Word Problem

Moy12

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May 23, 2013
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The 12-hour digital clock above shows one example of a time at which the sum of the digits representing the time is equal to 20 (time shown is 8:57). During a 12-hour period, starting at noon, for how many minutes would the sum of the digits displayed be greater than or equal to 20?

I made a chart running from 12-noon to 12 am.

12 sum of digits can't be equal or greater than 20
1 "dido"
2 "dido"
3 "dido"
4 "dido"
5 "dido"
6 from 6:59-7:00 we get 1 minute
7 from 7:58-8:00 we get 2 minutes
8 from 8:57-9:00 we get 3 mins
9 from 9:56-10:00 we get 4 mins
10 sum of digits can't be equal or greater than 20
11 dido
12 dido

Sum is then 1+2+3+4=10

but according to my book, the answer is 20. Where am I going wrong?
 
Got it

I found the explanation for it in my book: I guess I didn't think hard enough.

7 7:49 is another minute that counts
8 8:48-8:49 and 8:39 also count
9 9:47-9:49 and 9:38-9:39 and 9:29 also count


The total minutes are actually 20.
 
Hello, Moy12!

The 12-hour digital clock above shows one example of a time at which
the sum of the digits representing the time is equal to 20 (time shown is 8:57).
During a 12-hour period, starting at noon, for how many minutes
would the sum of the digits displayed be greater than or equal to 20?

Note: The number 5 ⁣: ⁣37\displaystyle 5\!:\!37 represents one minute,
. . . . .the time from 5 ⁣: ⁣37 ⁣: ⁣00\displaystyle 5\!:\!37\!:\!00 through 5 ⁣: ⁣37 ⁣: ⁣59\displaystyle 5\!:\!37\!:\!59.
Then we have:     {6 ⁣: ⁣59}  1{7 ⁣: ⁣497 ⁣: ⁣587 ⁣: ⁣59}  3{8 ⁣: ⁣398 ⁣: ⁣488 ⁣: ⁣498 ⁣: ⁣578 ⁣: ⁣588 ⁣: ⁣59}  6{9 ⁣: ⁣299 ⁣: ⁣389 ⁣: ⁣399 ⁣: ⁣479 ⁣: ⁣489 ⁣: ⁣499 ⁣: ⁣569 ⁣: ⁣579 ⁣: ⁣589 ⁣: ⁣59}  10\displaystyle \text{Then we have: }\;\;\begin{Bmatrix}6\!:\!59\end{Bmatrix} \; 1 \qquad \begin{Bmatrix}7\!:\!49 \\ 7\!:\!58 \\ 7\!:\!59\end{Bmatrix} \; 3 \qquad \begin{Bmatrix}8\!:\!39 \\ 8\!:\!48 \\ 8\!:\!49 \\ 8\!:\!57 \\ 8\!:\!58\\8\!:\!59 \end{Bmatrix} \; 6 \qquad \begin{Bmatrix}9\!:\!29 \\ 9\!:\!38 \\ 9\!:\!39 \\ 9\!:\!47 \\ 9\!:\!48 \\ 9\!:\!49 \\ 9\!:\!56 \\ 9\!:\!57 \\ 9\!:\!58 \\ 9\!:\!59 \end{Bmatrix}\; 10
Therefore: 1+3+6+10=20 minutes.\displaystyle \text{Therefore: }\:1+3+6+10 \:=\:20\text{ minutes.}
 
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