMI will be $$\frac{69}{\left(1.6\right)^2}=27$$

Question 24

The BMI of the oldest person considered as normal weight is approximately

Video Solution

Solution

The BMI of 1st oldest person= $$\frac{40}{\left(1.5\right)^2}=\ 17.77$$

The BMI of next oldest person = $$\frac{61}{\left(1.75\right)^2}=19.9$$

Instructions

For the following questions answer them individually

Question 25

The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?

Video Solution

Solution

Let ED = $$\sqrt{\ 3}x$$
In triangle CDE, $$\tan\ 30\ =\ \frac{CD}{\sqrt{\ 3}x}$$ => CD = x

In triangle BDE, $$\tan\ 45\ =\ \frac{BD}{\sqrt{\ 3}x}$$ => BD = $$\sqrt{\ 3}x$$ => BC = $$\sqrt{\ 3}x\ -x$$

In triangle ADE, $$\tan\ 60\ =\ \frac{AD}{\sqrt{\ 3}x}$$ => AD = 3x => AB = $$3x\ -\ \sqrt{\ 3}x$$

AB : BC : CD = $$(3 - \sqrt 3) : (\sqrt 3 - 1) : 1$$

Question 26

Two circles P and Q, each of radius 2 cm, pass through each other’s centres. They intersect at points A and B. A circle R is drawn with diameter AB. What is the area of overlap (in square cm) between the circles R and P?

Video Solution

Solution

We know that radius of circle P is 2 cm

Length of MO = 1 cm

radius of circle R = AO = $$\sqrt{\ 2^2-1^2}$$ = $$\sqrt{\ 3}$$

Area of overlap between the circle R and P(shaded region) = semi circle area of R + area of segment ANBOA

Area of segment ANBOA = area of sector ANBM - area of triangle AMB

= $$\frac{120}{360}\pi\ \left(2\right)^2$$ - $$\frac{1}{2}\left(1\right)\left(2\sqrt{\ 3}\right)$$

= $$\frac{4\pi}{3}-\sqrt{\ 3}$$

Area of overlap between circle R and P = $$\frac{\pi\ \left(\sqrt{\ 3}\right)^2}{2}$$+ $$\frac{4\pi}{3}-\sqrt{\ 3}$$

= $$\ \frac{\ 17\pi\ }{6}-\sqrt{\ 3}$$

Answer is option E.

Question 27

Four friends, Ashish, Brian, Chaitra, and Dorothy, decide to jog for 30 minutes inside a stadium with a circular running track that is 200 metres long. The friends run at different speeds. Ashish completes a lap exactly every 60 seconds. Likewise, Brian, Chaitra and Dorothy complete a lap exactly every 1 minute 30 seconds, 40 seconds and 1 minute 20 seconds respectively. The friends begin together at the start line exactly at 4 p.m. What is the total of the numbers of laps the friends would have completed when they next cross the start line together ?

Video Solution

Solution

All the four friends will meet at the starting point after LCM(60,90,40,80) = 720 seconds.

Number of laps by A in 720 seconds = 12

Number of laps by B in 720 seconds = 8

Number of laps by C in 720 seconds = 18

Number of laps by D in 720 seconds = 9

Together they complete = 47 laps

Question 28

Zahir and Raman are at the entrance of a dark cave. To enter this cave, they need to open a number lock. Raman sees a note on a rock: “ ... chest of pure diamonds kept for the smart one ... number has six digits ... second last digit is 2, third last is 4 ... divisible by all prime numbers less than 15 ...”. Excited, Zahir and Raman seek your help: which of these can be the first digit of the six-digit number that will help them open the lock?

Video Solution

Solution

Let the 6 digit number be _ _ _ 42_

It is divisible by 2,3,5,7,11,13

Since the number is divisible by both 2 and 5 the last digit of the number must be 0.

The number is also divisible by 3, 7, 11, and 13.

Hence the number must also be divisible by 7*11*13.

=7*11*13 = 1001.

A number which is a multiple of 1001 is of the form abcabc.

This is because abc*(1001) = abc*(1000+1) = abc000 + abc = abcabc.

Hence the number is 420420.

The first digit is 4.

Question 29

Read the following statements and answer the question that follows.
1. Some countries are, at least, trying to curb emissions.
2. Morocco is building a colossal solar-power plant in the desert.
3. States in the Middle East and North Africa can do little on their own to mitigate climate change.
4. Saudi Arabia is not going to stop exporting oil, but it plans to build a solar plant that will be about 200 times the size of the biggest such facility operating today.
5. Politics often gets in the way of problem solving.
Arrange the above five statements in a logical sequence.

Video Solution

Solution

The given excerpt is about what different countries in the Middle East and North Africa are doing about Climate Change.

Sentence 3 introduces the topic by saying that the mentioned countries can do little about climate change.

Sentence 5 mentions the reason for the above problem.

Statement 1 says that some countries are at least trying.

Sentences 2 and 4 build on the above idea by mentioning the projects in Morocco and Saudi Arabia.

Thus, the correct sequence is 3-5-1-2-4.

The answer is option D.

Question 30

Read the following statements and answer the question that follows.
1. Behavioral models in finance most often critique the efficient market hypothesis, which states that if investors behave rationally then prices should reflect all available information about the financial asset in consideration.
2. A number of behavioral models, including feedback models where investors bid up the price, have been used to explain this phenomenon.
3. But asset price bubbles and crashes belie this conclusion.
4. Finance is one of the fields where behavioral models have been used extensively, enough for behavioral finance.
5. This idea of “irrational exuberance” is now widely accepted and used in financial analysis, especially while analyzing asset price bubbles.
Arrange the above five statements in a logical sequence.

Video Solution

Solution

4 is the opening statement as it introduces the idea of using behavioural models in finance. Hence, options B and D are eliminated.

1-3-2 forms a logical sequence as 1 introduces the "efficient market hypothesis", 3 contradicts 1 by giving the example of "asset price bubbles". Statement 2 talks further about the phenomenon.

Statement 5 builds up on 2 by talking about the "irrational exuberance" referring to the "investors bidding up" in 1.

Thus, the required sequence is 4-1-3-2-5.

CAT Content

XAT 2021 Question Paper

The average age of the female patients who weigh 50 kg or above is approximately

The highest BMI among all patients is approximately

The BMI of the oldest person considered as normal weight is approximately

Two circles P and Q, each of radius 2 cm, pass through each other’s centres. They intersect at points A and B. A circle R is drawn with diameter AB. What is the area of overlap (in square cm) between the circles R and P?

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