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# M05-06

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:24
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50% (00:35) correct 50% (00:35) wrong based on 438 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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15 Sep 2014, 23:24
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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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Manager
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08 Dec 2016, 16:31
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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08 Dec 2016, 19:23
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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16 Jun 2017, 23:39
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, 22:47
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, 22:58
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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14 May 2018, 23:13
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, 00:02
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, 00:11
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, 00:44
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, 08:48
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.
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11 Aug 2019, 14:14
Good question.

Posted from my mobile device
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11 Aug 2019, 19:31
I can't see the option.

Posted from my mobile device
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11 Aug 2019, 21:11
1
juthi223 wrote:
I can't see the option.

Posted from my mobile device

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.

Hope this helps.
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14 May 2020, 08:06
What is the product of 6 consecutive integers?

(1) The greatest integer is 4 --> suff: max is 4, so 6 consecutive integers = {-1 0 1 2 3 4 --> it has 0, so product will be 0

(2) The sequence has both positive and negative integers --> -ve & +ve number, so 6 consecutive integers has 0 in it, so product will be 0
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14 May 2020, 10:19
hero_with_1000_faces wrote:
Hello,

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.

You are right that:
0! == 1 >> This is true by definition

But also, the definition of factorial is:
n! = n(n-1)(n-2)...(3)(2)(1) >> It does not include 0!, also by definition

To evaluate option (2), you need to check if
- The product
- Of 6 consecutive integers
- Containing both negative and positive values
>> Gives you a unique solution

{-1, 0, 1, 2, 3, 4} is such a series:
- The product is (4)(3)(2)(1)(0)(-1) = 0
- The product can also be written as (4!)(0)(-1) = 0 >> (Anything) x 0 = 0
>> Since all series of 6 consecutive integers containing both negative and positive values MUST include 0, the product of any such series is always 0 - Unique solution
>> There is no way to re-write the product of this series with 0!

Also:
- (0)(-1) is not equal to 0!
>> 0! is defined as 1, not as n(n-1)(n-2)....
>> n! is defined as n(n-1)(n-2)...(3)(2)(1) <--- It stops at 1
>> Again, indisputably n x 0 = 0 for all n all values of n. Therefore (0)(-1) = 0, not 0! (= 1)
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14 May 2020, 19:44
Bunuel wrote:
What is the product of 6 consecutive integers?

(1) The greatest integer is 4

(2) The sequence has both positive and negative integers

Asked : Product of 6 consecutive integers

(1) The greatest integer is 4
The numbers are -1,0,1,2,3,4. Product = 0

(2) The sequence has both positive and negative integers

Looks insufficient but try to use brains from Statement 1.

As long as you have both positive and negative integers in a consecutive order you also have a 0 in between them. Product will be 0.

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18 May 2020, 11:10
This is a great question! As a sidebar, under what conditions would one NOT be able to calculate the product of consecutive integers? Thank you!
Re: M05-06   [#permalink] 18 May 2020, 11:10

# M05-06

Moderators: chetan2u, Bunuel