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If x and y are integers, and w = x2y + x + 3y, which of the
[#permalink]
27 Oct 2018, 16:39

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Question Stats:

If x and y are integers, and \(w = x^2y + x + 3y\), which of the following statements must be true?

Indicate all such statements.

A. If w is even, then x must be even.

B. If x is odd, then w must be odd.

C. If y is odd, then w must be odd.

D. If w is odd, then y must be odd.

_________________

Indicate all such statements.

A. If w is even, then x must be even.

B. If x is odd, then w must be odd.

C. If y is odd, then w must be odd.

D. If w is odd, then y must be odd.

_________________

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Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

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Re: If x and y are integers, and w = x2y + x + 3y, which of the
[#permalink]
29 Oct 2018, 09:34

1

Expert Reply

Carcass wrote:

If x and y are integers, and \(w = x^2y + x + 3y\), which of the following statements must be true?

Indicate all such statements.

A. If w is even, then x must be even.

B. If x is odd, then w must be odd.

C. If y is odd, then w must be odd.

D. If w is odd, then y must be odd.

Indicate all such statements.

A. If w is even, then x must be even.

B. If x is odd, then w must be odd.

C. If y is odd, then w must be odd.

D. If w is odd, then y must be odd.

This is a great candidate for testing all possible cases

If x and y are integers, then there are 4 possible cases:

case 1) x is ODD and y is ODD

case 2) x is ODD and y is EVEN

case 3) x is EVEN and y is ODD

case 4) x is EVEN and y is EVEN

For each case, we can either apply the rules for even and odd numbers, or we can plug in nice values (0 for even and 1 for odd)

Let's use the second strategy.

case 1) x is ODD and y is ODD

w = x²y + x + 3y = (1²)(1) + 1 + 3(1) = 5

So, w is ODD

case 2) x is ODD and y is EVEN

w = x²y + x + 3y = (1²)(0) + 1 + 3(0) = 1

So, w is ODD

case 3) x is EVEN and y is ODD

w = x²y + x + 3y = (0²)(1) + 0 + 3(1) = 3

So, w is ODD

case 4) x is EVEN and y is EVEN

w = x²y + x + 3y = (0²)(0) + 0 + 3(0) = 0

So, w is EVEN

Check the statements:

A. If w is even, then x must be even.

w is even ONLY in case 4. In case 4, x is even

This statement is TRUE

B. If x is odd, then w must be odd.

x is odd in cases 1 and 2.

In both cases w is odd

This statement is TRUE

C. If y is odd, then w must be odd.

y is odd in cases 1 and 3.

In both cases w is odd

This statement is TRUE

D. If w is odd, then y must be odd.

w is odd in cases 1, 2 and 3

In case 2, y is EVEN

This statement is NOT true

Answer: A, B, C

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_________________

Re: If x and y are integers, and w = x2y + x + 3y, which of the
[#permalink]
17 Nov 2018, 04:51

Is thEre a shorter way to get the answer?

Re: If x and y are integers, and w = x2y + x + 3y, which of the
[#permalink]
17 Nov 2018, 05:28

Expert Reply

ShefaliSahu wrote:

Is thEre a shorter way to get the answer?

If x and y are integers, and \(w = x^2y + x + 3y\), which of the following statements must be true?

Indicate all such statements.

A. If w is even, then x must be even.

B. If x is odd, then w must be odd.

C. If y is odd, then w must be odd.

D. If w is odd, then y must be odd.

Indicate all such statements.

A. If w is even, then x must be even.

B. If x is odd, then w must be odd.

C. If y is odd, then w must be odd.

D. If w is odd, then y must be odd.

since all choices have w as odd or w as even, let us check when can w be odd and when even

1) when both x and y are even, w becomes \(E^2*E+E+3E=E\)

2) when both x and y are odd, w becomes \(O^2*O+O+3O=O\)

3) when both x and y are different, w becomes \(O^2*E+O+3E=E+O+E=O\)

so

w will be even, only if x and y are even

w will be odd, whenever any one or both of x and y are odd

let us see choices..

A. If w is even, then x must be even. => w will be even, only if x and y are even YES

B. If x is odd, then w must be odd. =>w will be odd, whenever any one or both of x and y are odd YES

C. If y is odd, then w must be odd. =>w will be odd, whenever any one or both of x and y are odd YES

D. If w is odd, then y must be odd. =>w will be odd, whenever any one or both of x and y are odd so it may be that just one , that is x , is odd and y is not.. so, not MUST

A, B, and C

_________________

Some useful Theory.

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: If x and y are integers, and w = x2y + x + 3y, which of the
[#permalink]
04 May 2021, 01:45

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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