XAT 2019

Options A and D focus on poor and rich kids only. They can be easily eliminated. Option E makes no sense. Between options B and C, the latter states how empowerment can be achieved. Option B is too general in nature. Eliminate option B.

Hence, the correct answer is option C.

The main concern of Divya is that the financial risk of opening a franchisee is high as she will have to take out a huge loan and invest a lot in the infrastructure. Thus, the option that can let her know that the franchisee will be financially stable will help her make the decision.

Option A can be dismissed as it does not relate to the main concerns of Divya.

Getting a loan is not a problem for Divya, but to be able to repay it. Thus, option B can be dismissed.

Option D talks about a restaurant's business. This does not ensure that Divya's business would also work.

Option E will have the opposite effect.

Option C is the best choice. If Divya can charge higher prices while retaining the customers, it will increase her confidence in the ability to cover all the costs.

Hence, the answer is option C.

We have to select an option which will not demotivate Divya.

Options A, B, C and D are all negative in tone and will discourage Divya from opening a franchisee.

Hence, the answer is option E.

Option A can be dismissed as real estate is not the criteria for choosing Kazipeth. As the franchisee also needs to generate revenue.

Option B is about Jangaon and not Kazipeth. Hence, it can be dismissed.

Option C mentions teenagers being attracted to rollover ice cream. But it doesn't necessarily convert into higher sales.

Option D talks about higher population density in Warangal and Jangaon. Hence it will not encourage her to open a shop in Kazipeth.

Option E is the best choice as it is mentioned that one of the reasons Divya was attracted to Kazipeth is because it is an education hub.

Hence, the answer is option E.

The most crucial criterion for Divya would be a steady increase in business as she has to take a huge loan and invest money in the shop's infrastructure.

Options A, C and D, can be dismissed as they do not relate to the above point.

Among B and E, B is more important, as a consistent increase in the number of customers will make sure that the business flourishes.

Hence, the answer is option B.

Strategy 1 will lead to the customers moving to the competition. The objective is to keep the customers engaged with the company. Hence, this can be dismissed.

Strategy 2 is unethical as it tells the dealers to be dishonest to their customers.

Strategy 3 is a valid one as it will keep the awareness of the "limo" among the public.

Strategy 4 is also a valid one as it will allow the company to start shipping the cars quickly and the company can retain their customers.

Strategy 5 is also a valid one as the company needs the manufacturing plants to make the cars after procuring the parts.

Strategy 6 can be dismissed as it might lead to other manufacturing plants creating unrest for higher pay.

Thus, the valid strategies are 3, 4 and 5.

Hence, the answer is option E.

Since Mr Murugan is willing to deposit an amount and wait for the first car to be available, option B makes the most sense. It ensures that Mr Murugan purchases the car and also lets him know about policy.

Option A is also valid but not as suitable as B.

Transferring the amount to Electro Automobile's account does not make sense. Hence, C can be dismissed.

Options D and E can lead to Mr Murugan cancelling his order.

Hence, the answer is option B.

Let the initial salary of A,B,C,D,E be $$a,b,c,d,e$$ respectively and let the final salary of everyone be $$x$$ 

Now, $$a*(1+ \frac{p}{100})*(1+ \frac{p+1}{100}) = x$$

$$\Rightarrow a = \frac{x}{(1+ \frac{p}{100})*(1+ \frac{p+1}{100})}$$

$$\Rightarrow a = \frac{x*100*100}{(100+p)*(100+p+1)}$$

$$\Rightarrow a = \frac{x*100*100}{(p+100)*(p+101)}$$

Similarly, $$b= \frac{x}{(1+ \frac{p+2}{100})*(1+ \frac{p-1}{100})}$$

$$\Rightarrow b = \frac{x*100*100}{(p+102)*(p+99)}$$

Similarly, $$c= \frac{x}{(1+ \frac{p+3}{100})*(1+ \frac{p-2}{100})}$$

$$\Rightarrow c = \frac{x*100*100}{(p+103)*(p+98)}$$

Similarly, $$d= \frac{x}{(1+ \frac{p+4}{100})*(1+ \frac{p-3}{100})}$$

$$\Rightarrow d = \frac{x*100*100}{(p+104)*(p+97)}$$

Similarly, $$e= \frac{x}{(1+ \frac{p+5}{100})*(1+ \frac{p-4}{100})}$$

$$\Rightarrow e = \frac{x*100*100}{(p+105)*(p+96)}$$

The numerators of the fractions are same, therefore the one with the smallest value of denominator will have the greatest value. If we compare the denominators, we can find out the fraction with the highest value. The person with the highest initial salary got the least raise, as we know that the final salary of all the candidates is same. 

Thus, denominator of a, $$a_{den}= (p+100)*(p+101)= p^{2}+201p+100*101$$

Similarly, $$b_{den}= (p+102)*(p+99)= p^{2}+201p+102*99$$

$$c_{den}= (p+103)*(p+98)= p^{2}+201p+103*98$$

$$d_{den}= (p+104)*(p+97)= p^{2}+201p+104*97$$

$$e_{den}= (p+105)*(p+96)= p^{2}+201p+105*96$$

We see that we need to compare only the last terms of the denominators as the other terms are same. 

Thus, last term of a, $$a_{lt}= 100*101= 100.5^{2}-0.5^{2}$$

 last term of b, $$b_{lt}= 102*99= 100.5^{2}-1.5^{2}$$

 last term of c, $$c_{lt}= 103*98= 100.5^{2}-2.5^{2}$$

 last term of d, $$d_{lt}= 104*97= 100.5^{2}-3.5^{2}$$

 last term of e, $$d_{lt}= 105*96= 100.5^{2}-4.5^{2}$$

Thus, we can see that since denominator of $$e$$ is the smallest, therefore E has the highest initial salary.

There are 9 employees in the firm. Median of any set is the element which occurs in the middle of the set when the elements are positioned in increasing or decreasing order. The number of elements in this set = 5+3+1 = 9

Thus, the middle element will be in the position $$\frac {9+1}{2}$$ = 5th. Since we know that the clerks are paid the least so the clerk salaries would be in the beginning of the set if arranged in ascending order. Thus, the 5th element will be a clerk's salary as the number of clerks is 5. 

Thus, median of the set = Rs 15,000.

To find the mean salary, we first need to find the sum total salary of the people involved. 

Total salary = (Number of clerks*salary of 1 clerk) + (Number of assistants*salary of 1 assistant) + (Number of accountants*salary of 1 accountant) 

$$ \Rightarrow$$ Total salary = (5*15,000)+(3*40,000)+(1*66,000)

$$ \Rightarrow$$ Total salary = 75,000+1,20,000+66,000 

$$ \Rightarrow$$ Total salary = 2,61,000 

Mean salary = $$\frac{\textrm{Total Salary}}{\textrm{Total number of employees}} $$

$$ \Rightarrow $$ Mean salary = $$ \frac{261000}{9} $$

$$ \Rightarrow $$ Mean salary = Rs 29,000 /-

Thus, difference between mean and median salary = 29,000-15,000 = Rs 14,000

Inverse proportionality is expressed as follows : 

$$a\propto \frac{1}{b}$$

$$\Rightarrow$$ a*b = constant 

When value of a changes, the value of b changes accordingly such that their product remains same.

Thus, new value of a $$a^{'} = a + a = 2a $$

Thus, the new value of b $$b^{'}$$ can be solved by : 

$$a^{'}*b^{'}=a*b$$

$$\Rightarrow 2a*b^{'}= a*b $$

$$\Rightarrow b^{'}= \frac{b}{2} $$

Thus b decreases by 50%.