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# If x and y are positive integers, then what is the value of (–1)^x + (

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If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

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05 Jul 2018, 05:47
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95% (hard)

Question Stats:

22% (02:30) correct 78% (01:56) wrong based on 66 sessions

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GMAT CLUB'S FRESH QUESTION:

If x and y are positive integers, then what is the value of $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$ ?

(1) x does not have a prime factor greater than 1.
(2) y is a common factor of all prime numbers between 101 to 202

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If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

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05 Jul 2018, 07:17
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION:

If x and y are positive integers, then what is the value of $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$ ?

(1) x does not have a prime factor greater than 1.
(2) y is a common factor of all prime numbers between 101 to 202

Given, x and y are positive integers

St1:- x does not have a prime factor greater than 1
So, x=1 implies$$(-1)^x=(-1)^1=-1$$
when y=even, (-1)^y=1
So, $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$=-1+1+(-1)(1)=-1
when y=odd, $$(-1)^y=-1$$
So, $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$=-1+(-1)+(-1)(-1)=-1
hence sufficient.
St2:-y is a common factor of all prime numbers between 101 to 202
So, y=1 implies $$(-1)^y=(-1)^1=-1$$
when x=even, $$(-1)^x=1$$
So, $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$=1+(-1)+1(-1)=-1
when x=odd, (-1)^x=-1
So, $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$=-1+(-1)+(-1)(-1)=-1
hence sufficient.

Ans. D
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Re: If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

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05 Jul 2018, 08:01
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION:

If x and y are positive integers, then what is the value of $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$ ?

(1) x does not have a prime factor greater than 1.
(2) y is a common factor of all prime numbers between 101 to 202

$$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$

value of this expression depends on Even/Odd property of x and y , so we need to find this property of x and y

s1 the smallest Prime Number is 2, x > 0 and positive therefore x =1(Odd).
no info about y therefore not sufficient

s2 There are only two factors of any prime number, 1 and the number itself. Therefore y = 1(Odd)
no info about x therefore not sufficient.

together we have values of both x and y therefore sufficient. Answer : C
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Re: If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

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05 Jul 2018, 11:27
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION:

If x and y are positive integers, then what is the value of $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$ ?

(1) x does not have a prime factor greater than 1.
(2) y is a common factor of all prime numbers between 101 to 202

Given x, y > 0

Asked is value of Expression E = $$(–1)^x + (–1)^y + (–1)^x*(–1)^y$$

We know that (-1)^{even} = 1 & (-1)^{odd} = -1

Hence we have cases
(i) x = even, y = even, then E = 1 + 1 + 1*1 = 3

(ii) x = even, y = odd, then E = 1 - 1 + 1*(-1) = -1

(iii) x = odd, y = odd, then E = (-1) + (-1) + (-1)*(-1) = -1

(iv) x = odd, y = even, then E = (-1) + 1 + (-1)*1 = -1

Statement 1: x does not have a prime factor greater than 1. Therefore x = 1, hence x = odd

We have from cases (iii) & (iv), for x = odd, y = odd/even, E = -1

Hence statement 1 is Sufficient.

Statement 2: y is a common factor of all prime numbers between 101 to 202. Therefore y = 1, hence y = odd

We have cases (ii) & (iii), for y = odd, x = odd/even, E = -1

Hence Statement 2 is Sufficient.

Thanks,
GyM
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Re: If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

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06 Jul 2018, 01:14

Solution

Given:
• x and y are positive integers in the expression $$(-1)^x + (-1)^y + (-1)^x * (-1)^y$$

To find:
• The value of the given expression

Approach and Working:
• Considering all the three possible scenarios
o If, x and y, both are even, then the value of the expression will be (1 + 1 + 1) = 3
o If, x and y, both are odd, then the value of the expression will be (-1) + (-1) + 1 = -1
o If one is even and the other is odd, then the value of the expression will be (-1) + 1 + (-1) = -1
• Therefore, we can conclude that,
o The value of the expression will be 3, if both x and y are even
o The value of the expression will be -1, if at least one of them is odd

Analysing Statement 1
“x does not have a prime factor greater than 1”
• This statement implies that x = 1 (since x does not have any prime factor)
• Since x is odd, the value of the expression = -1 (for any value of y)

Therefore, Statement (1) ALONE is sufficient to answer this question

Analysing Statement 2
“y is a common factor of all prime numbers from 101 to 202”
• The common factor for any two prime numbers is 1
• Thus, the value of y is equal to 1
• Since y is odd, the value of the expression = -1 (for any value of x)

Therefore, Statement (2) ALONE is sufficient to answer this question

Hence, the correct answer is option D.

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