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primary 5 | Maths
| Whole Numbers
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Can’t understand the question. Please help, thank you.
Date Posted: 4 years ago
Views: 227
(A) 12 can be easily obtained at the end by doing this "time-waster" operation:
Times 2, divide 2, times 2, divide 2, times 2, divide 2, ...
(B) 18 can be obtained because 18 = 12 times 3 divided by 2.
For the other 58 operations needed, all I need to do is to include a "time-waster" i.e. times 2, divide 2, times 2, divide 2, ...
(c) 36 CANNOT be obtained because 36 = 12 * 3, leaving an odd number of operations remaining (59). The "time-waster" works only in pairs.
(d) 72 can be obtained via 12 x 3 x 2 and the remaining 58 operations can be put into the "tme-waster".
(e) 108 can be obtained via 12 x 3 x 3 and then use the "time-waster" again.
Only 36 cannot be obtained via time time waster.
My answer here is 36, (C).
Times 2, divide 2, times 2, divide 2, times 2, divide 2, ...
(B) 18 can be obtained because 18 = 12 times 3 divided by 2.
For the other 58 operations needed, all I need to do is to include a "time-waster" i.e. times 2, divide 2, times 2, divide 2, ...
(c) 36 CANNOT be obtained because 36 = 12 * 3, leaving an odd number of operations remaining (59). The "time-waster" works only in pairs.
(d) 72 can be obtained via 12 x 3 x 2 and the remaining 58 operations can be put into the "tme-waster".
(e) 108 can be obtained via 12 x 3 x 3 and then use the "time-waster" again.
Only 36 cannot be obtained via time time waster.
My answer here is 36, (C).
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Whenever we do operations in opposite orders for the same number (times versus divide, plus versus minus), we get back the original number. This has to be done in pairs.
Eg.
12 + 2 - 2 = 12
85 - 10 + 10 = 85
5 x 10 / 10 = 5
8 / 2 x 2 = 8
Only 36 cannot be put as one operation (x 3) is needed, leaving 59 operations to do and after 29 pairs of opposing operations, we are left with one operation to do to the 36. We cannot get back number 36 after this final operation.
Eg.
12 + 2 - 2 = 12
85 - 10 + 10 = 85
5 x 10 / 10 = 5
8 / 2 x 2 = 8
Only 36 cannot be put as one operation (x 3) is needed, leaving 59 operations to do and after 29 pairs of opposing operations, we are left with one operation to do to the 36. We cannot get back number 36 after this final operation.
Date Posted:
4 years ago
Thank you so much
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