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What is the value of 3digit integer X ? (1) X has exactly [#permalink]
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02 Jun 2009, 21:35
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This topic is locked. If you want to discuss this question please repost it in the respective forum. What is the value of 3digit integer \(X\)? (1) \(X\) has exactly two prime factors. (2) Any 2 digits of \(X\) add to the same number.
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Hades



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Re: Tough DS 2 [#permalink]
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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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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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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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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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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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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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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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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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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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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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11 Jun 2009, 21:07
Hades wrote: What is the value of 3digit 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. 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. Therefore questions/statements should be clear, and unambigious.
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Re: Tough DS 2 [#permalink]
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12 Jun 2009, 02:35
GMAT TIGER wrote: Hades wrote: What is the value of 3digit 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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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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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










