GMAT 2025 Sample Paper 1 Question Paper with Answer Key and Solutions PDF

GMAT 2025 Sample Paper 1 Question Paper with Answer Key and Solutions PDF is available for download. GMAT lasts for a total of 2 hours and 15 minutes, with an optional 10-minute break. Throughout the test, candidates will be required to answer 64 questions, distributed as follows:

  • Quantitative Reasoning: 21 questions, to be completed in 45 minutes.
  • Verbal Reasoning: 23 questions, to be completed in 45 minutes.
  • Data Insights: 20 questions, to be completed in 45 minutes.

GMAT 2025 Sample Paper 1 Question Paper with Solutions PDF

GMAT 2025 Sample Paper 1 Question Paper with Solutions PDF download iconDownload Check Solutions
GMAT 2025 Sample Paper 1 Question Paper with Solutions PDF

Question 1:

Consider a function f satisfying f(x * y) = f(x) + f(y) where x, y are positive integers, then what is the value of \( \frac{f(3) + f(12)}{f(12) - f(4) + f(2)} \)?

  • (A) 2
  • (B) 6
  • (C) 3
  • (D) 8
  • (E) 4

Question 2:

A merchant sold a car at 60% of the marked price and obtained a loss of 20%. If the cost price of the car is three times the cost price of the bike, then what should be the selling price of the bike to make a profit of 20%?

  • (A) 120% of the Marked Price of the car
  • (B) 20% of the Marked Price of the car
  • (C) 30% of the Marked Price of the car
  • (D) 80% of the Marked Price of the car
  • (E) 50% of the Marked Price of the car

Question 3:

Two trains, P and Q, pass a pole in 40 seconds and 2 minutes 20 seconds, respectively. If the length of train P is two-thirds that of train Q, what is the ratio of the speed of train P to that of train Q?

  • (A) 9:4
  • (B) 5:2
  • (C) 7:3
  • (D) 12:5
  • (E) 14:3

Question 4:

If a and b are positive integers satisfying \(4a + 3b = 17\) and \( \frac{(5ab)!}{3^p} \) is an integer, then the maximum value of p is

  • (A) 13
  • (B) 14
  • (C) 15
  • (D) 16
  • (E) 17

Question 5:

Alex has two children - Ben and Chloe. The current age of Alex is 4 times that of Ben. 4 years later, the age of Alex is 4 times that of Chloe. What is the age difference between Ben and Chloe?

  • (A) 2
  • (B) 3
  • (C) 4
  • (D) 5
  • (E) 6

Question 6:

In a college there are 150 students out of which 60% of the students play cricket, 30% of the students play football and 40% of the students play hockey. If it is know that no student plays all three sports and all the students play at least one sport, then what is the number of students that play exactly one sport?

  • (A) 45
  • (B) 65
  • (C) 105
  • (D) 85
  • (E) 75

Question 7:

A beaker contains a solution in which the concentration of milk is 80%. On the addition of some water, this ratio of milk to water becomes 8:5. On replacing 39 L of this solution with pure milk, the ratio of milk to water changes to 9:4. What is the volume of water added initially?

  • (A) 30 litres
  • (B) 45 litres
  • (C) 50 litres
  • (D) 35 litres
  • (E) 60 litres

Question 8:

In a class of 150 students, the average weight is 42 kg. If the number of girls increases by 50% and the number of boys becomes two-thirds of its original value, while keeping the total number of students the same, the new average weight of the class becomes 43 kg. It is also observed that the average weight of boys and girls remains the same as before. Find the sum of the average weights of boys and girls.

  • (A) 80
  • (B) 75
  • (C) 85
  • (D) 90
  • (E) 95

Question 9:

An unfair dice consisted of two faces with 1 on them, two faces with 2 on them, and one face each of 3 and 5 on them. If the dice is rolled thrice, then what is the probability that the sum of the three rolls is greater than or equal to 11?

  • (A) \( \frac{21}{216} \)
  • (B) \( \frac{19}{216} \)
  • (C) \( \frac{17}{216} \)
  • (D) \( \frac{8}{216} \)
  • (E) \( \frac{7}{216} \)

Question 10:

Let \(a_n\) and \(b_n\) be two sequences such that \(a_n = 13 + 6(n-1)\) and \(b_n = 15 + 7(n-1)\) for all natural numbers n. Then, the sum of all the three-digit numbers that are common in both series is

  • (A) 11487
  • (B) 11987
  • (C) 11687
  • (D) 11615
  • (E) 11944

Question 11:

Find the remainder when \(2^{88} \times 5^{41}\) is divided by 7.

  • (A) 1
  • (B) 2
  • (C) 3
  • (D) 5
  • (E) 6

Question 12:

Nihal took a 1,00,000 loan at 15% interest per year. If he repays in two equal yearly instalments, the amount per instalment is x. If he repays in three equal yearly instalments, the amount per instalment is y. What is the approximate difference between x and y?

  • (A) 16925
  • (B) 15834
  • (C) 17714
  • (D) 17981
  • (E) 19815

Question 13:

\(y(x) = mx + c\) represents a linear relation in y and x. If \(y(-1) = 3\) and \(y(3) = 11\), find the value of \(y(y(2))\)

  • (A) 9
  • (B) 23
  • (C) 62
  • (D) 12
  • (E) 45

Question 14:

The value of the expression \( \frac{81^3 + 28^3 - 109^3}{86^2 - 23^2} \) is?

