CAT 2021 Slot 1 - Quant

Suppose the length of each side of a regular hexagon ABCDEF is 2cm. If T is the midpoint of CD, then the length of AT, in cm, is 

Q.1 Suppose the length of each side of a regular hexagon ABCDEF is 2cm. IT T is the midpoint of CD, then the length of AT, in cm is

If r is a constant such that |x²-4x-13| = r has exactly three distinct real roots, then the value of r is

The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 cc bottles are filled with indigo solutions of strengths 33% and 17%, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to 21% then the volume, in cc, of the solution left in the second bottle is

Q.3 The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 cc bottles are filled with indigo solutions of strengths 33% and 17%, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to 21% then the volume, in cc of the solution left in the second bottle is:

A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

Q.4 A basket of 2 apples, 4 oranges and 6 mangoes cost the same as a basket of 1 apple, 4 oranges and 8 mangoes or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is:

Amal purchases some pens at ?8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ?12 each. If the remaining pens are sold at ?11 each, then he makes a net profit of ?300, while he makes a net loss of ?300 if the remaining pens are sold at ?9 each. The wage of the employee, in INR, is 

Q.5 Amal purchases some pens at Rs.8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at Rs.12 each. If the remaining pens are sold at Rs.11 each, then he makes a net profit of Rs.300, while he makes a net loss of Rs.300 if the remaining pens are sold at Rs.9 each. The wage of the employee, in INR is:

Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of the chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to

Q.6  Identical chocolates pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to:

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

Q.9 How many three digit number are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length in m, is

Q.10  Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160m long and crosses a lamp post in 12 seconds, if the speed of the other train is 6km/hr less than the faster one, its length, in m, is

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery dates for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B than the number admitted in hospital A was

Q.11 Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 month is closest to

Q.12 Onion is sold for 5 consecutive months at the rate of Rs. 10, 20, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closes t to

If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12cm, then the length, in cm, of each side of the hexagon is 

Q.13 If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length in cm, of each side of the hexagon is.

A circle of diameter 8 inches is inscribed in a triangle ABC where

If BC = 10 inches then the area of the triangle in square inches is

Q.14 A circle of diameter 8 inches is inscribed in a triangle ABC where

 If BC=10 inches then the area of the triangle in square inches is:

Q.15 The number of integers n that satisfy the inequalities |n-60| < |n=100|< |n-21| is

The amount of Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

Q.16 The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equal what Geeta alone earns in 2 days. The ratio of the daily earning of the one who earns the most to that of the one who earns the least is

The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is

Q.17 The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is

Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is

Q.19  Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest not the slowest works alone, the time in month he will take to complete the project is:

The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), …. And so on. Then the sum of the numbers in the 15^th group is equal to 

Q.20  The natural numbers are divided into groups as (1), (2,3,4), (5,6,7,8,9), …… and so on. Then, the sum of the numbers in the 15^th group is equal to

Q.21 Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are Rs 806.25 and Rs 886.72, respectively, the interest accrued, INR during the fourth year in nearest to

Q.22 Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works every day. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is: