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# If x is an integer divisible by 15 but not divisible by 20,

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Director
Joined: 01 May 2007
Posts: 772
If x is an integer divisible by 15 but not divisible by 20,  [#permalink]

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Updated on: 14 Jun 2007, 12:21
00:00

Difficulty:

(N/A)

Question Stats:

75% (01:07) correct 25% (00:00) wrong based on 16 sessions

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3. If x is an integer divisible by 15 but not divisible by 20, then x
CANNOT be divisible by which of the following?

6
10
12
30
150

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Originally posted by jimmyjamesdonkey on 14 Jun 2007, 11:32.
Last edited by jimmyjamesdonkey on 14 Jun 2007, 12:21, edited 1 time in total.
Director
Joined: 01 May 2007
Posts: 772

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14 Jun 2007, 11:46
Correct, but I do not understand the Princeton Review answer. According to this explanation shouldn't "C" have been removed by the bold. Please give me a new "OA". Thanks.

If x is divisible by (i.e., a multiple of) 15 but not 20, then x could be, for instance, 15, 30, or 45, but not 60. If a number is divisible by 15, then it is also divisible by factors of 15, i.e. 3 and 5. Just looking at the rule of divisibility for 3, (A), (B), and (D) are out. Let’s look at answer choice (E): 150 is divisible by 15 but not 20; thus x could be 150 and (E) is out. So by POE, the answer must be (C).
Manager
Joined: 22 May 2007
Posts: 119

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14 Jun 2007, 11:56
I've no idea how to solve these problems. I just do trial and error.
Director
Joined: 01 May 2007
Posts: 772

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14 Jun 2007, 11:58
Terrific. Damn I hate these factor problems too.

It makes no sense. PR says it elimated A, B, and D based on the rules of divisibility of 3. 6 is divisible for 3! 10 is not, and 30 is. The explanation by PR seems messed up. Can one of our 700+'s give us a good answer.
VP
Joined: 08 Jun 2005
Posts: 1136

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14 Jun 2007, 12:30
lets see what will happae if x is divisable by 15 and 20.

15 = 3*5
30 = 3*5*2
45 = 3*5*3
60 = 3*5*2*2
75 = 3*5*5

20 = 2*2*5
40 = 2*2*2*5
60 = 3*2*5*2
80 = 2*2*5*2*2

we can see that x will be divided by 15 and 20 when the number is 3*5*2*2 but we know that x is not divisiable by 20 meaning any number that has 3*5*2*2 or any combination of 3*5*2*2 isn't the correct answer.

6 = 2*3
10 = 2*5
12 = 2*2*3
30 = 2*3*5
150 = 2*3*5*5

you can tell that only 2*3*5*5 cannot be the answer.

Director
Joined: 01 May 2007
Posts: 772

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14 Jun 2007, 12:39
Killer, The OA from the PR materials is C. These materials are from the PR Course. Are the materials wrong?
Manager
Joined: 22 May 2007
Posts: 119

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14 Jun 2007, 12:43
KillerSquirrel wrote:
lets see what will happae if x is divisable by 15 and 20.

15 = 3*5
30 = 3*5*2
45 = 3*5*3
60 = 3*5*2*2
75 = 3*5*5

20 = 2*2*5
40 = 2*2*2*5
60 = 3*2*5*2
80 = 2*2*5*2*2

we can see that x will be divided by 15 and 20 when the number is 3*5*2*2 but we know that x is not divisiable by 20 meaning any number that has 3*5*2*2 or any combination of 3*5*2*2 isn't the correct answer.

6 = 2*3
10 = 2*5
12 = 2*2*3
30 = 2*3*5
150 = 2*3*5*5

you can tell that only 2*3*5*5 cannot be the answer.

Squirrel, 150 is divisible by 15 and not by 20 so it can be X.
150 is divisible by 150.

I'm sticking with 12 or C!
Director
Joined: 01 May 2007
Posts: 772

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14 Jun 2007, 12:45
I agree with C, but the PR explanation is screwy. I agree it needs to be factored somehow though.
Manager
Joined: 04 Jan 2006
Posts: 58

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14 Jun 2007, 13:05
1
Factors of 15 -> 3 and 5
factors of 20 ->5 and 2 and 2.

Since X is divisible by 15, it has 3 and 5 as factors.
it is notdivisible by 20. so it does not have 4 as a factor for sure.

among the choices, 12 is the only no. with 4 as a factor.
So we can confirm that X is not divisible by 4.
SVP
Joined: 01 May 2006
Posts: 1775

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14 Jun 2007, 13:10
3
(C) as well

As x is divible by 15 = 5*3, we have:
o x divisble by 5
o x divisble by 3

As x is not divisible by 20=5*4, we know that x is not divisible by 4 (5 is OK just seen).

