Arithmetic Progressions (IMO Mathematics Olympiad Class 10): Questions 53  59 of 84
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Question number: 53
» Arithmetic Progressions
Question
A number 196 is divided into four parts that are in A. P. such that the product of the first and fourth is to the product of the second and third is . Find the largest part.
Choices
Choice (4)  Response  

a.  70 

b.  28 

c.  42 

d.  56 

Question number: 54
» Arithmetic Progressions
Question
If , then is equal to ________
Choices
Choice (4)  Response  

a.  1228 

b.  1428 

c.  1328 

d.  1128 

Question number: 55
» Arithmetic Progressions
Question
Find the sum of all threedigit natural numbers, which on being divided by 4, leave remainder equal to 2.
Choices
Choice (4)  Response  

a.  1, 99, 270 

b.  4, 41, 680 

c.  1, 94, 780 

d.  1, 23, 525 

Question number: 56
» Arithmetic Progressions
Question
If the sum of terms of an A. P. are respectively, then is ________
Choices
Choice (4)  Response  

a.  1 

b.  2 

c.  0 

d.  3 

Question number: 57
» Arithmetic Progressions
Question
Find the sum of all fourdigit natural numbers, which on being divided by 20, leave remainder equal to 5.
Choices
Choice (4)  Response  

a.  69, 65, 000 

b.  24, 70, 500 

c.  60, 27, 000 

d.  32, 23, 001 

Question number: 58
» Arithmetic Progressions
Question
The value of is ________
Choices
Choice (4)  Response  

a.  97 

b.  99 

c.  96 

d.  92 

Question number: 59
» Arithmetic Progressions
Question
The sum of all terms of the arithmetic progression having ten terms except for the first term, is 126, and except for the sixth term, 62. Find the third term of the progression if the sum of the first and the fifth term is equal to 16.
Choices
Choice (4)  Response  

a.  7 

b.  3 

c.  9 

d.  8 
