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Manager  Joined: 15 Jul 2004
Posts: 56
The integers from 1 to 100 inclusive are each written on a  [#permalink]

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12 00:00

Difficulty:   65% (hard)

Question Stats: 62% (01:58) correct 38% (01:53) wrong based on 812 sessions

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The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%

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Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

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Zem wrote:
The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%

# of multiples of 2 in the range (100-2)/2+1=50 (check this: totally-basic-94862.html#p730075);
# of multiples of 3 in the range (99-3)/3+1=33;
# of multiples of both 2 and 3, so multiples of 6, in the range (96-6)/6+1=16 (to get the overlap of above two sets);

Hence there are total of 50+33-16=67 numbers from 1 to 100, inclusive, which are multiples of 2 or 3, which means that the probability of selecting neither multiple of 2 nor multiple of 3 is 1-67/100=33/100=33%.

Hope it's clear.
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VP  Joined: 30 Sep 2004
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67%...

50/100 (all multiples of 2) + 33/100 (all multiples of 3) - 1650/10000 (multiples of 3 and 2) =6650/10000=67%...
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Senior Manager  Joined: 19 Feb 2005
Posts: 392
Location: Milan Italy

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1
odd multiples of 3 are 17/100
3 3+6 3+6+6 3+6+6+6 etc
50/100+17/100=67/100
Senior Manager  Joined: 15 Mar 2005
Posts: 361
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2
Nither even nor a multiple of 3.

Even numbers between 1 and 100 are 2, 4, 6 ... 100 (50 numbers).

Numbers that are multiple of 3 are 3, 6, 9 ... 99. However, all even multiples of 3 have been counted already in even numbers. Therefore, this set includes 3, 9, 15, 21 ... 99. (17 numbers).

Thus total numbers that are to be excluded = 50 + 17 = 67.

Therefore probability that a randomly picked number is nither even nor a multiple of 3 = 33%
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Senior Manager  Joined: 19 Feb 2005
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why I added instead of subtracting? Options >=50% should be ruled out soon because numbers range from 1 to 100, and thus subtracting 50 even you can't have more than 49 (you know at least that 3 is an odd multiple of 3, son you have at least 1 in 50 remaining numbers)

This question is asking nothing more than:
"how many odd numbers are in the first 100 positive ones that are not multiple of 3?"
Senior Manager  Joined: 15 Mar 2005
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thearch wrote:
why I added instead of subtracting? Options >=50% should be ruled out soon because numbers range from 1 to 100, and thus subtracting 50 even you can't have more than 49 (you know at least that 3 is an odd multiple of 3, son you have at least 1 in 50 remaining numbers)

This question is asking nothing more than:
"how many odd numbers are in the first 100 positive ones that are not multiple of 3?"

Careful theArch, that wall is rather fragile !!!

Btw what're you saying? Your answer matches mine?
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Senior Manager  Joined: 19 Feb 2005
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My first answer was 67/100.
However, I was deceived by christoph, because I calculated 67/100 and then I looked at answers already given, and forgot to subtract. This wouldn't happen in the actual test Manager  Joined: 17 Dec 2004
Posts: 56

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2
33%

100 slips of paper: 50 are even, and 17 are odd multiples of 3

100-(50+17)=33
Director  Joined: 18 Feb 2005
Posts: 563

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thearch wrote:
why I added instead of subtracting? :wall

Options >=50% should be ruled out soon because numbers range from 1 to 100, and thus subtracting 50 even you can't have more than 49 (you know at least that 3 is an odd multiple of 3, son you have at least 1 in 50 remaining numbers)

This question is asking nothing more than:
"how many odd numbers are in the first 100 positive ones that are not multiple of 3?"

This happens with many of us....We get there to the answer and forget subtracting.......GMAT has both the answers as a trap and we should be careful enough not to fall in it........
Senior Manager  Joined: 15 Mar 2005
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Zem wrote:
but how you found the number: 17?

Zem, we are trying to find the numbers that are nither divisible by 2 nor 3.

If you take the numbers that are divisible by 2 away, you've taken all even numbers between 1 and 100 away. They are (100-1)/2 = 50 numbers.

We could repeat the same process with 3. However, there are numbers that are common to 2 and 3, and we don't have to take them out (they were accounted for in the even numbers list anyway).

So we see what are these numbers we're looking at (odd multiples of 3).
They are 3, 9, 15, 21 and so on.

There're a plathora of ways to figuring out how many such numbers would exist between 1 and 100. I'd list out two here.

One is the way of sequences.

the last number in this list would be 99.
99 = 3 + (n - 1) 6 => n = 17.

Else do a 100/16 = 16.xxx. 16*6 = 96. but since it starts at 3, the 16th multiple would be 99. 16 multiples, and add one (for 3) and you've 17.

Thus we have the number 17.

Hope that helps.
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Director  Joined: 13 Jun 2004
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I think that in this problem it's easier to find directly the prob than to use the formula 1-(opposite prob)

from 1 to 100 : 100 numbers
even numbers : 50
multiples of 3 : 33 (3*1, 3*2, ...3*33) however in those 33 numbers there are already even numbers and you have to be careful to not repeat the even numbers you've already taken out so finally you will get 17 odd and 16 even (you can see that everytime 3 is multiply by an even number the final result is obviously even so 1/2 of the multiples of 3 will be even and 1/2 odd, howver the last one is odd so there is an additionnal odd one)

17 odd multiples of 3 + 50 even numbers = 67

100-67 = 33 Manager  Joined: 22 Jan 2012
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Location: India
Concentration: General Management, Technology
GPA: 3.3
WE: Engineering (Consulting)
Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

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Simple to solve using P(n) = 1-X concept

P = 1 - [ P(even 0r multiples of 2)+P(multiples of 3) - P(multiples of 2 and 3 or multiples of 6)]
P = (1 - [ 50/100+33/100 - 16/100]) = 33%
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Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

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Zem wrote:
The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%

Bunuel is this approach correct?

Ballparking from 1 to 10 there are only 3 numbers that satisfy these conditions: 1,5 and 7. Then 3/10 so approximately 30% only answer choice that is close is D

If you do it for other ranges you are basically going to have 4,3,4,3,4,3 so in theory it would be something like 3.5/10 or between 30% and 35%

Cheers
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GMAT 1: 780 Q51 V46 Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

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Zem wrote:
The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%

Multiple of 3: 100/3 = 33 numbers
Multiple of 2: 100/2 = 50 numbers

Multiple of 6: 100/6= 16 numbers

Total numbers divisible by 2 or 3: 50 + 33 - 16 = 67

Neither = 100 - 67 = 33

Probability = 33/100

Pushpinder Gill
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Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

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Even numbers = 100/2 = 50
Numbers divisible by 3 = 99/3 = 33
Even or divisible by 3 =
50 + 33 - duplicates(divisible by 3 and even)
Duplicates = 32/2 = 16
Even or divisible by 3 = 50 + 33 - 16
= 67
Numbers that are not even or divisible by 3 = 100 - 67 = 33
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GRE 1: Q169 V154 Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

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Even => 50
Multiples of 3 => 33
multiples of 6 => 16
Not cases => 67
cases =33
P(cases) = 33/100
percentage =33
hence D
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Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

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_________________ Re: The integers from 1 to 100 inclusive are each written on a   [#permalink] 20 Oct 2018, 05:06
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