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# If the product of 7 consecutive integers is not zero, is the product

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Math Expert
Joined: 02 Sep 2009
Posts: 46283
If the product of 7 consecutive integers is not zero, is the product [#permalink]

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05 Oct 2017, 04:47
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Difficulty:

45% (medium)

Question Stats:

56% (00:54) correct 44% (00:43) wrong based on 71 sessions

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If the product of 7 consecutive integers is not zero, is the product negative?

(1) The largest number is less than 7
(2) At least on of the numbers is negative

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Joined: 27 Dec 2016
Posts: 231
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Re: If the product of 7 consecutive integers is not zero, is the product [#permalink]

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05 Oct 2017, 05:15
1
Bunuel wrote:
If the product of 7 consecutive integers is not zero, is the product negative?

(1) The largest number is less than 7
(2) At least on of the numbers is negative

$$a*b*c*d*e*f*g = not zero.$$

Does $$a*b*c*d*e*f*g < 0$$?

Statement 1.
- $$g < 7$$.
- g cannot be 6, because it makes a = 0, and the product is not 0.
- So does g cannot be the number between 0 and 6, because it will make the product become 0.
- Possibility is that a,b,c,d,e,f,g all negative numbers.
- SUFFICIENT.

Statement 2
- At least one of the numbers are negative.
- If one is negative and the other is positive, so there MUST be 0 in the set, so the product can be 0
- That's why, the number should be ALL NEGATIVE.
- SUFFICIENT.

D.
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Manager
Joined: 16 May 2017
Posts: 51
Location: India
If the product of 7 consecutive integers is not zero, is the product [#permalink]

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05 Oct 2017, 05:29
If the product of 7 consecutive integers is not zero, is the product negative?

(1) The largest number is less than 7
(2) At least on of the numbers is negative

Stmnt :1 statement 1 only simply states that it is product of number less than 7.as provided in original statement..number were
consecutive integers. hence number starts from -7X-6X-5X-4X-3X-2X-1 hence stmnt one alone is sufficient

Stmnt:2 it says at least one number is negative hence ..number cant be zero.

I needs to start less than -1 ,hence stmnt 2 alone is sufficient..

hence it option D
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Re: If the product of 7 consecutive integers is not zero, is the product [#permalink]

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08 Oct 2017, 03:11
Option D fits well

1. Since the largest number is less than 7 and product is not equal to 0 hence the largest will be -1.
its said that total no. of digits are 7 so we get product as negative (Sufficient)

2. Similarly if one digit is negative then rest of the digits has to be negative such that product is not 0. hence, sufficient.
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Re: If the product of 7 consecutive integers is not zero, is the product [#permalink]

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08 Oct 2017, 04:30
Bunuel wrote:
If the product of 7 consecutive integers is not zero, is the product negative?

(1) The largest number is less than 7
(2) At least on of the numbers is negative

since the integers are consecutive and since their product is non zero thus they are all at one side of 0 on the number line ( all +ve or all -ve) , thus if we know the sign of one we know the sign of their product

from 1

since they are 7 and the largest is less than 7 thus they must be all -ve .... suff

from 2
if one is negative then all are ... suff

D
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Joined: 07 Feb 2017
Posts: 47
Re: If the product of 7 consecutive integers is not zero, is the product [#permalink]

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09 Oct 2017, 07:19
IMO its A
a∗b∗c∗d∗e∗f∗g=notzero.

Does a∗b∗c∗d∗e∗f∗g<0 ?

Statement 1
consecutive number are less than 7
6*5*4*3*2*1*-1 = -ve
sufficient

Statement 2
At least one of the numbers is negative
-1*1*2*3*4*5*6 = -ve
-2*-1*1*2*3*4*5 = +ve
Insufficient
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Joined: 20 Jan 2016
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If the product of 7 consecutive integers is not zero, is the product [#permalink]

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11 Oct 2017, 10:38
IMO its A
a∗b∗c∗d∗e∗f∗g=notzero.

Does a∗b∗c∗d∗e∗f∗g<0 ?

Statement 1
consecutive number are less than 7
6*5*4*3*2*1*-1 = -ve
sufficient

Statement 2
At least one of the numbers is negative
-1*1*2*3*4*5*6 = -ve
-2*-1*1*2*3*4*5 = +ve
Insufficient

Here is how statement 2 is sufficient

"-1*1*2*3*4*5*6 = -ve" this is wrong because the 7 numbers are consecutive. with your given example, it will be -1*0*1*2*3*4*5. But here, the product is zero which is wrong. Therefore, when the statement says one of the numbers is negative, it means all are negative. We cannot have zero in the product

"-2*-1*1*2*3*4*5 = +ve" similarly here, it should be -2,-1 0 1 2 3 4 . Again the product will be zero and that is wrong

Statement 2 basically tells us that the numbers are all negative. Therefore, statement 2 is sufficient.

Statement 1 is sufficient however, your reasoning is wrong. The question itself says the numbers are consecutive and their product is not zero.

Statement 1 tells that the largest number is less than 7. Since any of the 7 numbers cannot be 0, the numbers have to be anything less than -1. its odd number so the product will be negative.

Hope this helps.
If the product of 7 consecutive integers is not zero, is the product   [#permalink] 11 Oct 2017, 10:38
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