You've got 100 numbers between 1 and 100.
50 of them are even, so they're divisible by 2.
Now, you have 100 divided by 3 = 33 + 1 remainder. This means that there are 33 numbers from 1 to 100 divisible by 3, but you have to pick only the odd ones, since you;ve already eliminated the even ones. The number off odd multiples of 3 between 1 and 100 will be 33/2 = 16 remainder 1. Since both 3 (the smallest multiple of 3) and 99 (the greatest multiple of 3) are both odd, this means that you have 17 odd numbers divisible by 3 between 1 and 100.
So your number will be 100 - 50 - 17 = 33.
Is this the OA?
numbers between 1-100
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hrishikesh05
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between 1 to 100 there are
50 numbers divisible by 2 (100/2)
33 numbers divisible by 3 (100/3)
That gives a total of 83 numbers
However there are numbers which area also divisible by 2 and 3 i.e. by 6.
16 numbers divisible by 6 (100/6)
Total numbers = 50+33-16 = 67
Answer = 100- 67 = 33
50 numbers divisible by 2 (100/2)
33 numbers divisible by 3 (100/3)
That gives a total of 83 numbers
However there are numbers which area also divisible by 2 and 3 i.e. by 6.
16 numbers divisible by 6 (100/6)
Total numbers = 50+33-16 = 67
Answer = 100- 67 = 33
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Uri
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there are (100/3) or 33 numbers between 1 and 100 which will be divisible by 3.
Since the problem deals with numbers "between 1 and 100", I feel we should exclude both 1 and 100. Therefore, there are (99/2) or 49 numbers divisible by 2 between 1 and 100.
But some numbers will be divisible by both 2 and 3 and these numbers will obviously be divisible by 6. We find that there are (100/6) or 16 numbers between 1 and 100 which are divisible by 6.
So, the number of numbers between 1 and 100 which are divisible by both 2 and 3 is (33+49-16) or 66.
Therefore, the required number is (98-66) or 32.
Could you please share the Official Answer, Mariah?
Since the problem deals with numbers "between 1 and 100", I feel we should exclude both 1 and 100. Therefore, there are (99/2) or 49 numbers divisible by 2 between 1 and 100.
But some numbers will be divisible by both 2 and 3 and these numbers will obviously be divisible by 6. We find that there are (100/6) or 16 numbers between 1 and 100 which are divisible by 6.
So, the number of numbers between 1 and 100 which are divisible by both 2 and 3 is (33+49-16) or 66.
Therefore, the required number is (98-66) or 32.
Could you please share the Official Answer, Mariah?
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lunarpower
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an official gmat problem would NEVER contain ambiguous wording such as this. if this problem were official, it would contain "...not divisible by 2 or 3?"dimonya wrote:ugh, such clumsy wording "not divisible by 2 and 3"
i read it as not divisible by 6.....
should be "not divisible by 2 and/or 3"
thats how u lose marks , darn it
two things, though.
1 * first of all, even though the gmat won't contain ambiguous problem statements**, you still must know the default meaning of certain terms in problem statements. for example, "two integers" are allowed to be the same (e.g., 5 and 5 are "two integers that multiply to give a product of 25"); "or" allows the possibility that both things are true; etc.
2 * on this problem, the answer choices give away the problem's meaning, even though the wording is horrible. it's not hard to see that there are 50 numbers from 1-100 that aren't divisible by 2 (49, if the problem says "between 1 and 100"), so the fact that all choices are under 49 resolves the ambiguity.
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**the gmat will actually go out of its way to avoid ambiguity in problem statements. for instance, it will specify, every time, that you should consider "positive factors", not just "factors". etc.
because the gmat is this precise, make sure that you pay very, very close attention to the wording of problems, be very literal, and avoid making assumptions.
see OG11 data sufficiency #146 (don't post details here), on which you must actively avoid the assumption that the variable n stands for an integer.
Last edited by lunarpower on Sun Feb 08, 2009 1:39 pm, edited 1 time in total.
Ron has been teaching various standardized tests for 20 years.
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Alara533
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I have a doubt here, since its mentioned between, should we include 100?mariah wrote:114. How many numbers between 1 and 100 are ...
In that case, the number of multiples of 2 will be 49 and not 50!!
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lunarpower
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you are correct.Alara533 wrote:I have a doubt here, since its mentioned between, should we include 100?mariah wrote:114. How many numbers between 1 and 100 are ...
In that case, the number of multiples of 2 will be 49 and not 50!!
by default, "between" is exclusive of the stated endpoints of the interval. if the problem writers intend that "between" be inclusive, they'll write "inclusive".
also note that, as mentioned above, the gmat writers often go out of their way to be very clear in their wording. if the problem literally means "between 1 and 100", then the wording will often say "greater than 1 and less than 100", or something else equally explicit.
Ron has been teaching various standardized tests for 20 years.
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Alara533
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thanks Ronlunarpower wrote:you are correct.Alara533 wrote:I have a doubt here, since its mentioned between, should we include 100?mariah wrote:114. How many numbers between 1 and 100 are ...
In that case, the number of multiples of 2 will be 49 and not 50!!
by default, "between" is exclusive of the stated endpoints of the interval. if the problem writers intend that "between" be inclusive, they'll write "inclusive".
also note that, as mentioned above, the gmat writers often go out of their way to be very clear in their wording. if the problem literally means "between 1 and 100", then the wording will often say "greater than 1 and less than 100", or something else equally explicit.
