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

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Manager
Joined: 14 May 2009
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What is the value of 3-digit integer X ? (1) X has exactly  [#permalink]

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02 Jun 2009, 22:35
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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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Senior Manager
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03 Jun 2009, 01:44

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..

Manager
Joined: 14 May 2009
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03 Jun 2009, 01:49
Neochronic wrote:

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..

In your combined, did you check to see how many prime factors each one had?
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03 Jun 2009, 23:36
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 ?
Manager
Joined: 14 May 2009
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04 Jun 2009, 00:04
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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Senior Manager
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04 Jun 2009, 01:05

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 ?
Manager
Joined: 16 Apr 2009
Posts: 209
Schools: Ross

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04 Jun 2009, 09:01
111 =37x3 --> X has only two prime factors.
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Manager
Joined: 14 May 2009
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04 Jun 2009, 10:11
Neochronic wrote:

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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Manager
Joined: 24 Apr 2009
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04 Jun 2009, 10:34
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..
Manager
Joined: 08 Feb 2009
Posts: 139
Schools: Anderson

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11 Jun 2009, 05:33
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 ?
SVP
Joined: 29 Aug 2007
Posts: 2420

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11 Jun 2009, 22:04
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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SVP
Joined: 29 Aug 2007
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11 Jun 2009, 22:07
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.

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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Manager
Joined: 08 Feb 2009
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Schools: Anderson

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12 Jun 2009, 03:35
GMAT TIGER 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 ?
Intern
Joined: 28 Mar 2009
Posts: 23

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12 Jun 2009, 04:07
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)

(IF however, repeat prime factors are counted as an extra, (which I've never come across before), then 111 is the only solution)
Manager
Joined: 14 Jun 2009
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15 Jun 2009, 22:00
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

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Tough DS 2 &nbs [#permalink] 15 Jun 2009, 22:00
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