  • (A) 110
  • (B) -108
  • (C) 3428
  • (D) -34
  • (E) 8192

Question 15:

What is the highest power of 12 in 99!?

  • (A) 96
  • (B) 95
  • (C) 48
  • (D) 47
  • (E) 8

Question 16:

Peter takes 4 hours longer than Samuel to prepare 30 sandwiches. Working together, they can make 50 sandwiches in 150 minutes. How long would it take Peter alone to make 40 sandwiches?

  • (A) 6 hours
  • (B) 8 hours
  • (C) 10 hours
  • (D) 12 hours
  • (E) 5 hours

Question 17:

The sum of two numbers is 16. Thrice the smaller number is greater than twice the larger by 3. The product of the numbers is ?

  • (A) 35
  • (B) 45
  • (C) 63
  • (D) 55
  • (E) 62

Question 18:

What is the remainder when \(43^{380}\) is divided by 20?

  • (A) 5
  • (B) 2
  • (C) 4
  • (D) 1
  • (E) 8

Question 19:

If \(2x^2 + 10 = 7y - 5x\) and \(4y^2 - 5y = -(7x + 17)\), then find the value of \((x + y)\)?

  • (A) \( \frac{3}{2} \)
  • (B) \( \frac{5}{2} \)
  • (C) \( -\frac{3}{2} \)
  • (D) \( -\frac{5}{2} \)
  • (E) \( \frac{7}{2} \)

Question 20:

Find the value of \( \sqrt{11 + \sqrt{72}} + \sqrt{11 - \sqrt{72}} \)

  • (A) 9
  • (B) \(2\sqrt{2}\)
  • (C) 22
  • (D) 61
  • (E) 6

Question 21:

Find the possible number of integral values of \(x\) satisfying \(2x^2 + 11x - 138 < 0\)

  • (A) 16
  • (B) 18
  • (C) 17
  • (D) 30
  • (E) 22

Question 22:

Raju, a cake seller, mixes flour, cream, and sugar in a ratio of 5:3:2 and sells it at the cost price. Their prices are in the ratio 4:10:5. What ratio should the three be mixed in to get a 10% profit selling at the earlier proportions' price?

i) The proportion of sugar should remain the same.

ii) The price of sugar is Rs. 30 per kg

  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • (D) EACH statement ALONE is sufficient.
  • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

Question 23:

In a meeting held by ACS, there were 10 attendees. If N attendees are selected to deliver speeches during the meeting, and it is given that N is a positive integer, what is the value of N?

Statement 1: N is a multiple of 3.

Statement 2: There are 210 ways to select the N attendees to deliver speeches.

  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • (D) EACH statement ALONE is sufficient.
  • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

Question 24:

24 a. Asheville had the highest percentage increase in the number of independent bookstores from 2023 to 2024.

Correct Answer: True
View Solution




Step 1: Understanding the Concept:

We need to calculate the percentage increase for each city that saw an increase in the number of bookstores and then compare these percentages to find the highest one.


Step 2: Key Formula or Approach:
\[ Percentage Increase = \frac{New Value - Old Value}{Old Value} \times 100% \]

Step 3: Detailed Explanation:

We only need to calculate the percentage increase for cities where the number of bookstores grew from 2023 to 2024.


Asheville: \( \frac{51 - 45}{45} \times 100% = \frac{6}{45} \times 100% = \frac{2}{15} \times 100% \approx 13.33% \)

Chicago: \( \frac{72 - 70}{70} \times 100% = \frac{2}{70} \times 100% = \frac{1}{35} \times 100% \approx 2.86% \)

Denver: \( \frac{76 - 74}{74} \times 100% = \frac{2}{74} \times 100% = \frac{1}{37} \times 100% \approx 2.70% \)

Minneapolis: \( \frac{65 - 58}{58} \times 100% = \frac{7}{58} \times 100% \approx 12.07% \)

Portland: \( \frac{100 - 90}{90} \times 100% = \frac{10}{90} \times 100% = \frac{1}{9} \times 100% \approx 11.11% \)

San Francisco: \( \frac{70 - 68}{68} \times 100% = \frac{2}{68} \times 100% = \frac{1}{34} \times 100% \approx 2.94% \)

Seattle: \( \frac{88 - 85}{85} \times 100% = \frac{3}{85} \times 100% \approx 3.53% \)



Step 4: Final Answer:

Comparing the calculated percentages, Asheville's increase of approximately 13.33% is the highest. Therefore, the statement is true.
Quick Tip: When comparing percentage changes, be mindful of the base value (the denominator). A smaller base can lead to a larger percentage change even for a small absolute increase.


Question 25:

24b. Austin and Boston were the only cities that saw a decline in the number of independent bookstores between 2023 and 2024.

Correct Answer: True
View Solution




Step 1: Understanding the Concept:

We need to examine the data for each city and identify which ones experienced a decrease in the number of bookstores from 2023 to 2024.


Step 2: Detailed Explanation:

Let's check the change for each city by comparing the 2024 value to the 2023 value.


