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What is the value of 3-digit integer X ? (1) X has exactly

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What is the value of 3-digit integer X ? (1) X has exactly [#permalink]

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New post 02 Jun 2009, 21:35
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What is the value of 3-digit integer \(X\)?

(1) \(X\) has exactly two prime factors.

(2) Any 2 digits of \(X\) add to the same number.
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Re: Tough DS 2 [#permalink]

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New post 03 Jun 2009, 00:44
Answer shud be E

1, insufficient.. 11*13, 11*17, 11*19 all satisfy..
2, insufficient.. 111, 222, 333,444,555,666, etc.

combined.. 333 ( 111*3), 555 (111*5), 222 (111*2) all satisfy the conditions..

hence answer is E.
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Re: Tough DS 2 [#permalink]

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New post 03 Jun 2009, 00:49
Neochronic wrote:
Answer shud be E

1, insufficient.. 11*13, 11*17, 11*19 all satisfy..
2, insufficient.. 111, 222, 333,444,555,666, etc.

combined.. 333 ( 111*3), 555 (111*5), 222 (111*2) all satisfy the conditions..

hence answer is E.


In your combined, did you check to see how many prime factors each one had? :)
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Re: Tough DS 2 [#permalink]

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New post 03 Jun 2009, 22:36
1 is neither a prime number nor a composite number..

and i am not considering the number itself to be its own prime factor..

in such case, the answer shud be E.. imo..

whats the OA ?
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Re: Tough DS 2 [#permalink]

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New post 03 Jun 2009, 23:04
OA is C

1 is not considered prime on the GMAT

111 is the only answer, as 222 = 2*111 (factors of 111 + 1),333 = (factors of 333 + 1), etc...
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Re: Tough DS 2 [#permalink]

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New post 04 Jun 2009, 00:05
Hades,

sorry but i still dont get you on this..


222 = prime factors are 111, 2
333 = prime factors are 111, 3
555 = priome fators are 111, 5

and all these 3 numbers satisfy the 2 conditions given...

Am i missing something somewhere ?
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Re: Tough DS 2 [#permalink]

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New post 04 Jun 2009, 08:01
111 =37x3 --> X has only two prime factors.
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Re: Tough DS 2 [#permalink]

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New post 04 Jun 2009, 09:11
Neochronic wrote:
Hades,

sorry but i still dont get you on this..


222 = prime factors are 111, 2
333 = prime factors are 111, 3
555 = priome fators are 111, 5

and all these 3 numbers satisfy the 2 conditions given...

Am i missing something somewhere ?


\(111 = 3(37)\)

Sum up the digits -- they add up to 3, a multiple of 3
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Re: Tough DS 2 [#permalink]

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New post 04 Jun 2009, 09:34
so, this doesn't mean that it has no factors other than 2 prime factors.
it might be possible that statement 1 means that it has only 2 prime factors. it can mean that 3 can come twice.. right??
i mean in that case the answer would be E..
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Re: Tough DS 2 [#permalink]

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New post 11 Jun 2009, 04:33
atomy wrote:
so, this doesn't mean that it has no factors other than 2 prime factors.
it might be possible that statement 1 means that it has only 2 prime factors. it can mean that 3 can come twice.. right??
i mean in that case the answer would be E..


I agree.
the answer should be E, because three numbers satisfy the conditions.

111, 333 and 999 (all of them have exactly two prime factors).

111 = 1, 3, 37, 111
333 = 1, 3, 9, 37, 111, 333
999 = 1, 3, 9, 27, 37, 111, 333, 999


can anyone explain ?
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Re: Tough DS 2 [#permalink]

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New post 11 Jun 2009, 21:04
atomy wrote:
so, this doesn't mean that it has no factors other than 2 prime factors.
it might be possible that statement 1 means that it has only 2 prime factors. it can mean that 3 can come twice.. right??
i mean in that case the answer would be E..


The following statement is never correct:

A number or an integer has only 2 factors and both are primes. For ex: N has only 2 factors (a and b) and both (a and b) are primes. This is always wrong. Lets say a and b are 2 and 3. Then N must be 6 but N has other factors (1 and 6) as well.
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Re: Tough DS 2 [#permalink]

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New post 11 Jun 2009, 21:07
Hades wrote:
What is the value of 3-digit integer \(X\)?

(1) \(X\) has exactly two prime factors.
(2) Any 2 digits of \(X\) add to the same number.



Statement 1 is ambigious. The questions with prime factors can easily be ambigious. :oops:

How one defines "two prime factors"? 6 and 36 both have 2 prime factors. (3^k)(3x37) or (37^k)(3x37) has also 2 prime factors. However it doesnot mean that there are not any other factors. :shock:

Therefore questions/statements should be clear, and unambigious.
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Re: Tough DS 2 [#permalink]

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New post 12 Jun 2009, 02:35
GMAT TIGER wrote:
Hades wrote:
What is the value of 3-digit integer \(X\)?

(1) \(X\) has exactly two prime factors.
(2) Any 2 digits of \(X\) add to the same number.



Statement 1 is ambigious. The questions with prime factors can easily be ambigious. :oops:

How one defines "two prime factors"? 6 and 36 both have 2 prime factors. (3^k)(3x37) or (37^k)(3x37) has also 2 prime factors. However it doesnot mean that there are not any other factors. :shock:

Therefore questions/statements should be clear, and unambigious.



I agree.
Is this question from gmat prep ?
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Re: Tough DS 2 [#permalink]

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New post 12 Jun 2009, 03:07
Normally repeat prime factors are not counted as an extra prime factor. So 111, 333, and 999 all have only 2 prime factors:

111 = 3 x 37 (2 prime factors)

333 = 3 x 3 x 37 (2 prime factors)

999 = 3 x 3 x 3 x 37 (2 prime factors)

Answer should be E

(IF however, repeat prime factors are counted as an extra, (which I've never come across before), then 111 is the only solution)
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Re: Tough DS 2 [#permalink]

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New post 15 Jun 2009, 21:00
I agree normally repeat prime factors are not counted. thus answer shuld be (E)

I gathered from the solutions that the 2nd condition gve numbers as 111,222,333.

But this statement was slightly confusing::


2) Any 2 digits of X add to the same number
Re: Tough DS 2   [#permalink] 15 Jun 2009, 21:00
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What is the value of 3-digit integer X ? (1) X has exactly

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