If d is a positive integer and f is the product of the first : GMAT Data Sufficiency (DS) - Page 2
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# If d is a positive integer and f is the product of the first

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Manager
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19 Aug 2006, 09:48
Got it! After carefully tracing back my steps I reached the same conclusion.

I actually approached this problem the same way you did, but I counted way too many 10s in 30! (Somehow 20 produced two 10s for me instead of one!)
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I CANT GET IT (INTIGERS AND FACTORIALS) [#permalink]

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04 Sep 2006, 10:53
If d is a positive integer and f is the prodcut of the first 30 positive integers, what is the value of d?

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

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04 Sep 2006, 11:17
This question is testing ur understanding of number properties...

f=30!

D is a factor of f..

(1) 10^d is a factor of F....

well..10 is a fator of F, so is 100...Insuff

think of it this way...what are the prime factors of 10?

10=2*5, then 10^d, will have prime factors=2^a * 5^b..

now..we know that there are going to be fewer 5s in 30 factorial...so whatever the power of 5 is...will determine the power of 10^d.

in other words 5^b=10^d (the biggest possible value of 10 tht is a factor of 30!)

(2) d is greater than 6...

well that by itself is insuff

together Sufficient...

here is how..

30/5=6 fives...
25 has 2 fives, so there is one additional 5...

so we know that 5^b; where b=7...

so ..10^7 is the highest possible factor of 10 in 30!...

Sufficient...
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04 Sep 2006, 11:32
Thanks a lot ... i appreciate the time you gave me

to write this detailed explanation
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26 Nov 2006, 12:02
If d is a positive integer and f is the product of the first 30 positive integers, what's the value of d?

1. 10^d is a factor of f
2. d>6

I did this Q right, however when I checked the factorial of "f" in Excel I got a different result... is Bill gates wrong
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Last edited by ugo_castelo on 27 Nov 2006, 03:26, edited 1 time in total.
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27 Nov 2006, 00:23
ugo_castelo wrote:
If d is a positive integer and f is the product of the first 30 integers, what's the value of d?

1. 10^d is a factor of f
2. d>6

I did this Q right, however when I checked the factorial of "f" in Excel I got a different result... is Bill gates wrong

What does first 30 integers mean? What is the FIRST Integer anyway?
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27 Nov 2006, 03:26
yes, it's Positive... integers ( typed too fast)
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27 Nov 2006, 08:58
If d is a positive integer and f is the product of the first 30 positive integers, what's the value of d?

1. 10^d is a factor of f
2. d>6

1st 30 = 1*2*3*4*... *30
we know this has 5*10*15*20*30 so 10^1 is fcator 10^2 is factor
(1) 10^d is factor insuff
(2) insuff on its own

Togather

Lets check how many multiple 5s are in product

5*10*15*20*25*30
5*5*2*5*3*5*4*5*5*5*6 so 5^7
we also have many 2s 2,4,8,... surely we can find 7 or more

5^7*2*7=10^7

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27 Nov 2006, 13:30
that's correct
the same way I did
However , when I checked the Factorial of 30 in excel, I got more then 10^7

that's why the surprise
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01 Jan 2007, 01:36
If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?

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

What is the best way of handling this type of question

OA to follow
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01 Jan 2007, 02:57
(C) for me

f = 30!

To me, I decompose 10 in prime factor.

10 = 5*2.

Obviously, in 30!, there is a lot of "2" prime factors. So, the limit comes from the number of 5 prime factors.

5 is contained in : 5, 10, 15, 20, 25, 30.

So, we have 6 5 prime factors available.

From 1
f = k*10^d
Following what we said about 5, d could be anything from 1 to 6.

INSUFF.

From 2
d > 6 : d = 7 or d = 8. It gives nothing alone.

INSUFF.

Both (1) and (2)
We know the maximum is 6... Is it a typo? I would say d >= 6. Because d cannot be 7. But we can conclude impossible

SUFF.
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01 Jan 2007, 03:03
OA is ......

