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gmatophobia
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If p, q, x, and y are non-zero integers and 03 Dec 2023, 10:43
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

46% (01:50) correct 54% (01:22) wrong based on 57 sessions

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If \(p, q, x,\) and \(y\) are non-zero integers and '\(x\)' is even, is \(p * (x^q * y)\) = even

1) '\(q\)' is an odd integer

2) '\(p\)' is an even integer
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E
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VivekSri
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If p, q, x, and y are non-zero integers and 07 Dec 2023, 22:59
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gmatophobia
If \(p, q, x,\) and \(y\) are non-zero integers and '\(x\)' is even, is \(p * (x^q * y)\) = even

1) '\(q\)' is an odd integer

2) '\(p\)' is an even integer
Show more

In my take statement 1 and Statement 2 are not necessary to give the answer as the answer is always even no matter whether q/p is even or odd.

Why?

x =even so all the power of x is always even.

when even is multiplied with any number it will always be even, so what the value of q is not necessary.

similarly the (x^q * y) is even so any nonzero number when multiplied with it will always be even so value of p is not necessary.

So OA is E.
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If p, q, x, and y are non-zero integers and 08 Dec 2023, 00:31
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VivekPrateek
gmatophobia
If \(p, q, x,\) and \(y\) are non-zero integers and '\(x\)' is even, is \(p * (x^q * y)\) = even

1) '\(q\)' is an odd integer

2) '\(p\)' is an even integer

In my take statement 1 and Statement 2 are not necessary to give the answer as the answer is always even no matter whether q/p is even or odd.

Why?

x =even so all the power of x is always even.

when even is multiplied with any number it will always be even, so what the value of q is not necessary.

similarly the (x^q * y) is even so any nonzero number when multiplied with it will always be even so value of p is not necessary.

So OA is E.
Show more

VivekPrateek - I believe the highlighted portions of the statements are not very accurate.

Consider this

If x is even, \(x^q \) is NOT guaranteed to be even for all integer values of \(q\). The obvious example is when the power is zero. \(x^0 = 1\), which is not even.

Another scenario is when the power is negative.

Example : \(x = 2, x^{-1} = \frac{1}{2}\).

\(\frac{1}{2}\) is not even.

The answer to the above question is not E, because the value is always even regardless of the statements. If that were the case, the answer would have been D (and the question would be an incorrect DS question to begin with :lol: )
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If p, q, x, and y are non-zero integers and 08 Dec 2023, 00:44
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gmatophobia
If \(p, q, x,\) and \(y\) are non-zero integers and '\(x\)' is even, is \(p * (x^q * y)\) = even

1) '\(q\)' is an odd integer

2) '\(p\)' is an even integer
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Official Explanation

Given

  • \(p, q, x,\) and \(y\) are non-zero integers
  • \(x\) is even

Question

Is \(p * (x^q * y)\) = even

Statement 1

1) '\(q\)' is an odd integer

While we know that the value of q is odd, we do not know whether the value is positive or negative. Without that information, we cannot determine the even/odd nature of \(x^q\)

Consider the following -

Case 1

\(x = 2, p = 2 , q = -1, y = 1\)

\(2 * (2^{-1} * 1) = 2 * (\frac{1}{2} * 1) = 1\)

The value is odd.

Case 2

\(x = 2, p = 2 , q = 1, y = 1\)

\(2 * (2^{1} * 1) = 2 * (2 * 1) = 4\)

The value is even.

As we have multiple possible answers, the statement alone is not sufficient and we can eliminate A and D.

Statement 2

2) '\(p\)' is an even integer

We know that \(p\) is even, however, we do not know the positive-negative nature of \(q\). The cases taken to evaluate Statement 1 are valid in this case as well.

We know that Statement 1 is not sufficient, hence Statement 2 is also not sufficient to arrive at a definite answer.

Eliminate B.

Combined

Statement 2 doesn't provide any additional information to resolve the positive negative nature of q. Hence, the statements combined are not sufficient as well.

Option E
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If p, q, x, and y are non-zero integers and 08 Dec 2023, 01:24
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gmatophobia
VivekPrateek
gmatophobia
If \(p, q, x,\) and \(y\) are non-zero integers and '\(x\)' is even, is \(p * (x^q * y)\) = even

1) '\(q\)' is an odd integer

2) '\(p\)' is an even integer

In my take statement 1 and Statement 2 are not necessary to give the answer as the answer is always even no matter whether q/p is even or odd.

Why?

x =even so all the power of x is always even.

when even is multiplied with any number it will always be even, so what the value of q is not necessary.

similarly the (x^q * y) is even so any nonzero number when multiplied with it will always be even so value of p is not necessary.

So OA is E.

VivekPrateek - I believe the highlighted portions of the statements are not very accurate.

Consider this

If x is even, \(x^q \) is NOT guaranteed to be even for all integer values of \(q\). The obvious example is when the power is zero. \(x^0 = 1\), which is not even.

Another scenario is when the power is negative.

Example : \(x = 2, x^{-1} = \frac{1}{2}\).

\(\frac{1}{2}\) is not even.

The answer to the above question is not E, because the value is always even regardless of the statements. If that were the case, the answer would have been D (and the question would be an incorrect DS question to begin with :lol: )
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Thanks for correcting me gmatophobia . Since they are non zero, I missed to take care of negative one. Thanks :)
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