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# M03-35

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Math Expert
Joined: 02 Sep 2009
Posts: 50672

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15 Sep 2014, 23:21
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Difficulty:

15% (low)

Question Stats:

75% (00:28) correct 25% (00:52) wrong based on 198 sessions

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Is the product $$abcd$$ even?

(1) $$a^2 + b^2 + c^2 + d^2 = 0$$

(2) $$a = b = c = d$$

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Math Expert
Joined: 02 Sep 2009
Posts: 50672

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15 Sep 2014, 23:21
Official Solution:

Statement (1) by itself is sufficient. All the variables equal zero, and the product of the variables is zero; therefore their product is even.

Statement (2) by itself is insufficient. The variables can be either odd or even. If all the variables are even, their product is even; if they are odd, their product is odd.

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Joined: 29 Dec 2014
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Concentration: Finance, Strategy
GMAT 1: 640 Q48 V29
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17 Jun 2015, 20:57
The key here is to realize that zero is even!
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20 Sep 2015, 03:22
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. All the variables equal zero, and the product of the variables is zero; therefore their product is even.

Statement (2) by itself is insufficient. The variables can be either odd or even. If all the variables are even, their product is even; if they are odd, their product is odd.

Hi Bunuel, Please elaborate on this:
"All the variables equal zero, and the product of the variables is zero;"
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Math Expert
Joined: 02 Aug 2009
Posts: 7038

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20 Sep 2015, 03:40
1
scofield1521 wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. All the variables equal zero, and the product of the variables is zero; therefore their product is even.

Statement (2) by itself is insufficient. The variables can be either odd or even. If all the variables are even, their product is even; if they are odd, their product is odd.

Hi Bunuel, Please elaborate on this:
"All the variables equal zero, and the product of the variables is zero;"

Hi,
if i may help
all four terms in $$a^2+b^2+c^2+d^2$$ are positive as square of any number is always positive, so only possibility for the sum to be zero is when all four terms are 0, otherwise the sum will be some positive integer or positive fraction...
zero is even so suff...
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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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Joined: 03 Nov 2015
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14 Apr 2016, 11:10
We should not consider irrational numbers?
Math Expert
Joined: 02 Sep 2009
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14 Apr 2016, 11:32
forsellingonline1 wrote:
We should not consider irrational numbers?

The square of an irrational number is still positive, so the sum of the squares of 4 irrational numbers will be positive, not 0.
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26 Jun 2017, 06:09
I'm getting lost in all this, can't a and b for example =-1 and c and d equal 1? Wouldn't the sum still be 0? Because 1^2=1 but -1^2=-1. I don't understand when we have to assume that all the numbers must be positive or can be either.
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26 Jun 2017, 07:08
stan3544 wrote:
I'm getting lost in all this, can't a and b for example =-1 and c and d equal 1? Wouldn't the sum still be 0? Because 1^2=1 but -1^2=-1. I don't understand when we have to assume that all the numbers must be positive or can be either.

The square of a number is always more than or equal to 0.

So, if b = -1, then b^2 = (-1)^2 = 1.

Is the product abcd even?

(1) a^2+b^2+c^2+d^2=0 --> number squared is always non-negative (zero or positive), so the sum of 4 non-negative values to be 0 then each must be zero, so abcd=0=even. Sufficient.

(2) a=b=c=d. Clearly insufficient.

Hope it's clear.
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04 Nov 2018, 19:30
Hi Bunuel,

What if both a and b are square root of negative one (-1) and both c and d are square root of positive one (1),
then the answer of first statement will still be zero.
Are we supposed to consider root of negative numbers?
Math Expert
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04 Nov 2018, 20:36
HrusheekeshJoshi wrote:
Hi Bunuel,

What if both a and b are square root of negative one (-1) and both c and d are square root of positive one (1),
then the answer of first statement will still be zero.
Are we supposed to consider root of negative numbers?

Even roots from negative numbers are not defined on the GMAT. All numbers on the GMAT are real numbers.
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Re: M03-35 &nbs [#permalink] 04 Nov 2018, 20:36
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