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Director  Joined: 07 Jun 2004
Posts: 539
Location: PA
Is the product of four consecutive even integers positive?  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 39% (01:55) correct 61% (02:06) wrong based on 156 sessions

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Is the product of four consecutive even integers positive?

(1) The sum of these integers is positive but smaller than 20
(2) The product of the middle two of these integers is positive

I got C

OA is A which i disagree can someone explain why its A

as for S1 we can have -2 0 2 4 sum is +ve and < 20 product is 0 which is not positive
Math Expert V
Joined: 02 Sep 2009
Posts: 65290
Re: Tough DS on number properties  [#permalink]

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rxs0005 wrote:
Is the product of four consecutive even integers positive?

The sum of these integers is positive but smaller than 20
The product of the middle two of these integers is positive

I got C

OA is A which i disagree can someone explain why its A

as for S1 we can have -2 0 2 4 sum is +ve and < 20 product is 0 which is not positive

In YES/No DS questions statement is sufficient if you can answer either definitive YES or definitive NO to the question

Is the product of four consecutive even integers positive?

First of all: the product of four consecutive even integers can be either 0 (when one of the eve integers is zero) or positive (when all integers are positive or negative).

(1) The sum of these integers is positive but smaller than 20:

If the greatest term is $$\geq{8}$$, eg {2,4,6,8}, then the sum will be equal or more than 20.
If the smallest term $$<-2$$, eg {-4,-2,0,2}, then the sum won't be positive.

Hence this statement gives only TWO possible sets {0,2,4,6} and {-2,0,2,4} --> $$sum<20$$ and $$product =0$$, so in either case the product is NOT positives. Sufficient.

(2) The product of the middle two of these integers is positive.

It's possible to have {0,2,4,6} --> product is zero OR {2,4,6,8} --> product is positive OR {-8,-6,-4,-2}--> product is positive. Not sufficient.

Hope it's clear.
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Re: Tough DS on number properties  [#permalink]

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Bunuel wrote:
In YES/No DS questions statement is sufficient if you can answer either definitive YES or definitive NO to the question

Is the product of four consecutive even integers positive?

First of all: the product of four consecutive even integers can be either 0 (when one of the eve integers is zero) or positive (when all integers are positive or negative).

(1) The sum of these integers is positive but smaller than 20:

If the greatest term is $$\geq{8}$$, eg {2,4,6,8}, then the sum will be equal or more than 20.
If the smallest term $$<-2$$, eg {-4,-2,0,2}, then the sum won't be positive.

Hence this statement gives only TWO possible sets {0,2,4,6} and {-2,0,2,4} --> $$sum<20$$ and $$product =0$$, so in either case the product is NOT positives. Sufficient.

(2) The product of the middle two of these integers is positive.

It's possible to have {0,2,4,6} --> product is zero OR {2,4,6,8} --> product is positive OR {-8,-6,-4,-2}--> product is positive. Not sufficient.

Hope it's clear.

Are negative numbers considered even or odd in GMAT?
I also chose A but because there is only one possibility here {0,2,4,6}.
Math Expert V
Joined: 02 Sep 2009
Posts: 65290
Re: Tough DS on number properties  [#permalink]

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TirthankarP wrote:
Bunuel wrote:
In YES/No DS questions statement is sufficient if you can answer either definitive YES or definitive NO to the question

Is the product of four consecutive even integers positive?

First of all: the product of four consecutive even integers can be either 0 (when one of the eve integers is zero) or positive (when all integers are positive or negative).

(1) The sum of these integers is positive but smaller than 20:

If the greatest term is $$\geq{8}$$, eg {2,4,6,8}, then the sum will be equal or more than 20.
If the smallest term $$<-2$$, eg {-4,-2,0,2}, then the sum won't be positive.

Hence this statement gives only TWO possible sets {0,2,4,6} and {-2,0,2,4} --> $$sum<20$$ and $$product =0$$, so in either case the product is NOT positives. Sufficient.

(2) The product of the middle two of these integers is positive.

It's possible to have {0,2,4,6} --> product is zero OR {2,4,6,8} --> product is positive OR {-8,-6,-4,-2}--> product is positive. Not sufficient.

Hope it's clear.

Are negative numbers considered even or odd in GMAT?
I also chose A but because there is only one possibility here {0,2,4,6}.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.

Thus, according to the above both negative and positive integers can be even or odd. For example, -2 is even and -3 is odd.

P.S. Zero is an even integer. Zero is nether positive nor negative, but zero is an even number.
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Re: Is the product of four consecutive even integers positive?  [#permalink]

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rxs0005 wrote:
Is the product of four consecutive even integers positive?

(1) The sum of these integers is positive but smaller than 20
(2) The product of the middle two of these integers is positive

I got C

OA is A which i disagree can someone explain why its A

as for S1 we can have -2 0 2 4 sum is +ve and < 20 product is 0 which is not positive

Let the 4 munbers be 2n,2n+2,2n+4,2n+6

Case1 : 0<8n+12<20 => n=-1,0 and product is 0 in both cases which is not positive.

Case2 : (2n+2)(2n+4)>0 => n<-2 or n>-1. if n=0 product is 0, if n=100 product is positive, ie not conclusive.

therefore ans is A

Hope it helped...
Math Expert V
Joined: 02 Aug 2009
Posts: 8757
Re: Is the product of four consecutive even integers positive?  [#permalink]

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rxs0005 wrote:
Is the product of four consecutive even integers positive?

(1) The sum of these integers is positive but smaller than 20
(2) The product of the middle two of these integers is positive

I got C

OA is A which i disagree can someone explain why its A

as for S1 we can have -2 0 2 4 sum is +ve and < 20 product is 0 which is not positive

Let the four consecutive integers be x, x+2, x+4, x+6.
Product will be positive-
a) when all 4 are positive
b) when all are negative
we cannot have a scenario of 2 negative and 2 positive, as then 0 will be one of them.

(1) The sum of these integers is positive but smaller than 20
As the numbers add up to less than 20, their average will be <$$\frac{20}{4}$$ or <5. Also average of 4 consecutive even integers will be ODD.
Consecutive means the average=median=(<5), so max possible median=3.
the least possible sum would be -2+0+2+4=4, and answer to ' Is product positive" will be NO...Median=1
the next case 0+2+4+6 will also give answer as NO...Median=3
Sufficient

(2) The product of the middle two of these integers is positive
The least integer can be 0, then NO, otherwise YES

A
_________________ Re: Is the product of four consecutive even integers positive?   [#permalink] 29 Jun 2020, 22:02

# Is the product of four consecutive even integers positive?  