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26 Jan 2016, 22:07
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:24) correct
33%
(02:38)
wrong
based on 418
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We make 4 digit codes and each digit of the code form from 1, 2, 3, and 4. If none of each digit use more than once, eg, 1234 can be a code but 1124 cannot be a code, what is the sum of all the possible codes?
A. 56,660
B. 58,660
C. 60,660
D. 66,660
E. 68,660
* A solution will be posted in two days.
A. 56,660
B. 58,660
C. 60,660
D. 66,660
E. 68,660
* A solution will be posted in two days.
27 Jan 2016, 02:14
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MathRevolution
Total Numbers that can be made by using digits 1,2,3,4 without repetition of any digit in a number = 4*3*2*1 = 4! = 24
Now Since every digit has equal chances to appear at any place out of 4 places so each digit will be used at each of the four places an equal number of times
i.e. each digit will be used at Unit digit = 24/4 = 6 times
i.e. 6 numbers will have 1 as unit digit, 6 numbers will have 2 as unit digit, 6 numbers will have 3 as unit digit and 6 numbers will have 4 as unit digit
i.e. Sum of Unit digits of the numbers = 6*(1+2+3+4) = 60
i.e. Number will be _ _ _ 0 with 6 as carry over on ten's place
Now sum of the tens digit will again be 60 and adding carry over will make it 66
i.e. Number will be _ _ 6 0 with 6 as carry over on Hundred's place
Now sum of the Hundreds digit will again be 60 and adding carry over will make it 66
i.e. Number will be _ 6 6 0 with 6 as carry over on Thousand's place
Now sum of the Thousand's digits will again be 60 and adding carry over will make it 66
i.e. Number will be 66 6 6 0
Answer: Option D
28 Jan 2016, 18:38
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We make 4 digit codes and each digit of the code form from 1, 2, 3, and 4. If none of each digit use more than once, eg, 1234 can be a code but 1124 cannot be a code, what is the sum of all the possible codes?
A. 56,660 B. 58,660 C. 60,660 D. 66,660 E. 68,660
--> (1,000*6+2,000*6+3,000*6+4,000*6)+(100*6+200*6+300*6+400*6)
+(10*6+20*6+30*6+40*6)+(1*6+2*6+3*6+4*6)
=10,000*6+1,000*6+100*6+10*6
=66,660
Therefore, the answer is D.
A. 56,660 B. 58,660 C. 60,660 D. 66,660 E. 68,660
--> (1,000*6+2,000*6+3,000*6+4,000*6)+(100*6+200*6+300*6+400*6)
+(10*6+20*6+30*6+40*6)+(1*6+2*6+3*6+4*6)
=10,000*6+1,000*6+100*6+10*6
=66,660
Therefore, the answer is D.
