Jacob spent 3 hours skiing and snowboarding. He skied for 1 hours 25 minutes.
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Answer:
(a) There are 257 numbers which are divisible by 5 and by 7
(b) There are 1286 numbers which are divisible by 7
(c) There are 4500 even numbers
(d) There are 514 numbers which are divisible by 5 but not by 7
Step-by-step explanation:
(a) Since, LCM(5, 7) = 35,
Thus, the numbers divisible by 5 and by 7 between 1000 and 9999,
1015, 1050, 1085............, 9975
Which is an AP,
Having first term, a = 1015,
Common difference, d = 35,
Last term, l = 9975
If n be the number of terms,
(b) Similarly, number divisible by 7,
1001, 1008, 1015............, 9996
Here, a = 1001, d = 7, l = 9996
(c) Even numbers between 1000 and 9999 inclusive
1000, 1002, 1004, 1006,........9998
Here, a = 1000, d = 2, l = 9998
(d) Number divisible by 5,
1000, 1005, 1010............, 9995
Here, a = 1000, d = 5, l = 9995
Hence, the number divisible by 5 but not by 7 = numbers divisible by 5 - number divisible by 7
= 1800 - 1286
= 514