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# M05-06

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:24
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35% (medium)

Question Stats:

52% (00:27) correct 48% (00:21) wrong based on 159 sessions

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What is the product of 6 consecutive integers?

(1) The greatest integer is 4

(2) The sequence has both positive and negative integers

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Joined: 02 Sep 2009
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16 Sep 2014, 00:24
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Official Solution:

(1) The greatest integer is 4. Since 4 is the greatest integer out of 6 consecutive integers, then all 6 integers can be found and thus the product calculated. Sufficient.

Just to illustrate: 6 consecutive integers would be {-1, 0, 1, 2, 3, 4}. Since there is a zero among them, the product will also be zero.

(2) The sequence has both positive and negative integers. Since a sequence of consecutive integers has both positive and negative numbers in it, then it must also contain zero, so the product of the terms of such sequence will also be zero. Sufficient.

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Concentration: Entrepreneurship, Marketing
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08 Dec 2016, 17:31
From 2 statement : The sequence has both positive and negative integers
I knew the condition is Consecutive Integer, I considerd 2 cases
Case 1: Odd consecutive integer
(-3,-1,1,3,5,7) In this case the Product is Negative Integer
Case 2: Even consecutive Integers
(-4,-2,0,2,4,6) In this case product is zero
So I have chosen A

Pls help me in any analysis.
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I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

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Joined: 02 Aug 2009
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08 Dec 2016, 20:23
kanusha wrote:
From 2 statement : The sequence has both positive and negative integers
I knew the condition is Consecutive Integer, I considerd 2 cases
Case 1: Odd consecutive integer
(-3,-1,1,3,5,7) In this case the Product is Negative Integer
Case 2: Even consecutive Integers
(-4,-2,0,2,4,6) In this case product is zero
So I have chosen A

Pls help me in any analysis.

Hi,
The statement talks of CONSECUTIVE integers, and it will always mean terms having difference of 1..
So -1,0,1,2...

Only if it is given CONSECUTIVE odd integers, you will take -1,1,3...
And if CONSECUTIVE even integers, -2,0,2,4...

Here you will have,-2,-1,0,1,2... or -4,-3,-2,-1,0,1..
Each time product will be 0
Hence sufficient
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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17 Jun 2017, 00:39
I think this is a high-quality question. This is an awesome question. I seriously faltered on the second statement. Presence of mind is important within the context what are we trying to find
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14 May 2018, 23:47
Hello Bunuel chetan2u,

I thought the Factorial of 0! is 1, therefore -1*0 = 0! = 1, so the numbers can be {-2,-1,0,-1,-2,-3} and any set such as {-1,0,-1,-2,-3, -4}
So both will have different product, I think I have misunderstanding with regard to "0!" can someone please explain me this concept.
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14 May 2018, 23:58
hero_with_1000_faces wrote:
Hello Bunuel chetan2u,

I thought the Factorial of 0! is 1, therefore -1*0 = 0! = 1, so the numbers can be {-2,-1,0,-1,-2,-3} and any set such as {-1,0,-1,-2,-3, -4}
So both will have different product, I think I have misunderstanding with regard to "0!" can someone please explain me this concept.

1. Yes, 0! = 1 but it's highly unlikely that you'll need this for the GMAT.
2. Factorial of integer n, n!, is defined for non-negative n.
3. -1*0 = 0, and it is not the same as 0!.
4. 0*1 = 0 and it is not the same as 0!.
5. Anything*0 = 0.
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15 May 2018, 00:13
I'm sorry but I do not understand your point "2. Factorial of integer n, n!, is defined for non-negative n." ?

Also, 7!/10! can be written as 7!/7! * 8*9*10, therefore cant we write -1*0*1*2*3*4 as 0!*1*2*3*4, thus giving us the answer "24" and not 0.
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15 May 2018, 01:02
hero_with_1000_faces wrote:
I'm sorry but I do not understand your point "2. Factorial of integer n, n!, is defined for non-negative n." ?

Also, 7!/10! can be written as 7!/7! * 8*9*10, therefore cant we write -1*0*1*2*3*4 as 0!*1*2*3*4, thus giving us the answer "24" and not 0.

Factorial of a positive integer $$n$$, denoted by $$n!$$, is the product of all positive integers less than or equal to n. For instance $$5!=1*2*3*4*5$$.

Note: factorial of negative numbers is undefined.
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15 May 2018, 01:11
Bunuel I am sorry to bother you, but in this question the set has a negative no., I am confused.
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15 May 2018, 01:44
hero_with_1000_faces wrote:
Bunuel I am sorry to bother you, but in this question the set has a negative no., I am confused.

So? What does a factorial has to do with the question at all?
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25 Jun 2018, 09:48
Thanks for posting this question. It highlights the value of visualizing/seeing the sequence on the pad/paper.
A quality question that could trip you to answer A if you don't visualize and put the pen to the pad.
Re: M05-06 &nbs [#permalink] 25 Jun 2018, 09:48
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# M05-06

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