IMO Mathematics Olympiad Class 10: Questions 517  521 of 908
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Question number: 517
Question
P is twice good a workman as Q and therefore is able to finish a job in 30 days less than Q. Working together they can do it in ________ days.
Choices
Choice (4)  Response  

a.  40 

b.  50 

c.  20 

d.  30 

Question number: 518
Question
28 integers are chosen from the interval [104, 208]. Show that there exit two of them having a common prime divisor.
Choices
Choice (4)  Response  

a.  2 

b.  0 

c.  3 

d.  1 

Question number: 519
Question
One year ago the ratio between Laxman’s and Gopal’s salary was . The ratios of their individual salaries between last year’s and this year’s salaries are and respectively. At present, the total of their salary is Rs. 4160. The salary of Laxman now, is ________
Choices
Choice (4)  Response  

a.  Rs. 3120 

b.  Rs. 1600 

c.  Rs. 2560 

d.  Rs. 1040 

Question number: 520
Question
P, Q and R start at the same time in the same direction to run around a circular stadium. P completes a round in 280 seconds, Q in 310 seconds and R in 200 seconds, all starting at the same point. After what time will they meet again at the starting point?
Choices
Choice (4)  Response  

a.  846 minutes 15 seconds 

b.  126 minutes 18 seconds 

c.  445 minutes 55 seconds 

d.  723 minutes 20 seconds 

Question number: 521
Question
The Gurgaon office of Microsoft has 1500 executives. Of these 900 subscribe to the Hindustan Times and 750 subscribe to the Hindu. 150 subscribe to both Hindustan Times and the Hindu. If an executive is picked at random, what is the probability that he has subscribed to Hindustan Times?
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 

