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If d is a positive integer and f is the product of the first

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If d is a positive integer and f is the product of the first [#permalink] New post 31 Jan 2007, 05:20
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If d is a positive integer and f is the product of the first 30 integers, what is the value if d?

(1) 10 (exp) d is a factor of f
(2) d > 6

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE
is sufficient.
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
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Re: DS - Product of the first 30 integers [#permalink] New post 31 Jan 2007, 06:58
TOUGH GUY wrote:
f is the product of the first 30 integers


Could anybody explain this?

If the question said that "f is product of the first 30 positive integer", I would assume f = 1 x 2 x 3 x ... x 30.
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Re: DS - Product of the first 30 integers [#permalink] New post 31 Jan 2007, 11:29
TOUGH GUY wrote:
If d is a positive integer and f is the product of the first 30 integers, what is the value if d?

(1) 10 (exp) d is a factor of f
(2) d > 6

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE
is sufficient.
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient


1) alone is not enough:
Since f=1x2x3x4x5x...x28x29x30
Multipying only the numbers that end in 2,5 and 0 you would get:
2x5x10x12x15x20x22x25x30 with several 10 factors there, like this it will be easier:
2
5
10=2x5
12=2x2x3
15=3x5
20=2x2x5
22=2x11
25=5x5
30=2x3x5

We have 8 numbers 2 and 7 numbers 5, so d can be from 1 do 7 by just taking these numbers...

2)d>6 alone is not enough either.

Putting them together: you have that d>6 from the 2) and that you have 7 possible numbers 10

C is the answer.


PS) - the important thing is to watch for the 5s and not the 2s, because we have plenty of 2s...
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 [#permalink] New post 31 Jan 2007, 16:31
the first 30 intigers is vague

intigers could be +ve or -ve or zero , tough guy need to revise the question
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 [#permalink] New post 31 Jan 2007, 17:27
answer has to be C..

f=1*2*3*4*5....30

lets take the easy choice first...

statement 2) easy Insuff

statement 1) 10^d * m=f

well, lets see 10 has prime factors 5 and 2, so in the first 30 integers there are how many 2s? 30/2=15, 4 gives one more 2, 8 gives 2 more, 16 gives 3 more etc...

lets see how many 5s are there in first 30 integers...30/5=6, 25 gives us one more 5...so we have 7 fives...

now..if 10^d is a factor of F, then power of D cannot be greater than 7..
..
rewrite 10^d as 5^a 2^b, where the power of a determines d.

so..going back to statment 1) d can be anynumber from 0-7...Insuff

together..if d>6 then the only number that fits this is 7...

d=7..C is sufficient
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 [#permalink] New post 31 Jan 2007, 17:29
yezz..it doesnt matter the sign of the integers...

yezz wrote:
the first 30 intigers is vague

intigers could be +ve or -ve or zero , tough guy need to revise the question
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 [#permalink] New post 01 Feb 2007, 02:07
fresenha , y not zero to be the first of the 30 intigers
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 [#permalink] New post 01 Feb 2007, 09:44
I second that Yezz. 1st 30 intergers is vague. Can anyone tell which is the one integer ? 0 or 1 or -1 ...?

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 [#permalink] New post 02 Feb 2007, 21:01
chief...if f was zero then statement 1 cannot be true..in gmat you have to know that the statements have to be true..

suppose f=0*1*2*3...29 then f=0

suppose d=0, then 10^0=1, which is not a factor of f;



yezz wrote:
fresenha , y not zero to be the first of the 30 intigers
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 [#permalink] New post 03 Feb 2007, 22:51
WELL Fresinha ,

i thought that if 0 is a mutliple of any iniger then

if F = 0

THEN ANY NUMBER IS A FACTOR AND THUS STATMENT ONE REMAINS VALID
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 [#permalink] New post 05 Feb 2007, 17:08
fresinha , any help on this one , i am really confused now?????
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 [#permalink] New post 05 Feb 2007, 17:20
yezz...think of it this way if F=0 then you cannot say its a multiple of d, unless d=0...

refresh your defination of factors and multiples..

supposed m is a factor of n..then..2*m=n..or 3*m=n...in other words N is a multiple of m...

ok having established what factors and multiples means...

if F=0..then we have no Factors of F..zero has no factors other than itself.

Now..the statement 1) says 10^d is a factor of F...then we have to take this to b true. F cannot be 0 otherwise d would have to -infiniti..

now d can be zero and 10^0=1, F can be 1..but we need to rule this out..

so statment 2) does just that..it tell us that d is not zero..


if you need help with the rest of how to solve the question...PM me.

yezz wrote:
fresinha , any help on this one , i am really confused now?????
  [#permalink] 05 Feb 2007, 17:20
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