Asheville: 51 (2024) \(>\) 45 (2023) \(\implies\) Increase

Austin: 80 (2024) \(<\) 82 (2023) \(\implies\) Decline

Boston: 84 (2024) \(<\) 87 (2023) \(\implies\) Decline

Chicago: 72 (2024) \(>\) 70 (2023) \(\implies\) Increase

Denver: 76 (2024) \(>\) 74 (2023) \(\implies\) Increase

Minneapolis: 65 (2024) \(>\) 58 (2023) \(\implies\) Increase

Portland: 100 (2024) \(>\) 90 (2023) \(\implies\) Increase

San Francisco: 70 (2024) \(>\) 68 (2023) \(\implies\) Increase

Seattle: 88 (2024) \(>\) 85 (2023) \(\implies\) Increase



Step 3: Final Answer:

Only Austin and Boston saw a decline in the number of bookstores. Therefore, the statement is true.
Quick Tip: For questions asking for "only," "all," or "none," be sure to check every single data point to confirm the condition holds universally as stated. A single exception would make the statement false.


Question 26:

24c. San Francisco accounted for less than 10% of the total independent bookstores across all listed cities in 2024.

Correct Answer: False
View Solution




Step 1: Understanding the Concept:

We need to calculate the total number of bookstores across all cities in 2024 and then find the percentage that San Francisco's bookstores represent out of this total.


Step 2: Detailed Explanation:

First, sum the number of bookstores for all cities in 2024: \[ Total_{2024} = 51 + 80 + 84 + 72 + 76 + 65 + 100 + 70 + 88 \] \[ Total_{2024} = 686 \]
The number of bookstores in San Francisco in 2024 is 70.

Now, calculate the percentage: \[ Percentage_{SF} = \frac{SF Bookstores}{Total Bookstores} \times 100% = \frac{70}{686} \times 100% \]
To check if this is less than 10%, we can compare 70 to 10% of 686.
\[ 10% of 686 = 0.10 \times 686 = 68.6 \]
Since 70 is greater than 68.6, San Francisco accounted for more than 10% of the total.


Step 3: Final Answer:

The statement that San Francisco accounted for less than 10% is false.
Quick Tip: For "percent of total" questions, you don't always need to calculate the exact percentage. You can often save time by calculating the threshold value (e.g., 10% of the total) and simply comparing it to the part.


Question 27:

The distance between Town X and Town Y is 150 miles. Car A leaves Town X for Town Y, and sometime later, Car B leaves Town Y for Town X. If the two cars meet exactly halfway between Town X and Town Y, what is the speed of Car B?

(1) Car B leaves Town Y exactly 45 minutes after Car A leaves Town X.

(2) Car B travels at a speed 10 mph faster than Car A.

  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • (D) EACH statement ALONE is sufficient.
  • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

Question 28:

If \(7x = 4y = 9z\), what is the value of \(9x - 5y + 4z\)?

Statement 1: \(3x - y = \frac{5}{14}\)

Statement 2: \(5y + 2z = \frac{53}{18}\)

  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • (D) EACH statement ALONE is sufficient.
  • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

Question 29:

A historical research archive is curating three new collections of ancient manuscripts. Each collection will contain four manuscripts: two from classical antiquity and two from the medieval period. Moreover, no single manuscript may appear in all three collections, and no two collections may share more than one of the same manuscript. It is further known that at least one collection must include both a manuscript by Homer and a manuscript by Bede. So far, three manuscripts in each collection have been selected:

Select a manuscript that must be added to one of the collections, and a manuscript that cannot be added to any collection. Make only two selections, one for each column.

Correct Selections:

Must be added to one of the collections: Bede (medieval)
Cannot be added to any collection: Homer (antiquity)


Question 30:

After a fundraiser, the event organisers surveyed all the participants who attended about how many different types of sweets they had during the party. The attendants could have taken any number of sweets available of any kind. The chart below shows the percentage of people surveyed who consumed a particular type of sweet. The participants could have taken one piece or more of the sweets they consumed.


Chart Data (picked by percentage): Ice-cream (80%), Chocolate (55%), Custard (75%), Tiramisu (60%), Jello (40%), Halwa (55%), Donuts (48%).

According to the data, the maximum percentage of people who would have taken at least one of every sweet would be \hspace{1cm}, while the minimum percentage of people who would have taken at least one sweet would be \hspace{1cm}.


Question 31:

A fruit seller sold 4 kg of oranges at Rs. 120 and incurred a loss of 25%. So, he decided to mark up the price of the remaining fruits. He made a total revenue of Rs. 1000 and an overall profit of 25%. What markup is made on the remaining fruits and the total quantity sold?


Options (Markup, Quantity): (37.5, 40), (40, 20), (20, 25), (25, 32.75)


Question 32:

A company placed orders with Suppliers A and B, buying at least eight units from each.
Supplier A's pricing: A fixed fee of
(120, with the first eight units at
)25 each, and
(7 for every additional unit.
Supplier B's pricing: A fixed fee of
)180, with the first eight units at
(18 each, and
)12 for each extra unit. After all purchases, including fixed costs, the average price per unit was
(23.
Select the number of units purchased from Supplier A and the number of units purchased from Supplier B that are jointly consistent with the given information. Make only two selections, one in each column.


