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primary 6 | Maths
| Algebra
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The answer is 950.
Date Posted: 4 years ago
Views: 336
Another way to do this question :
First 40 even and first 40 odd are the numbers from 1 to 80.
Notice that :
2 - 1 = 1
4 - 3 = 1
6 - 5 = 1
.
.
.
76 - 75 = 1
78 - 77 = 1
80 - 79 = 1
So sum of first 40 even numbers - first 40 odd numbers would just give you 40 since for each of these odd-even pairs, the difference is 1.
(2+4+6+ ... +76+78+80 - 1 - 3 - 5 - ... - 79-77-75)
= ( (2 -1) + (4 - 2) + (6 - 3) + ... (80 - 79) + (78 - 77) + (76 - 75) )
= (1 + 1 + 1 + ... + 1 + 1 + 1)
= 40 x 1 (since 40 pairs)
= 40
Now, add the remaining 10 even numbers
40 + 82 + 84 + 86 + 88 + 90 + 92 + 94 + 96 + 98 + 100
= 40 + (100-18) + (100-16) + (100-14) + (100-12 + (100-10) + (100-8) + (100-6) + (100-4) + (100-2) + 100
= 40 + 100 x 10 - 18 - 2 -16 - 4 - 14 - 6 - 12 - 8 - 10
= 40 + 1000 - 20 - 20 - 20 - 20 - 10
= 1040 - 20 x 4 - 10
= 1030 - 80
= 950
First 40 even and first 40 odd are the numbers from 1 to 80.
Notice that :
2 - 1 = 1
4 - 3 = 1
6 - 5 = 1
.
.
.
76 - 75 = 1
78 - 77 = 1
80 - 79 = 1
So sum of first 40 even numbers - first 40 odd numbers would just give you 40 since for each of these odd-even pairs, the difference is 1.
(2+4+6+ ... +76+78+80 - 1 - 3 - 5 - ... - 79-77-75)
= ( (2 -1) + (4 - 2) + (6 - 3) + ... (80 - 79) + (78 - 77) + (76 - 75) )
= (1 + 1 + 1 + ... + 1 + 1 + 1)
= 40 x 1 (since 40 pairs)
= 40
Now, add the remaining 10 even numbers
40 + 82 + 84 + 86 + 88 + 90 + 92 + 94 + 96 + 98 + 100
= 40 + (100-18) + (100-16) + (100-14) + (100-12 + (100-10) + (100-8) + (100-6) + (100-4) + (100-2) + 100
= 40 + 100 x 10 - 18 - 2 -16 - 4 - 14 - 6 - 12 - 8 - 10
= 40 + 1000 - 20 - 20 - 20 - 20 - 10
= 1040 - 20 x 4 - 10
= 1030 - 80
= 950
See 1 Answer
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Group the first and last number
Date Posted:
4 years ago
How do you know there is 25 sets of even numbers and 20 sets of odd numbers?
Simple. Because you paired them.
1 pair = 2
So for 50 numbers to be grouped into pairs,
50 ÷ 2 = 25 pairs.
Each pair has the same total value.
Same logic goes for the 40 odd numbers
So for 50 numbers to be grouped into pairs,
50 ÷ 2 = 25 pairs.
Each pair has the same total value.
Same logic goes for the 40 odd numbers
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