GMAT iphone app - question 85 : GMAT Problem Solving (PS)
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# GMAT iphone app - question 85

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GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 09:59
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Hi everybody,

In the iphone app : the quantitative set - question 85 :
How many three digit integers are not divisible by 3 ?

Answer seems to be 600. But i don't understand how !

I agree that 300 3-digit integers are divisible by 3, but why 600 are not ! what about the last 100's ?

Why it is not the rest : 700 ?

Fred
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Re: GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 11:50
The numbers from 1-99 are not 3 digits. Only numbers 100-999 are 3 digit (this is 900 numbers total).
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Re: GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 16:49
funboard70 wrote:
Hi everybody,

In the iphone app : the quantitative set - question 85 :
How many three digit integers are not divisible by 3 ?

Answer seems to be 600. But i don't understand how !

I agree that 300 3-digit integers are divisible by 3, but why 600 are not ! what about the last 100's ?

Why it is not the rest : 700 ?

Fred

My attempt:

3 digit integers -- 100 to 999.

Total there are ((999 - 100) +1) = 900 numbers.

Now for every 10 numbers -- 101, 102, 103,104, 105, 106, 107, 108, 109, 110 -- only 3 are divisible by 3 (i.e,. 102, 105, 108) and 7 numbers are not.

Hence for 900 numbers, only $$(7/10)*900$$ numbers are not divisible by 3.

=> 630 numbers are not divisible by 3.
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Re: GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 18:21
funboard70 wrote:
Hi everybody,

In the iphone app : the quantitative set - question 85 :
How many three digit integers are not divisible by 3 ?

Answer seems to be 600. But i don't understand how !

I agree that 300 3-digit integers are divisible by 3, but why 600 are not ! what about the last 100's ?

Why it is not the rest : 700 ?

Fred
.

Here is how i approached it.
Total no of 3 digit integers = 9*10*10 = 900 (First digit can't be zero)
Any multiples of 3 are divisible by 3. So if we can find the no of multiples of 3 between 100 and 999 that no can be subtracted from 900 to get the 3 digit integers not divisible by 3.
There are 333 multiples of 3 < 1000 (999 is the greatest multiple of 3 under 1000 and 999/3 =333)
There are 33 multiples of 3 < 100 (99 is the greatest multiple of 3 under 100 and 99/3 =33)
So There are 333-33=300 multiples of 3 between 100 and 999 and 900-300=600 3 digit integers which are not divisible by 3.
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Re: GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 19:17
well since there are 900 3 digit numbers, and every 3rd number is divisible by 3, then the number of numbers divisible by 3 = 900/3 does this approach make sense? by the same token the number of numbers divisible by 4 = 900/4 = 225, by 5 = 900/5=180... does this work in general?
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Re: GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 20:18
brau0300 wrote:
The numbers from 1-99 are not 3 digits. Only numbers 100-999 are 3 digit (this is 900 numbers total).

Thanks Brau... Stupid mistake that i made...
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Re: GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 20:26
mainhoon wrote:
well since there are 900 3 digit numbers, and every 3rd number is divisible by 3, then the number of numbers divisible by 3 = 900/3 does this approach make sense? by the same token the number of numbers divisible by 4 = 900/4 = 225, by 5 = 900/5=180... does this work in general?

Hi,

In fact, it is not a general rule ! Ex : 900 / 7 = 128.51...
How do i approach this kind of prob:
(larger multiple - smaller multiple) / multiple + 1

with the example of 3
Larger Multiple : 999
Smaller multiple : 102
So (999 - 102) / 3 + 1 = 300

Example of 5 :
Larger Multiple : 995
Smaller multiple : 100
Therefore : (995 - 100) / 5 + 1 = 180

Another way to check is to find the first and the result of the division
Ex with 3
102 / 3 = 34
999 / 3 = 333
333 - 34 + 1 = 300

Hope it's clear...

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Re: GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 20:29
ezhilkumarank wrote:
funboard70 wrote:
Hi everybody,

In the iphone app : the quantitative set - question 85 :
How many three digit integers are not divisible by 3 ?

Answer seems to be 600. But i don't understand how !

I agree that 300 3-digit integers are divisible by 3, but why 600 are not ! what about the last 100's ?

Why it is not the rest : 700 ?

Fred

My attempt:

3 digit integers -- 100 to 999.

Total there are ((999 - 100) +1) = 900 numbers.

Now for every 10 numbers -- 101, 102, 103,104, 105, 106, 107, 108, 109, 110 -- only 3 are divisible by 3 (i.e,. 102, 105, 108) and 7 numbers are not.

Hence for 900 numbers, only $$(7/10)*900$$ numbers are not divisible by 3.

=> 630 numbers are not divisible by 3.

Hi,

In Fact you can't use the solution of choosing 10 numbers and extrapolate after.
What about 180 till 189 ? there are 4 integers divisible by 3... not 3

Anyway thanks for your help !

Fred
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Re: GMAT iphone app - question 85 [#permalink]

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09 Aug 2010, 20:32
crack700 wrote:
funboard70 wrote:
Hi everybody,

In the iphone app : the quantitative set - question 85 :
How many three digit integers are not divisible by 3 ?

Answer seems to be 600. But i don't understand how !

I agree that 300 3-digit integers are divisible by 3, but why 600 are not ! what about the last 100's ?

Why it is not the rest : 700 ?

Fred
.

Here is how i approached it.
Total no of 3 digit integers = 9*10*10 = 900 (First digit can't be zero)
Any multiples of 3 are divisible by 3. So if we can find the no of multiples of 3 between 100 and 999 that no can be subtracted from 900 to get the 3 digit integers not divisible by 3.
There are 333 multiples of 3 < 1000 (999 is the greatest multiple of 3 under 1000 and 999/3 =333)
There are 33 multiples of 3 < 100 (99 is the greatest multiple of 3 under 100 and 99/3 =33)
So There are 333-33=300 multiples of 3 between 100 and 999 and 900-300=600 3 digit integers which are not divisible by 3.

Humm another way to find the solution...

Fred
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Re: GMAT iphone app - question 85 [#permalink]

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24 May 2011, 02:18
hi...first of all for division of 3 rule changing digits would not make the differce as far as the sum of the digits is divisible by 3. Hence the change that the Q mentions will not have any difference.

Now the total nos divisible by 3 are : (400-310)/3= 30 . Here the inclusion of 310 does not come into the picture because it is not divisible by 3. If the first no. would have been say 309 then we would have to add +1 to 30. I hope this clears the doubt....
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Re: GMAT iphone app - question 85 [#permalink]

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24 May 2011, 02:51
total integers = 1000-100 = 900
integers divisible by 3 = 999= 102 + (n-1) * 3
n=300.

thus 600 = 900-300
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Re: GMAT iphone app - question 85 [#permalink]

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27 May 2011, 09:38
Using AP(like in the post above mine) to solve such question is the quickest way..

@ezhilkumarank good approach
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Re: GMAT iphone app - question 85 [#permalink]

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20 Jul 2011, 06:18
I got 600 too.
My method is:

no. of 3 digit numbers div. by 3 => range from 100 to 999
we can also say that no. of 3 digit numbers range from 102 to 999 inclusive.
hence, we use the formula:
no. of digits = (Last - First)/increment + 1
= (999 - 102)/3 + 1 = 300
Similarly, we find number of integers from 100 to 999;
no. of digits = Last - First + 1
= 999 - 100 + 1
= 900
No. of integers NOT div. by 3 = Total no. of integers - No. of integers div. by 3
= 900 - 300
= 600
Re: GMAT iphone app - question 85   [#permalink] 20 Jul 2011, 06:18
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