Is the integer m an even number?

Question

(1) |m| = -m

(2) (m)(m - 1)(m + 2) = 0

mikemcgarry · Accepted Answer

I'm happy to help with this. Statement #1 is equivalent to the statement that m =< 0, that m is zero or a negative number. For more explanation of this, see this blog post: https://magoosh.com/gmat/2012/gmat-math- ... -of-minus/ We know from this that m is zero or negative, but not necessarily even or odd, so this statement, alone and by itself, is not sufficient . Statement #2: We solve this with the Zero Product Property. The ZPP says: If A*B = 0, then A = 0 or B = 0 Notice that, in this statement, the word "or" is no garnish, but rather an essential piece of mathematical equipment. By extension, If A*B*C = 0, then A = 0 or B = 0 or C = 0. Here, we have: (m)(m - 1)(m + 2) = 0 ===> m = 0 OR (m - 1) = 0 OR (m + 2) = 0 ===> m = 0 OR m = +1 or m = -2 From this statement, m could be any of these three, so it could be even or odd. This statement, alone and by itself, is not sufficient . Combined statements We look at our set from the second statement, m = {0, +1, -2}, and because of the constraint of the first statement, we know m must be zero or negative, so we can keep 0 and -2, but we have to exclude +1. Now we are down to m = {0, -2}. We don't know which one m equals, but since both of them are even, we now definitively know that m is even. Thus, combined, the statements are sufficient . Answer = C Does all this make sense? Mike :-)

WoundedTiger · Answer

Sol: Given in St 1 |m|=-m or  m+|m|=0  ----->this implies some a positive no + m= 0 and therefore m has to be a negative number.

Now m can be -2 then ans is Y but if m=-3 then no

So Option A and D are ruled out

St 2 tells you that possible values of m are 0,1 and -2 
Again if m=0,-2 then m is even number but if m=1 then m is odd. Option B ruled out

Combining we get that m is a negative number so m=-2. Ans is C

madn800 · Answer

Great explanation mike. I solved the problem but without understanding the importance of OR. Good job and please keep us enlightened

PerfectScores · Answer

Statement I is insufficient:

m = 0, m = -1 would be suffice the statement and m can be even or odd. M can be any negative number or zero

Statement II is insufficient:

Either m = 0 OR m = 1 OR m = -2

Combining:

m = 0 or m = -2 which states that m will be even

Hence E is the answer

pretzel · Answer

Is zero considered an even integer?

Bunuel · Answer

ZERO: 1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself, (or, which is the same, zero is a multiple of every integer). Check more here: https://gmatclub.com/forum/tips-and-hint ... l#p1371030 Hope it helps.

pretzel · Answer

Thank Bunnel for your prompt reply! I chose E because I narrowed down to 0 and 2 from the 2nd statement.

Bunuel · Answer

If from (2) we had that m is either 0 or 2, then the answer would be B. Because both 0 and 2 are even. But from (2) m is 0,  1 , or -2. If m is 0 or -2, then the answer to the question is YES but if m is 1, then the answer to the question is NO. So, (2) is not sufficient.

Anigr16 · Answer

From statement 1, we know LHS has absolute value. Since absolute value can never be negative, so the only plausible solution was 0 I am sure am missing out something- can anyone help me out? :shock:

Bunuel · Answer

This is explained above: from (1)  -m\geq 0  -->  m \leq 0  --> m can be any non-positive value to satisfy |m| = -m.

arvind910619 · Answer

Imo C 
Very tricky question 
From statement 1 we have m<=0 , m can take any value hence insufficient 
From statement 2 we have m=0,1,-2 hence insufficient .
Combining we have 0 and -2 hence sufficient

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Is the integer m an even number?

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Is the integer m an even number?

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