rnemani wrote:
How many three-digit integers between 310 and 400, exclusive, are divisible by 3 when the tens digit and the hundered digit are switched?
1) 3
2) 19
3) 22
4) 30
5) 90
Totally, lost on the solutions and the approach, please help
Alright, first off you have to remember the divisibility rule for 3: If all the numbers added together are divisible by 3 then the number itself is divisible by 3. Ex: 312, 3+1+2=6 (6 is divisible by 3, hence 312 is divisible by 3).
Now, start listing all the number after 310 that are divisible by 3 (because of the divisibility rule, switch the tens and hundreds place should make no difference).
312
315
318
321
324
327
330
333
336
339
342
345
348
..1
..4
..7
..0
..3
..6
..9
pattern repeats till 399.
you can count there are 10 numbers divisible by 3 between 310-340 and since the pattern repeats there should be 10 between 340-370 and 370-400.
hence, there are 30 numbers.