XAT 2025 Question Paper

Option A: average gender gap of the 10 cities in 2005 = 11.25.

average gender gap of the 10 cities in 2015 = 7.75. Average in 2015 is less when compared to 2005.

Option B: Median of men's income in 2005 = 32.5

Median of women's income in 2005 = 22.5

Median of men's income in 2015 = 32.5

Median of women's income in 2015 = 22.5

Median of men's income is higher than median of women's income in both the years.

Option C: The average men's income in all 10 cities in 2005 is more than or equal to 30,000. So, there is not way a for the average to be less than Rs. 30,000. 

So, option C is false.

Option D: We can clearly see that average montly income of men in 2005 in many cities is more than that in 2015.

Option E: There are some cities where the average income for women is less than Rs. 22,000.

Since the poopulation can be more in those cities, we can't say if the average income of women is less than Rs. 22,000. So, there is a case for this statement to be true.

We are told that a car always travelling at the maximum permissible speed, and always taking the shortest route takes 1 hour to reach Oldtown from Meereen, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown.

So, distance between Oldtown and Meereen is 100*1 = 100km

Distance between Gulltown and Oldtown is 25*2  = 50km.

Distance between Winterfell and Gulltown. is 120*3/4 = 90km.

Let the distance between Meereen and Winterfall be x.

Using the pythagoras theorem, $$(100+50)^2=90^2+x^2$$

x = 120 km

For convience, we are refering the vertices as the starting letters of towns.

Using the similar triangle rule, MOL is similar to MGW.

So, $$\frac{MO}{ML}=\frac{MG}{MW}$$

$$\frac{100}{ML}=\frac{150}{120}$$

ML = 80 km.

LW = 40 km.

$$\frac{MO}{LO}=\frac{MG}{WG}$$

$$\frac{100}{LO}=\frac{150}{90}$$

LO = 60 km

The path Tyrion Lannister took is MO, OL, LW.

Distances of these path are  100, 60, 40. The respective speeds are 90, 10, 110.

So, the total time taken will be $$\frac{100}{90}+\frac{60}{10}+\frac{40}{110}\ =\ 1.11+6+0.36\ \ =7.47$$

0.47 of an hour is 28 mins.

So, answer will be 7 hr 28 mins

We are told that a car always travelling at the maximum permissible speed, and always taking the shortest route takes 1 hour to reach Oldtown from Meereen, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown.

So, distance between Oldtown and Meereen is 100*1 = 100km

Distance between Gulltown and Oldtown is 25*2 = 50km.

Distance between Winterfell and Gulltown. is 120*3/4 = 90km.

Let the distance between Meereen and Winterfall be x.

Using the pythagoras theorem, $$(100+50)^2=90^2+x^2$$

x = 120 km

For convience, we are refering the vertices as the starting letters of towns.

Using the similar triangle rule, MOL is similar to MGW.

So, $$\frac{MO}{ML}=\frac{MG}{MW}$$

$$\frac{100}{ML}=\frac{150}{120}$$

ML = 80 km.

LW = 40 km.

$$\frac{MO}{LO}=\frac{MG}{WG}$$

$$\frac{100}{LO}=\frac{150}{90}$$

LO = 60 km

Path taken by Missandei is GO, OL at a speed of 25 kmph and 10 kmph. Path taken by Varys is LO at a speed of 20 kmph.

Missandei reaches O 2hrs after he start. In the mean time, Varys travells 20 * 2 = 40km.

Now, both are travelling in opposite direction and 20 km far. 

The speed of Varys is 20 and that of Missandei is 10 km.

The time taken for them to meet is 20/30 = 2/3 hr.

In 2/3 hr, travels Missandei 6.67 km and Varys travels 13.33 km.

So, they will meet at 6.67 km south of Oldtown.

We are told that a car always travelling at the maximum permissible speed, and always taking the shortest route takes 1 hour to reach Oldtown from Meereen, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown.

So, distance between Oldtown and Meereen is 100*1 = 100km

Distance between Gulltown and Oldtown is 25*2 = 50km.

Distance between Winterfell and Gulltown. is 120*3/4 = 90km.

Let the distance between Meereen and Winterfall be x.

Using the pythagoras theorem, $$(100+50)^2=90^2+x^2$$

x = 120 km

For convience, we are refering the vertices as the starting letters of towns.

Using the similar triangle rule, MOL is similar to MGW.

So, $$\frac{MO}{ML}=\frac{MG}{MW}$$

$$\frac{100}{ML}=\frac{150}{120}$$

ML = 80 km.

LW = 40 km.

$$\frac{MO}{LO}=\frac{MG}{WG}$$

$$\frac{100}{LO}=\frac{150}{90}$$

LO = 60 km

The direct path from M to K will $$120^2+50^2 = 130^2$$.

The shortest time taking path from Meereen to King's landing. Through M0GK, time taken = $$\frac{100}{100}+\frac{50}{25}+\frac{40}{120}\ =1+2+\frac{1}{3}=3.33$$

Through MWK, time taken = $$\frac{120}{120}+\frac{50}{120}\ =1.42$$

So, the second case that is MWK is the fastest route. Time taken will be 1 hr 25 mins.

If the travel time cuts down by 20 mins, the new time will be 1 hr 5 mins.So, it should take 13/12 hrs.

speed = $$\frac{130}{\frac{13}{12}}=120 kmph$$

The first thing we should do while solving this set is we should replace the average with the sum of the ratings as we have done in the following table:

We know that the ratings can be 1/2/3/4/5 only.

R1 has given 4 and 3 to B and D respectively and the sum of the ratings given by R1 in total is 16. 

