How many positive integers between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?
A. 3
B. 16
C. 75
D. 24
E. 26
Answer is 26
A. 3
B. 16
C. 75
D. 24
E. 26
Answer is 26
Hi shibsriz,
While it is possible to use a 3-circle Venn Diagram to answer this question, it's not the easiest way for most Test Takers to answer this question. With some basic notes and minor calculations, you can answer this question.
First, the range of numbers. 200 to 300, inclusive is 300 - 200 + 1 = 101 numbers
Now we need to eliminate the numbers that are divisible by 2, 3, 5. There will be some numbers that are divisible by more than one of those values, but those won't be hard to find.
First the 2s. We need to eliminate ALL the even values. From 201 to 300, we'd remove half the numbers = 50. Add in the "200" and that's 51 numbers
Next the 5s. About half of those 5s have been removed already (200, 210, etc.), so let's list the ones that haven't: 205, 215, 225...295 = 10 numbers
Finally, the 3s. We've already accounted for all the even multiples and all the multiples that end in 5, so focus on the ones that we haven't hit yet:
201, 207, 213, 219 (notice how we're increasing by 6? Just make sure that we aren't hitting anything that ends in a 5)......
231, 237, 243, 249, 261, 267, 273, 279, 291, 297. That is = 14 numbers
51 + 10 + 14 = 75 numbers eliminated.
[spoiler]101 - 75 = 26 numbers[/spoiler]
GMAT assassins aren't born, they're made,
Rich