Question 33:

A team of 5 must be selected from 4 men and 4 women. At least 2 men and 2 women must be included. X is the total number of valid teams possible if A and B (both women) refuse to work together. Y is the total number of valid teams possible when C (a man) must be included, and D (a woman) is included. Find the values of X and Y.


Options for X: \{30, 32\

Options for Y: \{18, 24, 30, 36, 48\


Question 34:

S is a set of consecutive numbers. What is the size of the set?

i) There are two multiples of 5 in the set.

ii) There are seven multiples of 2 in the set.

  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • (C) EACH statement ALONE is sufficient.
  • (D) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

Question 35:

A retail petrol seller mixes petrol that costs him Rs. 70 per litre with kerosene and sells the mixture at Rs. 77 per litre. What is his profit percentage?

i) He bought 10 litres of kerosene at 60 per litre.

ii) The total profit earned is Rs. 240.

  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • (D) EACH statement ALONE is sufficient.
  • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

Question 36:

The chart below displays the total number of online queries received by the tech company Citrus and the percentage of these queries resolved each day from Monday to Friday.
Use the drop-down menus to fill in the blanks in each of the following statements based on the information given by the graph.



Chart Data - Left Side

Mon: Quality(20), Quantity(10), Delivery(10)
Tue: Quality(40), Quantity(60), Delivery(30)
Wed: Quality(20), Quantity(50), Delivery(20)
Thu: Quality(30), Quantity(40), Delivery(40)
Fri: Quality(40), Quantity(50), Delivery(50)

Chart Data - Right Side (Total Queries):

Mon: Quality(100), Quantity(100), Delivery(100) -> Total 300
Tue: Quality(150), Quantity(150), Delivery(100) -> Total 400
Wed: Quality(100), Quantity(100), Delivery(100) -> Total 300
Thu: Quality(200), Quantity(100), Delivery(200) -> Total 500
Fri: Quality(150), Quantity(100), Delivery(150) -> Total 400

Statement 1: The graph shows that the maximum number of queries about Delivery is resolved on \hspace{1cm}.

Statement 2: The graph shows that on Friday, the total number of online queries resolved for all three parameters was the \hspace{1cm} highest.


Question 37:

35a. The percentage increase in average screen time for the 13-18 age group from 2010 to 2023 is more than 115%.

Correct Answer: Yes
View Solution



Step 1: Find the values for the 13-18 age group in 2010 and 2023.

2010 value = 3.2 hours
2023 value = 7.2 hours

Step 2: Calculate the percentage increase. \[ % Increase = \frac{New Value - Old Value}{Old Value} \times 100 = \frac{7.2 - 3.2}{3.2} \times 100 \] \[ % Increase = \frac{4.0}{3.2} \times 100 = \frac{40}{32} \times 100 = \frac{5}{4} \times 100 = 1.25 \times 100 = 125% \]
Step 3: Compare the result to 115%.
Since 125% is more than 115%, the statement is true. Select Yes.
Quick Tip: Read table-based questions very carefully to distinguish between requests for \textbf{absolute increase} (New - Old), \textbf{percentage increase} ((New - Old)/Old), and values like \textbf{median} (the middle value of a sorted set). Each requires a different calculation.


Question 38:

35b. If there are equal numbers of people in each age group, then the median average usage for all people in 2020 is more than 5 hours/day.


Question 39:

35c. The increase in the average screen time from 2010 to 2023 for the 30-49 age group is greater than the increase in average screen time for the 50-69 age group during the same period.

Correct Answer: No
View Solution



Step 1: Calculate the absolute increase for the 30-49 age group from 2010 to 2023.

2023 value = 6 hours
2010 value = 3.5 hours
Increase = \(6 - 3.5 = 2.5\) hours.

Step 2: Calculate the absolute increase for the 50-69 age group from 2010 to 2023.

2023 value = 4.9 hours
2010 value = 2.2 hours
Increase = \(4.9 - 2.2 = 2.7\) hours.

Step 3: Compare the two increases.
The increase for the 30-49 group (2.5 hours) is not greater than the increase for the 50-69 group (2.7 hours). Therefore, the statement is false. Select No.
Quick Tip: Read table-based questions very carefully to distinguish between requests for \textbf{absolute increase} (New - Old), \textbf{percentage increase} ((New - Old)/Old), and values like \textbf{median} (the middle value of a sorted set). Each requires a different calculation.


Question 40:



Among the given schools, the school with the highest proportion of students failing in Chemistry out of the total number of students failing is For that school, the number of students failing in Physics is approximately \hspace{1cm}% of the total failed students.


Question 41:

Neha is organising a weekend workshop and needs to print 200 brochures. She is considering two printing services: a nearby print shop and an online printing service. At the nearby print shop, each brochure will cost
(m with no additional costs. Each brochure will cost a bit less at
)n at the online service, but there's a flat setup fee of
(50. These are the only costs involved. Neha calculated that by choosing the online service over the print shop for 200 brochures, she would save exactly
)290.
Select a value for m and n that are jointly consistent with the information provided. Make only two selections, one in each column.


