If y and z are nonzero integers, is the square of (y + z) even?

Question

(1) y – z is odd. 
(2) yz is even.

gmat1220 · Answer

The question can rephrased as - Is y even and z odd or vice versa?

or

Are both even or both odd?

Answering any of these questions will answer our question.

1) Sufficient
y may be even or z odd and vice versa. The answer is always NO

PS : It is given that y and z are NON ZERO.

2) Insufficient

Both may be even or just one of them may be even. In the first case y + z = even. The answer is YES
In the second case y + z = odd. The answer is NO

Answer A

subhashghosh · Answer

(1)

One of y or z is even, and one of y or z is odd
 
 So y+z is odd
 
 hence (y+z)^2 = odd
 
 Sufficient

(2)
 
 y can be even, z can be odd
 
 y can be odd, z can be even
 
 y or z can both be even
 
 So square of (y+z) is even.
 
 Not Sufficient

Answer - A

amit2k9 · Answer

y-z = odd means either y is even and z is odd or vice versa. Hence A.
yz = even means y,z even or y is even and z odd and viceversa.

Thus A.

IanStewart · Answer

As I posted in another thread a moment ago, positive integer exponents never matter in an even/odd question, so we can just ignore the 'square of' part of the question: it's just asking if y+z is even. Addition and subtraction follow the same odd/even rules, so if y-z is odd, then y+z is odd, and Statement 1 is sufficient. From Statement 2, y and z can both be even, in which case y+z is even, or one can be even and the other odd, in which case y+z is odd. So the answer is A.

Spidy001 · Answer

1. Sufficient

y-z is odd
 => either 
 y is even,z is odd or 
 y is odd ,z is even

in both the scenarios mentioned above y+z is odd = > (y+z)^ 2 is odd

2. Not sufficient
 yz is even

atleast one of the above is even

when both y and z are even , given expression is even
 but when y is odd and z is even , given expression is odd

Answer is A.

Bunuel · Answer

Tough and Tricky questions: properties of numbers.

If y and z are nonzero integers, is the square of (y + z) even?

(1) y – z is odd. 
(2) yz is even.

WoundedTiger · Answer

We know that even +/- even= Even 
Even+/-Odd=Odd

Odd+/-Odd= Even..

St 1 tells us that y-z =odd : So one is even and other is odd..Sum of even+odd=Odd..Therefore (Odd)^2=Odd..St1 is sufficient
St2 says yz=even : this implies either both are even or atleast one is even...

We can have 2 cases: Even+Even =Even or Odd+Even=Odd

Ans is A

EMPOWERgmatRichC · Answer

Hi All,

It looks like everyone who posted in this thread was comfortable with the Number Property rules that this DS question was built on. If you don't recognize those rules when you look at this question, then you can still answer it by TESTing VALUES.

We're told that Y and Z are NON-ZERO INTEGERS. We're asked if (Y+Z)^2 is even. This is a YES/NO question.

Fact 1: Y - Z = ODD

Let's TEST VALUES

IF....
Y = 3
Z = 2
Y-Z = 1
(3+2)^2 = 25 and the answer to the question is NO.

Notice how in the first example, we used an odd number for Y and an even number for Z. Let's try something different next...

IF....
Y=6
Z=1
Y-Z=5
(6+1)^2 = 49 and the answer to the question is NO.

The 'restriction' that Fact 1 places on us means that Y and Z CANNOT have the same sign. Even - Even = Even (e.g. 6-2=4); Odd - Odd = Even (e.g. 3-1=2). But since we're supposed to have an ODD number as a result, neither of these options is a possibility. With the information from Fact 1, the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

Fact 2: YZ = EVEN

IF....
Y=2
Z=2
YZ = 4
(2+2)^2 = 16 and the answer to the question is YES.

IF...
Y=2
Z=3
YZ=6
(2+3)^2 = 25 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

gmat6nplus1 · Answer

square (y+z) = y^2+2yz+z^2 --> mixed term will always be even, so Case 1: y and z are both odd or even the whole expression will be even; Case 2 y and z are even/odd or viceversa the whole expression will be odd.

statement 1: y-z=O // Case 2. Sufficient.
statement 2: yz = E // Either Case 1 or Case 2 Not sufficient.

Answer A.

grimm1111 · Answer

In my opinion, this type of problem is super easy if you really understand what you're being asked, and then re-frame the question to be more straightforward. It's more about the question than the math.

Given:  (y,z) ≠ 0, y and z are integers

Original Question:  Is (y + z) even?

We know that  EVEN + EVEN = EVEN, and ODD + ODD = EVEN...

In other words, we know that when two numbers of the same parity are added together, the result is always even. When two numbers of different parity are added together (eg. odd + even), the answer is always odd. ("Parity" is the word that describes whether a number is odd or even)

So the real question being asked is:   Are "y" and "z" of the same parity?

A.) (y - z) is odd.

(y - z) can  only  be odd if they are different parities. Since we now know that Y and Z are of different parities, we know that (y + z) is odd.  SUFFICIENT.

B.) yz is even.

For yz to be even, either y, or z, or both can be even. We can't answer the question   "Are 'y' and 'z' of the same parity?"   with the information given here.  INSUFFICIENT.

answer is A

gaylord2000 · Answer

What exactly do the options A,B,C,D,E mean here? Cos I cant see them anywhere

Bunuel · Answer

Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.

If y and z are nonzero integers, is the square of (y + z) even?

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GMAT Data Sufficiency (DS) Questions

If y and z are nonzero integers, is the square of (y + z) even?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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