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

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

M36-98

PKN · Answer

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

LordStark · Answer

(–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

GyMrAT · Answer

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.

Answer D.

Thanks,
GyM

EgmatQuantExpert · Answer

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.

Answer: D

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

anant327 · Answer

Simple math -

For statement 1, let (-1)^y be A
From statement 1, we can interpret that x = 1
Therefore, the equation would be 
-1 + A - (1)*A.
This will result in -1. Sufficient!!

For statement 2, let (-1)^x be B
From statement 2, we can interpret that y = 1
Therefore, the equation would be 
B - 1 - (1)B
Which results in -1. Sufficient!!

Hence the answer is D

Bunuel · Answer

Official Solution:

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.
 
The above means that  x  must be 1. All other numbers are either composite or prime. 
 
In this case:  (–1)^x + (–1)^y + (–1)^x*(–1)^y=(–1)^{1} + (–1)^{y} + (–1)^{1}*(–1)^{y}=-1+(–1)^{y}-(–1)^{y}=-1 . Sufficient.
 
(2)  y  is a common factor of all prime numbers between 101 to 202
 
The only common factor those integer have is 1, so  y=1 .
 
In this case:  (–1)^x + (–1)^y + (–1)^x*(–1)^y=(–1)^{x} + (–1)^{1} + (–1)^{x}*(–1)^{1}=(–1)^{x}-1-(–1)^{x}=-1 . Sufficient.

Answer: D

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

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