Question 42:

1. A city with the highest collapse threshold doesn't have the lowest vulnerability index.

Correct Answer: No
View Solution



Step 1: Identify the city with the highest collapse threshold from the table. The highest value is 3000, which corresponds to London.

Step 2: Find the vulnerability index (VI) for London from the bar chart. London's VI is 4.5.

Step 3: Find the lowest vulnerability index among all cities. The lowest VI value on the chart is 4.5, shared by London and Prague.

Step 4: Evaluate the statement. The city with the highest collapse threshold (London) *does* have the lowest vulnerability index (4.5). The statement claims it "doesn't have" the lowest VI, which is false.
Quick Tip: When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.


Question 43:

2. The city with the second-lowest hospital surge capacity has political and economic instability at 'high'.

Correct Answer: No
View Solution



Step 1: Identify the city with the second-lowest hospital surge capacity from the table. Sorting the capacities: Cagliari (40), Brindisi (45), Catania (50), etc. The second-lowest is Brindisi.

Step 2: Check the political and economic instability levels for Brindisi from the table. Political Instability is Medium and Economic Instability is High.

Step 3: Evaluate the statement. The city (Brindisi) does not have both instabilities at 'High'. Therefore, the statement is false.
Quick Tip: When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.


Question 44:

3. Vulnerability index is directly proportional to the severity of the economic and political instability.

Correct Answer: No
View Solution



Step 1: To test for direct proportionality, the ratio of VI to a measure of instability must be constant. Let's assign numerical values: Low=1, Medium=2, High=3.

Step 2: Compare two cities with the same instability levels.

Cagliari: Political=High (3), Economic=High (3). Total instability score = 6. VI = 6. Ratio = 6/6 = 1.
Athens: Political=High (3), Economic=High (3). Total instability score = 6. VI = 8. Ratio = 8/6 \(\approx\) 1.33.

Step 3: Evaluate the statement. Since two cities with the same instability score have different VIs, the ratio is not constant. Therefore, the relationship is not a direct proportion. The statement is false.
Quick Tip: When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.


Question 45:

1. The city with the highest vulnerability index saw less than 30 new cases on Day 2.

Correct Answer: Yes
View Solution



Step 1: Identify the city with the highest VI. This is Athens with VI = 8.

Step 2: Find the Day 1 cases for Athens from the map: Cases\(_{D1}\) = 36.

Step 3: Use the formula to calculate total cases on Day 2. Cases\(_{t+1}\) = Cases\(_t\) \(\times\) (1 + VI/10).
Cases\(_{D2}\) = floor(36 \(\times\) (1 + 8/10)) = floor(36 \(\times\) 1.8) = floor(64.8) = 64.

Step 4: Calculate the number of new cases on Day 2. New Cases = Cases\(_{D2}\) - Cases\(_{D1}\) = 64 - 36 = 28.

Step 5: Evaluate the statement. 28 is less than 30. The statement is true.
Quick Tip: When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.


Question 46:

2. In the city with the lowest hospital surge capacity, the number of new cases on Day 3 was greater than the number of daily beds.


Question 47:

3. Cities with a vulnerability index less than 5 have fewer than 10 new cases on Day 2.


Question 48:

1. Catania saw more new cases than the available daily beds for the first time on Day 4.

Correct Answer: Yes
View Solution



Step 1: Get data for Catania: Daily beds = 50, VI = 7, Cases\(_{D1}\) = 39. Multiplier = 1.7.

Step 2: Project new cases day by day and compare to 50.

Day 2: Cases\(_{D2}\) = floor(39 \(\times\) 1.7) = 66. New cases = 66-39=27. (27 < 50)
Day 3: Cases\(_{D3}\) = floor(66 \(\times\) 1.7) = 112. New cases = 112-66=46. (46 < 50)
Day 4: Cases\(_{D4}\) = floor(112 \(\times\) 1.7) = 190. New cases = 190-112=78. (78 > 50)

Step 3: Evaluate the statement. Day 4 is the first day new cases (78) exceeded the daily beds (50). The statement is true.
Quick Tip: When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.


Question 49:

2. Prague saw the least number of total cases after 10 days.

Correct Answer: No
View Solution

N/A


Question 50:

3. Athens saw the highest number of total cases after 10 days.

Correct Answer: Yes
View Solution



Step 1: To find the city with the most cases, we should look for cities with high initial cases and high VI. The growth is dominated by the VI. Athens has the highest VI of 8.

Step 2: Let's project cases for Athens and another strong contender like Zaragoza (high initial cases).

Athens (VI=8, C1=36): Projection for 10 days gives a total of 7020 cases.
Zaragoza (VI=6.5, C1=43): Projection for 10 days gives a total of 3796 cases.

Step 3: The significantly higher VI of Athens leads to much faster exponential growth, resulting in the highest total number of cases. The statement is true.
Quick Tip: When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.


Question 51:

Based on the information provided in the Ethan Hunt scenario, for each of the following statements, select Yes if the statement accurately reflects the information given in the tabs. Otherwise, select No.




1. The city with the highest vulnerability index saw less than 30 new cases on Day 2.


Question 52:

Based on the information provided in the Ethan Hunt scenario, for each of the following statements, select Yes if the statement accurately reflects the information given in the tabs. Otherwise, select No.

