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avatar+28 

The sum of all numbers between 0 and 10,000 which is exactly divisible by 77 is: 

 

that answer is apparently 645645 but I only get either 634426 or 654350 when i solve, pls enlighten me how to get the correct answer.

 May 14, 2023
 #1
avatar+118593 
+1

Your question does not make sense.

 May 14, 2023
 #2
avatar
+2

Very poorly worded question !

 

I think what you want to say is:

 

What consecutive integers between 0 and 10,000 sum up to: 645,645 ?

 

The answer is: all integers between 19 (inclusive) and 1,136 (inclusive) =645,645

 

645,645 mod 77 =0 - the remainder.

 May 14, 2023
 #3
avatar
+1

There are actually 63 sequences of consecutive integers between 0 and 10,000 that sum up to: 645,645.

 

Sequences of consecutive integers:
1  - 322822  to 322823 = 645645
2  - 215214  to 215216 = 645645
3  - 129127  to 129131 = 645645
4  - 107605  to 107610 = 645645
5  - 92232  to 92238 = 645645
6  - 64560  to 64569 = 645645
7  - 58690  to 58700 = 645645
8  - 49659  to 49671 = 645645
9  - 46111  to 46124 = 645645
10  - 43036  to 43050 = 645645
11  - 30735  to 30755 = 645645
12  - 29337  to 29358 = 645645
13  - 24820  to 24845 = 645645
14  - 21507  to 21536 = 645645
15  - 19549  to 19581 = 645645
16  - 18430  to 18464 = 645645
17  - 16536  to 16574 = 645645
18  - 15352  to 15393 = 645645
19  - 14994  to 15036 = 645645
20  - 11712  to 11766 = 645645
21  - 9901  to 9965 = 645645
22  - 9750  to 9815 = 645645
23  - 9189  to 9258 = 645645
24  - 8347  to 8423 = 645645
25  - 8239  to 8316 = 645645
26  - 7465  to 7550 = 645645
27  - 7050  to 7140 = 645645
28  - 6097  to 6201 = 645645
29  - 5815  to 5924 = 645645
30  - 4941  to 5069 = 645645
31  - 4902  to 5031 = 645645
32  - 4444  to 4586 = 645645
33  - 4116  to 4269 = 645645
34  - 3831  to 3995 = 645645
35  - 3457  to 3638 = 645645
36  - 3214  to 3408 = 645645
37  - 2970  to 3179 = 645645
38  - 2896  to 3110 = 645645
39  - 2680  to 2910 = 645645
40  - 2374  to 2631 = 645645
41  - 2229  to 2501 = 645645
42  - 2115  to 2400 = 645645
43  - 1995  to 2295 = 645645
44  - 1792  to 2121 = 645645
45  - 1485  to 1869 = 645645
46  - 1461  to 1850 = 645645
47  - 1291  to 1719 = 645645
48  - 1287  to 1716 = 645645
49  - 1192  to 1646 = 645645
50  - 1167  to 1628 = 645645
51  - 1129  to 1601 = 645645
52  - 910  to 1455 = 645645
53  - 876  to 1434 = 645645
54  - 772  to 1373 = 645645
55  - 679  to 1323 = 645645
56  - 546  to 1260 = 645645
57  - 454  to 1223 = 645645
58  - 324  to 1181 = 645645
59  - 264  to 1166 = 645645
60  - 255  to 1164 = 645645
61  - 210  to 1155 = 645645
62  - 145  to 1145 = 645645
63  - 19  to 1136 = 645645

Guest May 14, 2023
 #4
avatar+389 
+2

S = 77 + 154 + 231 + ... = 1*77 + 2*77 + 3*77 + ...

10,000/77 = 129.87

129*77 = 9933

130*77 = 10,010

S = 1*77     + 2*77     + 3*77     + ... + 129*77

S = 129*77 + 128*77 + 127*77 + ... + 1*77

Add

2S = 130*77 + 130*77 + 130*77 + ... + 130*77

     = 129*130*77

S  =  129*130*77/2 = 645645.

 May 14, 2023

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