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thearch
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What is the sum of all 3-digit positive integers that leave 04 Jun 2005, 09:06
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What is the sum of all 3-digit positive integers that leave a remainder of "4" when divided by "6"?

(A) 83050
(B) 75500
(C) 75550
(D) 82500
(E) 151000



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What is the sum of all 3-digit positive integers that leave 04 Jun 2005, 09:26
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I would go with 82500

my way and I dont know if this is valid or not...

I pick 2 digit number which when divided by 6 give remainder 4...then I add 3 such numbers and noticed that when added all three number when divided by 6 leave no remainder...

all i did was divide the anwer choice by 6 and see which leaves no remainder...825000 is the only one!
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What is the sum of all 3-digit positive integers that leave 04 Jun 2005, 09:36
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I'd like to add that in my opinion the answer choices provided are not correct (in the sense that the correct option isn't among the choices)
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What is the sum of all 3-digit positive integers that leave 04 Jun 2005, 10:48
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Dan
82050.
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:yes
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HowManyToGo
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What is the sum of all 3-digit positive integers that leave 04 Jun 2005, 12:05
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thearch
Dan
82050.

:yes
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The first no is 100 and the last number is 994( and every number in between has a common difference of 6...i.e 106 and 888 are also numbers , the normal AP )

The total no. of such numbers is ((994 - 100 ) / 6) + 1 = 150
the Sum = (150/2)(100 + 994) = 82050.

(am I getting brownie points here :lol: )
HMTG.
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What is the sum of all 3-digit positive integers that leave 04 Jun 2005, 13:56
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thearch
What is the sum of all 3-digit positive integers that leave a remainder of "4" when divided by "6"?

(A) 83050
(B) 75500
(C) 75550
(D) 82500
(E) 151000
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The sum of such numbers equals 82050, by the way, computer verified.

Total numbers 165 - 15 = 150

so we need numbers from 96 to 990, plus 4.

The sum is 90*150 + 4*150 + 6*75*151 = 82050
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What is the sum of all 3-digit positive integers that leave 05 Jun 2005, 02:51
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yes sparky,
they probably added 100 because the first number of the sum is 100 :yikes



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