1. Catania saw more new cases than the available daily beds for the first time on Day 4.


Question 53:

A shopkeeper mixes rice of two types costing x and y per kg in the ratio 10:7, respectively. He sells the resulting mixture at 210 per kg making a profit of 19 percent. What is the price (per kg) of the cheaper rice?

Statement 1: The price of the expensive rice is 200 per kg.

Statement 2: The mean cost of both the type of rice is 180 per kg

  • (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • (D) EACH statement ALONE is sufficient.
  • (E) Statements (1) and (2) TOGETHER are NOT sufficient.

Question 54:

Nadia: Leaders in tech companies should have some background in software development. That kind of experience helps them understand the practical challenges their teams face and leads to better decision-making.

Omar: But just having a software background doesn't mean someone will be a good leader. Many engineers struggle with communication and team management.

Which one of the following most accurately describes a flaw in Omar's reasoning?

  • (A) He assumes that engineers cannot develop leadership skills over time.
  • (B) He criticizes a more extreme version of Nadia's position than she actually states.
  • (C) He confuses technical skill with leadership potential.
  • (D) He fails to consider whether all tech leaders need the same qualifications.
  • (E) He presumes that decision-making and communication skills are unrelated.

Question 55:

During a year-long cybersecurity breach, about 1,000 remote employees at Firm Z reported their accounts had been compromised. Around the same number of on-site employees also reported compromised accounts. Based on these figures, it can be hypothesized that working remotely was no more vulnerable to security breaches than working on-site.

Which of the following, if it could be carried out, would be most useful in an evaluation of the above hypothesis?

  • (A) Determining whether remote employees use more personal devices than on-site employees when accessing company systems
  • (B) Comparing the proportion of compromised accounts among remote employees to the proportion among on-site employees
  • (C) Investigating whether some of the compromised accounts involved employees who switched between remote and on-site work during the breach
  • (D) Analyzing the types of data accessed by compromised remote accounts compared to those accessed by compromised on-site accounts

Question 56:

The primary objective in the passage is to:

  • (A) critique governments for prioritising electoral gains over societal welfare by detailing reasons behind fiscal mismanagement.
  • (B) analyse how structural and psychological factors inherent to governance amplify present bias, undermining long-term policy success.
  • (C) argue that individual cognitive biases in leaders and political groups are the root cause of systemic governmental short-term focus.
  • (D) contrast the decision-making processes of individuals with those of governments to highlight how present bias impacts democratic systems.
  • (E) propose institutional reforms to mitigate the risks of present bias in governance, which has led to election-focused policymaking.

Question 57:

The author implies which of the following about the comparison between individual and governmental present bias?

  • (A) Governments, unlike individuals, are not shielded from short-term concerns due to institutional gaps.
  • (B) Present bias in governments is primarily rooted in political rather than economic pressures.
  • (C) Like individuals, governments may neglect long-term interests due to uncertainty and lack of immediate payoff.
  • (D) Governmental present bias results in more significant societal harm than individual present bias.
  • (E) The absence of structural continuity in governments ensures their decisions do not consistently benefit future administrations.

Question 58:

A government enacts a far-reaching environmental reform with delayed benefits and high upfront costs. According to the passage, this scenario would most likely occur if:

  • (A) The reform offers voters immediate tax incentives that mask its long-term costs.
  • (B) The opposition party forces the reform to pass during a political stalemate.
  • (C) The reform is framed as a symbolic gesture with no tangible enforcement mechanisms.
  • (D) The current administration is likely confident of long-term political dominance.
  • (E) A global coalition mandates reform, overriding national legislative decision-making.

Question 59:

A regional airline plans to replace complimentary meals on short flights with meals for purchase. Critics argue that eliminating free meals will lead to a decline in customer satisfaction. This concern is supported by recent surveys. Nevertheless, implementing the change is unlikely to reduce overall satisfaction. The airline also plans to lower ticket prices, and this is likely to attract more price-sensitive travelers who are less concerned about free meals and more focused on overall affordability.

In the argument above, the two boldfaced portions play which of the following roles?

  • (A) The first is an objection that has been raised against a certain plan; the second is a prediction that, if accurate, undermines the force of that objection.
  • (B) The first is a forecast about how consumers will respond to a proposed change; the second is a counterexample offered to challenge that forecast.
  • (C) The first is a hypothesis that the argument seeks to test; the second is evidence presented to support that hypothesis.
  • (D) The first is a consideration that weighs against a proposed policy; the second is a prediction that strengthens the case for adopting the policy.
  • (E) The first is an assumption that the argument later rejects; the second is an alternative explanation that supports that rejection.

Question 60:

The author implies which of the following about the impact of social media on emotional well-being?

  • (A) Its global reach exempts it from being a uniquely American psychological threat.
  • (B) Its influence is significant but insufficient to explain current American despair.
  • (C) Its role in influencing rude behaviour extends beyond its immediate users.
  • (D) It has replaced traditional American institutions that once fostered moral behaviour.
  • (E) It does not necessarily contribute to depression and rudeness in America.

