IPMAT Indore 2024 - QA (SA)

IPMAT 2024 Quantitataive Aptitude (SA)

Questions: 15 (+4/0)                               Total Test time: 40 mins

1. The number of factors of 1800 that are multiple of 6 is ________

2. The number of real solutions of the equation (𝑥2 − 15𝑥 +55)𝑥2−5𝑥+6 = 1 is _________

3. The following table shows the number of employees and their median age in eight companies located in a district.

Company	Number of Employees	Median Age
A	32	24
B	28	30
C	43	39
D	39	45
E	35	49
F	29	54
G	23	59
H	16	63

It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C..... the age of every employee in G is strictly less than the age of every employee in H.

The highest possible age of an employee of company A is ______

4. In a group of 150 students, 52 like tea, 48 like juice and 62 like coffee. If each student in the group likes at least one among tea, juice and coffee, then the maximum number of students that like more than one drink is _____

5. Let ABC be a triangle right-angled at B with AB = BC = 18. The area of largest rectangle that can be inscribed in this triangle and has B as one of the vertices is ______

6. A fruit seller has oranges, apples and bananas in the ratio 3:6:7. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is ______

7. The number of pairs (x, y) of integers satisfying the inequality |𝑥 − 5| + |𝑦 − 5| ≤ 6 is _____

8. The price of a chocolate is increased by x% and then reduced by x%. The new price is 96.76% of the original price. Then x is _____

9. Let f and g be two functions defined by f(x) = |x + |x|| and g(x) = 1 x for x ≠ 0. If f(a) + g(f(a)) = 13 for some real a, then the maximum possible value of f(g(a)) is ______

10. The following table shows the number of employees and their median age in eight companies located in a district.

Company	Number of Employees	Median Age
A	32	24
B	28	30
C	43	39
D	39	45
E	35	49
F	29	54
G	23	59
H	16	63

It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C..... the age of every employee in G is strictly less than the age of every employee in H.

The median age of an employee across the eight companies is ______

11. The following table shows the number of employees and their median age in eight companies located in a district.

Company	Number of Employees	Median Age
A	32	24
B	28	30
C	43	39
D	39	45
E	35	49
F	29	54
G	23	59
H	16	63

It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C..... the age of every employee in G is strictly less than the age of every employee in H.

In company F, the lowest possible sum of the ages of all employees is ______

12. If 4log2𝑥 − 4𝑥 + 9log3𝑦 − 16𝑦 +68 = 0, then 𝑦 −𝑥 equals _______

13. Person A borrows Rs. 4000 from another person B for a duration of 4 years. He borrows a portion of it at 3% simple interest per annum, while the rest at 4% simple interest per annum. If B gets Rs. 520 as total interest, then the amount A borrowed at 3% per annum in Rs. is _______

14. The number of triangles with integer sides and with perimeter 15 is _______

15 is _______ 15. If 𝐴 = [ 𝑥1 𝑥2 7 𝑦1 𝑦2 𝑦3 𝑧1 8 3 ] is a matrix such that the sum of all three elements along any row, column or diagonal are equal to each other, then the value of determinant of A is ______