Integers in list A that are not in B

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Feb 22, 2014 4:42 pm

Hello,

Can you please tell me how to solve this:

The integers between 1 and 100, inclusive, are put in list A if they are divisible by 2 and in list B if they are divisible by 3. How many integers in list A are not in list B?

OA: 34

I tried to solve as follows:

A = { 2, 4, 6, 8, 10, 12, 14, 16, ... }
B = { 3, 6, 9, 12, 15, 18, 21, 24, ... }

There are ((100 - 2)/2 ) + 1 integers in A i.e. 50 integers in A

2 out of 3 are not in B.

Hence, 2/3 = ?/50

I was stuck at this point though. Can you please assist?

Thanks,
Sri

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Source: Beat The GMAT — Problem Solving | Sat Feb 22, 2014 4:42 pm

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by [email protected] » Sat Feb 22, 2014 7:19 pm

Hi Sri,

To answer this question, you should try isolating each of the "lists" individually:

The numbers 1 to 100, inclusive...

How many are divisible by 2? 50
How many are divisible by 3? 33 (To be fair, this step isn't really necessary)

How many are divisible by BOTH? 16

So the number of integers that are divisible by 2 BUT NOT by 3 = 50 - 16 = 34

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sat Feb 22, 2014 7:38 pm

My Approach:

"How many integers between 1 and 100 inclusive are in list A (evens) are not in list B (are not multiples of 3)"

There are 50 evens in the list (2*1 to 2*50). Only 1 in 3 evens is a multiple of 3 (2, 4, 6, 8, 10, 12...), so about 2/3 of the 50 evens are not multiples of 3.

Solution: (2/3)*50 = 33.33. Pick the answer that is closest.

To be more exact, we can say 2/3 of the first 48 evens are non-multiples of 3. That's 32 numbers. Add to that the last 2 evens in the list (2*49=98, and 2*50=100) to get 34 total numbers

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Feb 22, 2014 8:03 pm

gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

The integers between 1 and 100, inclusive, are put in list A if they are divisible by 2 and in list B if they are divisible by 3. How many integers in list A are not in list B?

OA: 34

List A is composed of every integer between 1 and 100, inclusive, that is divisible by 2.
Since 100/2 = 50, the total number of integers is List A = 50.

Of these 50 integers that are divisible by 2, any that are also divisible by 3 are also in List B.
Any integer that is divisible by both 2 and 3 is a MULTIPLE OF 6.
Since 100/6 = 16, the number of multiples of 6 between 1 and 100, inclusive = 16.

Since these 16 multiples of 6 in both List A and List B, the number of integers that are in List A but NOT in List B = 50-16 = 34.

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murilomoraes: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun May 06, 2012 7:32 am; Thanked: 1 times

by murilomoraes » Mon Mar 03, 2014 12:01 pm

I did it in this way:

What is the greatest integer multiple of 2 that when you multiply for 3 will be less than 100?
You quickly figure out that the number 32, and 32 divided by 2 is 16, and you have a total of 50 integer multiple of 2 between 0 and 100 so 50 - 16 = 34 and this is the answer.

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