Question 61:

The anecdote of the restaurant owner in the passage most likely serves to:

  • (A) illustrate how societal pressures have transformed customer expectations and behaviour.
  • (B) highlight a unique trend in the hospitality sector that reflects broader social dynamics.
  • (C) function as evidence that community spaces are no longer regulated by cultural standards.
  • (D) reveal that consumer-facing roles are the first victims of the rise in hatred and despair among the populace.
  • (E) exemplify the growing disconnect between consumer behaviour and institutional norms of conduct.

Question 62:

Which of the following, if true, would most directly challenge the author's argument about the root cause of societal crisis?

  • (A) Regions with revitalised workplace ethics programs show no improvement in political polarisation or suicide rates.
  • (B) Some individuals who report strong familial moral instruction still engage in occasional online hostility and selfish behaviour.
  • (C) Nations with robust community organisations but high inequality exhibit similar rates of despair and rudeness.
  • (D) Deaths tied to despair correlate more strongly with stagnant wages than with declines in religious affiliation.
  • (E) Social media platforms that ban anonymous hateful postings see increased user kindness but unchanged depression metrics.

Question 63:

The discussion on "moral formation" most closely suggests which of the following about the nature of the current societal crisis?

  • (A) It is an inevitable consequence of modernisation and the decline of traditional norms in all globalised societies.
  • (B) It cannot be ascribed to external pressures such as economic insecurity and demographic change overwhelming social institutions.
  • (C) It is chiefly a social problem that manifests as emotional and relational dysfunction.
  • (D) It is fundamentally a failure of character development and interpersonal responsibility rather than solely structural or economic problems.
  • (E) It stems primarily from the increasing irrelevance of institutions as a unifying moral force in society.

Question 64:

Which of the following is most strongly supported by the discovery of southwest British tin in shipwrecks near Israel (1300 BC) and France (600 BC)?

  • (A) Mediterranean societies exclusively relied on British tin after 1300 BC.
  • (B) Long-distance tin trade networks persisted for centuries.
  • (C) French traders replaced Mediterranean merchants as intermediaries by 600 BC.
    (D) Tin from Cornwall was of higher quality than central Asian alternatives.
    (E) The sourcing of tin shifted considerably after 1300 BC.

Question 65:

The argument that southwest Britain was a major contributor to Bronze Age tin supplies depends on which of the following assumptions?

  • (A) The presence of British tin in a few shipwrecks implies regular and large-scale export activity.
  • (B) Mediterranean civilisations lacked their own local sources of tin during the Bronze Age.
  • (C) Trade between Britain and the Mediterranean must have been bilateral and continuous over centuries.
  • (D) The shipwrecks discovered to date are representative of the broader patterns of Bronze Age maritime trade.
  • (E) All tin used in Bronze Age Europe and the Mediterranean was transported by sea rather than overland routes.

Question 66:

The boldfaced sentence plays which of the following roles in the passage?

  • (A) It introduces a counterargument that the author later refutes using historical evidence.
  • (B) It outlines a widely held belief that is later disproven through archaeological evidence.
  • (C) It presents a long-standing scholarly uncertainty that the author addresses through new scientific findings.
  • (D) It emphasises the geographic distance between Britain and the eastern Mediterranean.
  • (E) It contrasts with the claim that copper was more readily available than tin in ancient Europe.

Question 67:

The core limitation with the last line of the passage is that it:

  • (A) assumes that all ancient societies required identical proportions of tin and copper in their bronze alloys.
  • (B) relies on the assumption that corrosion has not significantly affected the geochemical analysis of ancient tin ingots.
  • (C) underestimates the possibility that ancient societies may have substituted other materials for tin when necessary.
  • (D) presumes, without sufficient evidence, that no other tin sources besides those mentioned could have met the demand.
  • (E) confuses the presence of rich tin deposits with the certainty that those deposits were actively mined and exported at scale.

Question 68:

A study of professional chess players revealed that those who began formal coaching before the age of 10 were far more likely to become grandmasters than those who began coaching at an older age or not at all. Researchers concluded that early coaching significantly increases the likelihood of attaining elite status in chess. However, this conclusion is not entirely correct. Early achievers are typically individuals who show exceptional interest and aptitude for chess from a young age. It is this early talent and motivation-not the timing of coaching-that primarily accounts for their success.
Which one of the following, if true, most strengthens the objection to the researchers' conclusion?

  • (A) Players who began formal coaching after age 10 but practiced intensely often matched the performance of early-trained players in national tournaments.
  • (B) Players who started coaching early tended to practice for more hours each week than those who started later.
  • (C) Parents are much more likely to seek out formal chess coaching for their children if they observe early signs of exceptional aptitude in the game.
  • (D) Many grandmasters who began early coaching also had access to high-quality instructors and resources.
  • (E) Players who did not receive coaching but started playing young rarely became grandmasters.

Question 69:

For many years, biologists thought a certain frog species had gone extinct in a region because no individuals were found after a fungal outbreak. This belief was based on surveys conducted after the outbreak, which failed to detect any frogs. However, researchers recently found the species' remains buried in soil layers that appear to have been deposited after the time of the outbreak, suggesting the species might have survived longer than previously believed. This finding does not necessarily disprove the original belief, because \hspace{1cm}.

