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Eighty cards are numbered with a different number from 1 to 80. One card is removed and the numbers on the remaining cards are added. The result is a multiple of 32. Find the sum of the possible numbers that could have been on the removed card.

 Feb 17, 2020
edited by Guest  Feb 17, 2020
 #1
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No numbers..

 Feb 17, 2020
 #2
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sorry there was a glitch

 Feb 17, 2020
 #3
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Here's my best attempt  :

 

sum  of integers  1 - 80 =   (80) (81) / 2 =  40 * 81  = 3240

 

Nearest integer  < 3240  which is divisible by  32 =  3232

 

So.... the cards that could have  been removed are multiples of 8 + a multiple  of 32  = 

 

8 , 40 , 72

 

So....the sum on these cards  =  48 + 72 =   120

 

 

cool cool cool

 Feb 17, 2020
 #4
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CPhill: I think it says "ONE card" was removed and the total of the remaining cards is a multiple of 32.

 

So, [80 x 81] / 2 =floor[3240 / 32] =101 x 32 =3232. 

 

So, one card with No.8 on it was removed.

 Feb 17, 2020

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