Gradutate Record Exam

1. In a group of men and women, 1/3 are men. If 2 women leave the group, then men will be 2/5 of the group. How many members are there in the group?

2. The value of (5sqrt2+sqrt3)(sqrt2-sqrt3) = ?

3. If a < 0 < b < c, then
Col A: ac/b
Col B: ac

4.

Given a figure like above, here PQRS is a square of length 10 and the line VT is the perpendicular to the diameter of the semicircle PQ and it is also given that PU = 2, then find the length of VT?

5. Given 2 < a < 5 < b < 8 and if the average of 3, 6, 9, a, b is 6.2, then find the value of a + b?

6. Given that an investment of a company in 1990 has increased by 15% in a span of 5years i.e. by 1995 and the same investment increased by 30% in a span of 10years i.e. by 2000.
Col A: The percentage increase from 1995 to 2000
Col B: 15%

7.

Given a square PQRS with side length 8 as above and ‘Q’, ‘S’ points are centers of the circles. Find the area of the shaded region?

8. If the below lines are plotted
x + y = 5 &
2x + 2y = 8
Col A: The shortest distance between the lines
Col B: 1

9. Given two circles that are concentric having radii 2, 5. If the tangent to the smaller circle intersects the bigger circle at ‘S’ and ‘T’, then find the length of ‘ST’?

10. If a <> 0, then
Col A: a^-7 * b^-2
Col B: (a*b)^-14

11. A Data interpretation question is given, with the data about “The Available number of rooms in Top 12 hotels in a city” and the questions asked were….
i. The Ratio of available rooms of 3 large hotels to the total rooms in a city.
ii. The median value of the number of rooms of the 12 hotels.