Is the product of four consecutive even integers positive?

Question

(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

Bunuel · Answer

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? 
 
Firstly, the product of four consecutive even integers can be either 0 (when one of the even integers is zero) or positive (when all integers are positive or when all integers are negative).
 
(1) The sum of these integers is positive but smaller than 20:
 
If the smallest term is -4 or less, for example {-4, -2, 0, 2}, then the sum will not be positive. Hence, the smallest term must be greater than -4.
 
If the greatest term is 8 or more, for example {2, 4, 6, 8}, then the sum will be 20 or greater. Therefore, the greatest term must be less than 8.
 
Based on this statement, there are only TWO possible sets: {-2, 0, 2, 4} and {0, 2, 4, 6}. The product of the terms in either of these two sets is zero, so the answer to the question is NO. Sufficient.
 
(2) The product of the middle two of these integers is positive. 
 
All four integers can be positive, for example, consider {2, 4, 6, 8}, giving a YES answer (product = positive). However, we can also have the set where the smallest integer is 0: {0, 2, 4, 6}, giving a NO answer (product = 0). . Not sufficient.

Answer: A

Hope it's clear.

TirthankarP · Answer

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}.

Bunuel · Answer

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.

Anurag1334 · Answer

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...

chetan2u · Answer

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

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Is the product of four consecutive even integers positive?

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Is the product of four consecutive even integers positive?

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