  • (A) earlier surveys did not cover some of the more remote wetlands in the region
  • (B) other frog species in the area recovered quickly after the outbreak subsided
  • (C) sediment layers can contain remains of animals that died years before the layers were deposited
  • (D) the frog species is known to have a patchy and irregular distribution even in stable environments
  • (E) DNA from the fungus was also found in the same sediment layers as the frog remains

Question 70:

The prestigious Larchmont High School recently introduced a new magnet program for advanced STEM students. Over the past few months, the school has seen a sharp rise in enrollment, and several teachers have noted that classroom resources are becoming stretched. They argue that if the magnet program were relocated to a separate campus, both the STEM students and the general student body would have a better educational experience.
Which of the following is an assumption that supports drawing the conclusion above from the reasons given for that conclusion?

  • (A) The STEM students would prefer the focused environment of a separate campus.
  • (B) Students do not enrol in the general program as extensively as those in the magnet program.
  • (C) Students are frustrated with the limited access to school resources.
  • (D) Other local schools have begun to offer similar STEM programs.
  • (E) The increase in enrollment is primarily due to the introduction of the STEM magnet program.

Question 71:

Principle: An investment strategy is prudent only if it does not expose the investor to an unacceptable level of financial risk.
Application: Noah has recently begun using a strategy that includes investing in early-stage tech startups. Although the strategy diversifies his portfolio, it increases his exposure to assets that are less stable than traditional blue-chip stocks. Therefore, his strategy is not prudent.
The application of the principle is most vulnerable to criticism on which one of the following grounds?

  • (A) It overlooks the possibility that diversification may help manage financial risk, even if the assets are individually volatile.
  • (B) It takes for granted that any increase in exposure to less stable assets results in an unacceptable level of risk.
  • (C) It assumes that traditional investments are always less risky than alternatives.
  • (D) It fails to consider that some early-stage startups can provide exceptionally high returns.

Question 72:

In 2018, a medium-sized company implemented a remote work policy allowing employees to work from home two days a week. A study before the policy was introduced showed average employee productivity scores. A follow-up study conducted two years later showed that productivity among employees had increased by 25%. The company concluded that remote work boosts employee productivity. Meanwhile, a separate study of two similar companies that had allowed remote work for over a decade showed no significant change in productivity during the same two-year period.
The results of the final study mentioned above:

  • (A) indirectly supports the conclusion that remote work policies could enhance productivity at least in the short term.
  • (B) prove that factors aside from remote work might explain the productivity increase observed in the first company.
  • (C) reveal that employees at different companies may react differently to remote work arrangements.
  • (D) show that the effects of remote work on productivity do not differ significantly between short-term and long-term implementations.
  • (E) contradict the conclusion reached by the first company's study.

Question 73:

Astronomer: In 2022, Observatory Z discovered 12 comets within a two-month span, an unusually high figure compared to their typical average of 3-4 comet discoveries per year. Strikingly, most of these 12 comets were discovered using a decade-old telescope, while a recently acquired state-of-the-art telescope, capable of scanning larger portions of the sky and detecting fainter objects, identified only one comet in the same period. This discrepancy is puzzling, given that the new telescope was designed to vastly outperform the older model.
Which of the following, if true, most helps to explain the discrepancy described by the astronomer?

  • (A) The new telescope requires longer exposure times to gather detailed data, limiting the number of observations it can make in a given period.
  • (B) Observatory Z invested heavily in training staff to operate the new telescope, leaving less funding for additional research staff during 2022.
  • (C) The older telescope was positioned in a region of the sky where comet activity happened to be unusually high during the observation period.
  • (D) Comets detected by the new telescope tend to be smaller and less visible than those detected by the older telescope, which focuses on brighter objects.
  • (E) Observatory Z prioritized public outreach efforts in 2022, devoting significant time to showcasing comet discoveries made using the older telescope.

Question 74:

According to the passage, which of the following would apply to a person who reads a novel and later watches its film adaptation?

  • (A) The person will recall more perceptual details from the novel than from the film adaptation.
  • (B) The film adaptation alone would have been less effective in reinforcing the person's self-image.
  • (C) The novel's imagined scenes will be more resistant to distortion over time.
  • (D) Both experiences will contribute equally to the person's autobiographical memory bank.
  • (E) The film adaptation will create a stronger memory for sensory details due to direct perceptual input.

Question 75:

Which of the following, if true, would most strengthen the argument that fictional memories can influence decision-making similarly to autobiographical memories?

  • (A) Fictional narratives frequently contain moral lessons that align with widely held cultural values.
  • (B) Individuals who read fiction make decisions more slowly than those who do not.
  • (C) People often recall fictional events to explain or justify real-world choices.
  • (D) Emotional attachment to fictional characters correlates with vivid dreaming.
  • (E) Viewers of movies retain visual details more accurately than readers recall imagined scenes.

Question 76:

If a person identifies strongly with a fictional character who overcomes social anxiety, what would the author likely argue about this identification?

  • (A) The individual has likely experienced similar events in reality and is reliving them through fiction.
  • (B) This identification helps validate an aspirational self-image and may influence future behaviour.
  • (C) The character's story would not influence the individual unless it contains vivid perceptual details.
  • (D) Fictional identification replaces the need for autobiographical memory in shaping identity.
  • (E) Strong emotional connections to fiction hinder the ability to rely on real-world memories.

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