## QBM044

Q1. How many positive integers divide at least two of the following integers: 410, 620, 320?
(1)39

(2)40

(3)41

(4)None of these
Q2. A bucket with a capacity of 5 liters is used to draw water from a cylindrical tank of radius 7 m in which and water is filled upto a height of 2 m. The density of the bucket is 0.5 and the weight 2 kg. What is the level of water in the tank when the bucket is dipped the third time to draw water? (Density =Volume/Weight)
(a)1.8m

(b)1.9m

(c)1.96m

(d)2m
Q3. The remainder obtained when a prime number greater than 6 is divided by 6 is:
(1)1or3

(2)1or5

(3)3or5

(4)4or5
Direction for questions 4 and 5: Read the data below
The climb from the foot to the top of a hill is 800 m. Amar climbs at 16 m/min and tests for 2 minutes or 20 m in 2 min and rest for 1 minute. Bonny can climb at 10 m/min and rest for 1 minute or 16 m/min and rest for 2 minutes.
Q4. If Amar has to reach the top in exactly 2 hours, what is the maximum number of tests that he can take?
(a)40

(b)41

(c)39

(d)38
Q5. If both Amar and Bonny climb as fast as they can, then how far would Bonny be from the top when Amar reaches the top?
(a)630m

(b)170m

(c)640m

(d)160m
Q6. A merchant purchases 25% more goods spending Rs 240 after the price of the
goods fall by 20%. What are the old and new prices of the goods?
(a) 22, 20

(b) 24, 19.2

(c) 10, 8

(d) 30, 24
Q7. A trader buys goods from Delhi to sell in Bombay where he gets 20% higher price realisation. Per journey, he spends Rs. 2000 on travelling, Rs. 2500 as bribe to the parcel authority and makes a net profit of Rs. 20,000. Find the total value of goods purchased by the dealer in 7 journeys to Delhi.
(1)Rs.1,22,500

(2)Rs.2,45,000

(3)Rs.8,57,500

(4) None
Q8. What is the shortest distance between M1 and M2?
(1)11km

(2)7ï€ 2km

(3)7km

(4)14 km
Q9.A man invests Rs. 3000 at a rate of 5% per annum. How much more should he invest at a rate of 8%, so that he can earn a total of 6% per annum?
(1)Rs.1200

(2)Rs.1300

(3)Rs.1500

(4)Rs.2000
Q10. This is the last problem of the fall semester. The Problem of the Week will return for the spring semester. Hope to hear from everyone then.
What is the probability that the sum of three integers, each between 1 and 999, yields no "carry"?
Q11.What is the greatest integer so that each of its interior digits is less than the average of its neighbors?
Q12.The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then, the height of the wall is:
(1)12m

(2)15m

(3)18m

(4)11 m
Q13. If A and B are nonzero digits, the number of digits (not necessarily different) in the sum of 9876 + A32 + B1 is:
a.4

b.5

c.6

d.9

e. None of these
Q14. The Sum of the internal angle of a n-sided convex polygon is An + B, where A and B are constants. What is the value of A/B?
(a)â€“2

(b)â€“1/2

(c)2

(d)1/2
Q15. A starts from patna to bilaspur and walks at the rate of 5 kmph; B starts from bilaspur 3 hrs. later and walks towards- patna at the rate of 4.5 kmph; if they meet in 11 hrs after B started. After how much time of A's meeting with B, will A reach bilaspur?
(1)8 hrs

(2)9 hrs

(3)10 hrs

(4)11 hrs
END

## My attempts

Q1. How many positive integers divide at least two of the following integers: 410 & 620
410 = 2 x 5 x 41
620 = 2^{2} x 5 x 31
So common divisors are 1, 2, 5, 10 i.e 4
Between 410 and 320
320 = 2^{6} x 5
No new common divisors
Between 620 and 320
New common divisors : 4, 20
Q3. Ans 2 i.e 1 or 5
ex: 7 , 11
rest - after the weekend