Now let see the answers to find the one that contains a 4 as a factor.

A) 6 = 3*2 >>> No 4, so no.
B) 10 = 5*2 >>> No 4, so no.
C) 12 = 3*4 >>> Bingo 4 as a factor !
D) 30 =3*2*5 >>> No 4, so no.
E) 150 = 5*3*5*2 >>> No 4, so no.
Director
Joined: 01 May 2007
Posts: 772

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14 Jun 2007, 13:14
Thanks Fig - That was the answer I was looking for. Isn't the PR answer kind of screwy though. On its first pass it removes answers that are divisible by 3, but by that logic it would have removed (C).
SVP
Joined: 01 May 2006
Posts: 1775

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14 Jun 2007, 13:19
jimmyjamesdonkey wrote:
Thanks Fig - That was the answer I was looking for. Isn't the PR answer kind of screwy though. On its first pass it removes answers that are divisible by 3, but by that logic it would have removed (C).

PR OE is not that much accurate... I do agree ... In addition, we have found 1 or 2 problems that were simply wrong (Do not ask me to recall which ones )
VP
Joined: 08 Jun 2005
Posts: 1136

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14 Jun 2007, 13:36
Fig wrote:
(C) as well

As x is divible by 15 = 5*3, we have:
o x divisble by 5
o x divisble by 3

As x is not divisible by 20=5*4, we know that x is not divisible by 4 (5 is OK just seen).

Now let see the answers to find the one that contains a 4 as a factor.

A) 6 = 3*2 >>> No 4, so no.
B) 10 = 5*2 >>> No 4, so no.
C) 12 = 3*4 >>> Bingo 4 as a factor !
D) 30 =3*2*5 >>> No 4, so no.
E) 150 = 5*3*5*2 >>> No 4, so no.

yes ! my answer is wrong - great work Fig !

Director
Joined: 25 Oct 2006
Posts: 557

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14 Jun 2007, 13:46
I have the same reasoning as fig mentioned,

X divided by 15 So Can be 15,30,45,60 etc
X NOT divided by 20 So Can be 20, 40, 60 etc

So, X never satisfies the divisibility rule if the factor contains 4.

Hence, we should trim that factor if answer choice contains any multiple of 4. Wow, it's there in C) 12.
Manager
Joined: 23 Dec 2006
Posts: 126

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14 Jun 2007, 16:06
I say C, 12 for the following reason:

x/15 means that x/(5*3). 5 and three are two factors of x.

x/20 means x/(5*2^2). We know 5 is a factor of x so 2^2 must be the problem--therefore any number that is a multiple of four is out. Only C, 12 satisfies this condition.
Manager
Joined: 18 Apr 2007
Posts: 119

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14 Jun 2007, 17:00
I used a less than glamourous way, but I got the same answer, C.

I listed all the multiples of 15 from 15 to 150 (since this incorporated all the answer choices) --> 15,30,45,60,75,90,105,120,135,150

Then I crossed out all those that were multiples of 20 (60 and 120).

Then I looked at the answers and compared them to the remaining numbers. I just needed one number that was NOT divisible by the answer and obviously 12 didn't work.

However, as usual, Fig has summed everything up and made it simple. I'm definitely taking Fig's route going forward!
Senior Manager
Joined: 04 Mar 2007
Posts: 406

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16 Jun 2007, 06:28
Fig you rock
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1251
Re: 700+ Guys Help Us! PS: Divisibility question  [#permalink]

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16 Jun 2007, 07:44
jimmyjamesdonkey wrote:
3. If x is an integer divisible by 15 but not divisible by 20, then x
CANNOT be divisible by which of the following?

6
10
12
30
150

If x is a multiple of 15, it is a multiple of 5. Since x is not divisible by 20 and is divisible by 5, x cannot be divisible by 4. Look for multiples of 4 among the answer choices.
Director
Joined: 26 Feb 2006
Posts: 865
Re: 700+ Guys Help Us! PS: Divisibility question  [#permalink]

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16 Jun 2007, 11:46
jimmyjamesdonkey wrote:
3. If x is an integer divisible by 15 but not divisible by 20, then x CANNOT be divisible by which of the following?

6
10
12
30
150

it is C for me as well. if x is divisible by 15 but not 20, then x is not divisible by 4. among the answer choices, 12 is the only choice that is a multiple of 4. so it is 12.
Non-Human User
Joined: 09 Sep 2013
Posts: 8776
Re: If x is an integer divisible by 15 but not divisible by 20,  [#permalink]

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21 Sep 2018, 11:14
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Re: If x is an integer divisible by 15 but not divisible by 20, &nbs [#permalink] 21 Sep 2018, 11:14
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