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If x and y are integers, is x^3+3x-y an even number?

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If x and y are integers, is x^3+3x-y an even number?  [#permalink]

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New post 22 Aug 2018, 00:43
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[Math Revolution GMAT math practice question]

If \(x\) and \(y\) are integers, is \(x^3+3x-y\) an even number?

\(1) x=11\)
\(2) y=10\)

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Re: If x and y are integers, is x^3+3x-y an even number?  [#permalink]

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New post 22 Aug 2018, 00:49
x^3 + 3x will be even.
Since we have no info about y.
Statement 1 is insufficient.

From statement 2: Y is even.
Since x^3+3x is even and y is also even.
The whole equation is even.

2 is sufficient.

B is the answer.

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Re: If x and y are integers, is x^3+3x-y an even number?  [#permalink]

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New post 22 Aug 2018, 04:57
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Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x\) and \(y\) are integers, is \(x^3+3x-y\) an even number?

\(1) x=11\)
\(2) y=10\)


-----ASIDE-------------------------
Some important rules:
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN
4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN

-------------------------------------
Target question: Is x³ + 3x - y an even number?

Statement 1: x = 11
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 11 and y = 0. In this case, x³ + 3x - y = 11³ + 3(11) - 0 = ODD + ODD - EVEN = EVEN. So, the answer to the target question is YES, x³ + 3x - y is even
Case b: x = 11 and y = 1. In this case, x³ + 3x - y = 11³ + 3(11) - 1 = ODD + ODD - ODD= ODD. So, the answer to the target question is NO, x³ + 3x - y is NOT even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = 10
IMPORTANT: Notice that x³ + 3x is EVEN for all integer values of x. Here's why.
If x is EVEN, then x³ + 3x = EVEN³ + 3(EVEN) = EVEN + EVEN = EVEN
If x is ODD, then x³ + 3x = ODD³ + 3(ODD) = ODD + ODD = EVEN
So, we can see that x³ + 3x is always EVEN, regardless of the value of x.

Statement 2 tells us that y is EVEN.
So, x³ + 3x - y = EVEN - EVEN = EVEN
This means the answer to the target question is YES, x³ + 3x - y is even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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If x and y are integers, is x^3+3x-y an even number?  [#permalink]

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New post 22 Aug 2018, 08:39
Quote:
If \(x\) and \(y\) are integers, is \(x^3+3x-y\) an even number?

\(1) x=11\)
\(2) y=10\)


From the fact that \(x\) is an integer, note that \({x^3} + 3x = x\left( {{x^2} + 3} \right)\) is even, because it is the product of an even number and an odd number.
(This is a consequence of the fact that x and x squared are both even, or both odd.)

Hence the question simplifies to: is y even?

(1) Not sufficient:
Take (x,y) = (11,0) to answer in the affirmative ;
Take (x,y) = (11, 1) to answer in the negative.

(2) Sufficient

The solution above follows the notations and rationale taught in the GMATH method.
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Re: If x and y are integers, is x^3+3x-y an even number?  [#permalink]

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New post 23 Aug 2018, 23:50
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

\(x^3+3x\) is always even number, regardless of the value of \(x\). If \(y\) is even, then \(x^3+3x-y\) is an even number, and if \(y\) is odd, then \(x^3+3x-y\) is odd.

Thus, condition 2) is sufficient.

Condition 1) is not sufficient since it tells us nothing about the value of \(y\).

Therefore, B is the answer.
Answer: B
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Re: If x and y are integers, is x^3+3x-y an even number? &nbs [#permalink] 23 Aug 2018, 23:50
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