So, the sum of the ratings given by R1 to A and C is (16-4-3 = 9)

Now, this sum is only possible when he has given 4 to one of them and 5 to another. 

Let's make both the cases:

Now, with this, we can derive the score given by R3 to C. 

In case 1, it will be (16-4-4-5) = 3

In case 2, it will be (16-5-4-5) = 2

Now, R2 gave 3 and 4 score to A and C respectively. Hence, he would have given a sum of (16 - 3 - 4 = 9) to B and D. It could be possible when he gave 4 to one and 5 to the other one. 

Hence, we can make the possible cases and sub cases:

With this only, we can fill the complete table. Hence, we get:

However, Case - 2 is not possible as there no reviewer can give 6 points to any gadget. 

Now, according to the question, we have to find what rating R1 give to A so that we can find remaining ratings uniquely.

Now, R1 give 5 ratings according to two cases and 4 rating to A according to the one another. 

If R1 gives 5 rating, we still can't figure out the remaining ratings uniquely. Hence, R1 has to give 4 to A in order to find the remaining ratings uniquely.

The first thing we should do while solving this set is we should replace the average with the sum of the ratings as we have done in the following table:

We know that the ratings can be 1/2/3/4/5 only.

R1 has given 4 and 3 to B and D respectively and the sum of the ratings given by R1 in total is 16. 

So, the sum of the ratings given by R1 to A and C is (16-4-3 = 9)

Now, this sum is only possible when he has given 4 to one of them and 5 to another. 

Let's make both the cases:

Now, with this, we can derive the score given by R3 to C. 

In case 1, it will be (16-4-4-5) = 3

In case 2, it will be (16-5-4-5) = 2

Now, R2 gave 3 and 4 score to A and C respectively. Hence, he would have given a sum of (16 - 3 - 4 = 9) to B and D. It could be possible when he gave 4 to one and 5 to the other one. 

Hence, we can make the possible cases and sub cases:

With this only, we can fill the complete table. Hence, we get:

However, Case - 2 is not possible as there no reviewer can give 6 points to any gadget. 

Now, according to the three possible cases, R2 give either 4 or 5 to B.

The first thing we should do while solving this set is we should replace the average with the sum of the ratings as we have done in the following table:

We know that the ratings can be 1/2/3/4/5 only.

R1 has given 4 and 3 to B and D respectively and the sum of the ratings given by R1 in total is 16. 

So, the sum of the ratings given by R1 to A and C is (16-4-3 = 9)

Now, this sum is only possible when he has given 4 to one of them and 5 to another. 

Let's make both the cases:

Now, with this, we can derive the score given by R3 to C. 

In case 1, it will be (16-4-4-5) = 3

In case 2, it will be (16-5-4-5) = 2

Now, R2 gave 3 and 4 score to A and C respectively. Hence, he would have given a sum of (16 - 3 - 4 = 9) to B and D. It could be possible when he gave 4 to one and 5 to the other one. 

Hence, we can make the possible cases and sub cases:

With this only, we can fill the complete table. Hence, we get:

However, Case - 2 is not possible as there no reviewer can give 6 points to any gadget. Hence, there are only three possible combinations. 

Let us examine the given choices - 

Option A: Being appreciated for her performance is a positive sign, but it doesn’t directly relate to the decision about whether to join the online management certificate program or prepare for an MBA entrance exam. Aarya needs to focus on what will bring long-term growth and career advancement.

Option B: Shruti's personal experience with the MBA entrance exams may offer some perspective, but it doesn’t directly help Aarya make a decision between the two options. Each individual's circumstances are different, and Aarya needs to focus on factors that directly apply to her own situation.

Option C: This consideration is relevant in terms of work-life balance, but it is largely a secondary concern. Aarya might be able to manage her time, but if the program doesn’t provide substantial career growth or opportunities, simply managing her schedule won’t be the deciding factor. The overall impact on her career trajectory should be more important than how manageable the program is.

Option D: Like C, networking is a benefit, but it’s secondary to ensuring that the program actually delivers career opportunities and growth. Aarya should focus on how the program will enhance her career prospects first.

Option E: This factor directly addresses the potential benefit of enrolling in the program - career advancement and success after completion. Aarya’s main goal is to improve her career trajectory, and if the certificate program leads to better job prospects or career growth, it would help her make an informed decision. While other options provide context (like the program's ease or the desire for a strong alumni network), the tangible outcome of career success is the most compelling reason for her to consider the program over other paths.

Among the given choices, only Option D best aligns with Aarya's aspirations, as it highlights that the one-year executive MBA program offers an opportunity to further her career in a field that she is interested in, unlike the agribusiness program, which does not align with her career goals. 

None of the other choices offer a compelling reason to select a particular program. For example, while the scholarship mentioned in Option A could be a financial incentive, it does not directly address Aarya’s main concern: whether the program is a good fit for her and her long-term career goals.

Similarly, the consideration in Option B reflects Aarya’s lack of confidence, but it does not focus on the core question of whether the one-year executive MBA program is the best option for her career. While avoiding another year of exam prep might be appealing, it’s more of a personal emotional response and does not necessarily lead to the most strategic or fitting choice for her professional growth.

Option C compares the agribusiness program with another program but doesn’t address Aarya’s lack of interest in agribusiness. The fact that it is not the flagship program is secondary to the main issue: Aarya’s disinterest in the subject matter of the program. A good fit for her interests and career goals should be the main consideration. Option E is also tangential: what matters more is whether the program will offer Aarya the tools and career trajectory she seeks, not just its popularity.