Answer:
Number of apple = 119
Step-by-step explanation:
Given
[tex]Max_{Apple} = 150[/tex]
Required
Find the actual number of apples;
When counted in any numbers, the number being counted is the divisor;
Take for instance, when counted in pairs, the divisor is 2
When counted in threes, the divisor is 3
and so on...
So; from the question, we understand that; when the apple is counted in 2s,3s,4s,5s, and 6s; what's left is always one less than the divisor
This means that the number of apple must satisfy the following conditions
- Less than 150
- 1 less than the Common Multiple of 2,3,..,6
- Divisible by 7
The common multiple of 2,3,..6 are 60, 120 ,180,240.....
Recall that, these multiples must satisfy the three conditions above;
1. Less than 150: Only 60 and 120 satisfy condition.
At this point, we'll discard other numbers (180,240,300.....)
2. 1 less than the Common Multiple of 2,3,..,6:
1 less than 60: 60 - 1 = 59
1 less than 120: 120 - 1 = 119
3. Divisible by 7
At this point, we'll divide 59 and 119 by 7 to see if they satisfy this condition;
[tex]\frac{59}{7} = 8.42857142857[/tex]
[tex]\frac{119}{7}=17[/tex]
The results of these division shows that 59 is not divisible by 7;
Hence, the actual number of apple is 119
Number of apple = 119
