IMO Mathematics Olympiad Class 10: Questions 623  629 of 908
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Question number: 623
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: 624
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: 625
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: 626
Question
The value of is ________
Choices
Choice (4)  Response  

a.  97 

b.  99 

c.  96 

d.  92 

Question number: 627
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 

Question number: 628
Question
The sum of the first term and the fifth term of an ascending A. P. is 30 and the product of the second term by the fourth term is 200. Find the sum of the first seven terms of this A. P
Choices
Choice (4)  Response  

a.  140 

b.  130 

c.  190 

d.  160 

Question number: 629
Question
The sum of all terms of the arithmetic progression having ten terms except for the first term, is 99, and except for the sixth term, 89. Find the third term of the progression if the sum of the first and the fifth term is equal to 10.
Choices
Choice (4)  Response  

a.  10 

b.  15 

c.  5 

d.  8 