C

The question for 2 is d > 6, no typo

Last edited by lfox2 on 01 Jan 2007, 03:09, edited 1 time in total.
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01 Jan 2007, 03:09
Fig wrote:
(C) for me

f = 30!

To me, I decompose 10 in prime factor.

10 = 5*2.

Obviously, in 30!, there is a lot of "2" prime factors. So, the limit comes from the number of 5 prime factors.

5 is contained in : 5, 10, 15, 20, 25, 30.

So, we have 6 5 prime factors available.

From 1
f = k*10^d
Following what we said about 5, d could be anything from 1 to 6.

INSUFF.

From 2
d > 6 : d = 7 or d = 8. It gives nothing alone.

INSUFF.

Both (1) and (2)
We know the maximum is 6... Is it a typo? I would say d >= 6. Because d cannot be 7. But we can conclude impossible

SUFF.

No typo :p... I have forgotten 25 = 5*5 ... 7 5 are available
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01 Jan 2007, 05:03
c for me as well.

10 has 2 and 5 as factors,

2 occurs

30 / 2 = 15;
15/2 = 7;
7/2 = 3
3/2 = 1;

(15 + 7 + 3 + 1) = 26 times

While 5 occurs,

30/ 5 = 6
6/5 = 1

6 + 1 = 7 times

there for 10 will have 7 instances in 30!
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25 Apr 2007, 05:00
If d is a positive integer and f is the product of the first 30 positive integers what is the value of d?

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

Can someone suggest a good technique for this one please!
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25 Apr 2007, 11:31
doc14 wrote:
If d is a positive integer and f is the product of the first 30 positive integers what is the value of d?

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

Can someone suggest a good technique for this one please!

The best way to solve problems like that is to brake it into small pieces:

f = 1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20*
21*22*23*24*25*26*27*28*29*30

First off - try to convert the number above into something that you can work with - look at the statements first to get more info.

I left only the numbers that are multiplication of 10 !

2*4*5*10*20*15*25*30 = convert into = 2*2*5*10*2*10*3*5*5*5*10*3

get rid off the 3 = 10*10*10*10*10*10*10 (total of 7)

now the magic begins !

statement 1

we were asked about 10^n as a factor of - f - so look up - there no way to know - d can be 1,2,3,4,5,6,7

insufficient

statement 2

dosen't say much by itself

insufficient

statment 2&1

since there is 7 exponents of 10 that are a factor of - f
if n>6 n has to be 7.

sufficient

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25 Apr 2007, 11:38
I think the best way to solve the problem is this:

10 can only be made up of 2s and 5s (2x5). In the list of 1x2x3...x30, there are plenty of 2s, but only 7 5s (5, 10, 15, 20, 30 have one each, and 25 has 2 5s). So, f has 7 10s .. ie, f = k x 10^7

So, from statement one, d can be anything from 1 to 7

From statement two, d should be >6

Neither of the statements are sufficient in themselves, but together, they make d = 7

Hence C
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25 Apr 2007, 19:16
f = 30!

St1:
10^d is a factor of f. d can be 1,2,3 etc... Insufficient.

St2:
Uesless. We know nothing much else. Insufficient.

St1 and St2:
If d = 7, then we have 10^7 = (2^7)*(5^7). That's all the 5's we have in 30!. So d cannot be 8 and up. Sufficient.

Ans C
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25 Apr 2007, 23:08
OA is C.

Thanks for all the replies!
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Re: DS : product of first 30 positive integers [#permalink]

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10 Aug 2007, 00:23
trahul4 wrote:
If d is a positive integer and f is the product if the first 30 positive integers, what is the value of d?

1. 10^d is a factor of f.
2. d>6

I get C as well.

Stat1: d =1 or 2; insuff

Stat2: insuff

Stat 1&2: d=7, suff.

If 10^d is a factor of 30! and d>6 then d has to be 7 since 10^d is not a factor of 30! if d>7.
Re: DS : product of first 30 positive integers   [#permalink] 10 Aug 2007, 00:23

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