## QBM040

Q1. A field in the shape of a right triangle is to be subdivided into two fields of equal size by building a straight fence between two sides of the field. If the lengths of the sides of the field are 300 and 400 feet long, respectively, with the hypotenuse being 500 feet long, what is the shortest fence that will do the job and where should the fence be built? Q2. A straight bar of metal, initially 800 feet long, expands 8 inches in length. The ends are fixed so that the bar becomes distorted into the shape of an arc of a circle, for which the original bar would now be a chord. What is the approximate height above the center of the original bar of this new distorted bar? Q3. Which of the following is NOT true? (1)|a + b| = | b + a|
(2) |a - b| = |b - a|
(3) |a + b | < |a| +|b|
(4) | a - b | > |a| - |b| Q4. The ratio of two numbers is 7:3. The sum of these two numbers is 30. What is the difference of these two numbers? a.9
b.10
c.11
d.12
e.13 Q5. The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the manager whose salary was Rs. 720, was replaced with a new manager, then the average salary of the team went down to 580. What is the salary of the new manager? A.570
B.420
C.690
D.640 Q6. The sides of a triangle are 6 cm, 11 cm and 15 cm. The radius of its incircle is: a) 5√2/4 cm
b) 3√2 cm
c) 6√2 cm
d) 4√2/5 cm Q7. Three consecutive positive even numbers are such that thrice the first number exceeds double the third by 2; then the third number is: (1)10
(2)14
(3)16
(4)12 Q8. If in the previous question, Akshay's speed from home to bank was 30 m/min and from bank to market was 20 m/ 10 min, find his average speed. (a)2.8 m/10 min
(b)3 m/min
(c)3.6 m/10 min
(d) 4.8 m/min Q9. A rectangular block of wood has for its three dimensions a different odd prime number of inches. Its volume and (total) surface area are, respectively, a three digit number and a four digit number. What are the dimensions of the block? Q10. Fix a positive integer n. How many sequences (a1, a2, ... , an) of positive integers are there with the property that at most i of the terms are greater than n-i, for all i = 0,1,...,n? Q11. Show that n4 + 4n is composite for all integers n > 1. Q12. The side of equilateral triangle is 96 cm. the mid points of its side are joined to form another triangle whose mid points are turn joined to form still another triangle. This Process is repeated indefinitely. Find the sum of the perimeter of all the triangles. (1)1176 cm
(2)1275 cm
(3)576 cm
(4) None of these Q13. The largest value of min (2 + x2, 6 - 3x) when x > 0 is (1)1
(2)2
(3)3
(4)4 Q14. Let x, y and z be natural numbers satisfying x < y < z and x + y + z = k. which of the following is the smallest values of k which does not determine x, y, z uniquely? (1)9
(2)6
(3)7
(4) 8 Q15. Two ferry boats sail back and forth across a river, each traveling at a constant speed, and turning back without any loss of time. They leave opposite shores at the same instant, pass for the first time 700 feet from one shore, continue on their way to the banks, return and pass for the second time 400 feet from the opposite shore. What is the width of the river? END

Is it 8 ??

## Answer to Question No. 14

Q14. Let x, y and z be natural numbers satisfying x < y < z and x + y + z = k. which of the following is the smallest values of k which does not determine x, y, z uniquely?
(1)9
(2)6
(3)7
(4) 8

Solution:

For k = 6, we have the unique combination: 1 + 2 + 3

For k = 7, we have the unique combination: 1 + 2 + 4

For k = 8, we have two possibilities: 1 + 2 + 5 and 1 + 3 + 4

Hence the required answer is 8.

Thank You.

Ravi Raja