GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 13:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58381
If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

### Show Tags

05 Jul 2018, 05:47
1
9
00:00

Difficulty:

95% (hard)

Question Stats:

34% (02:11) correct 66% (01:53) wrong based on 158 sessions

### HideShow timer Statistics

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

_________________
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1017
WE: Supply Chain Management (Energy and Utilities)
If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

### Show Tags

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
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Tuck School Moderator
Status: Valar Dohaeris
Joined: 31 Aug 2016
Posts: 301
GMAT 1: 700 Q49 V37
Re: If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

### Show Tags

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
_________________
Director
Joined: 14 Dec 2017
Posts: 516
Location: India
Re: If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

### Show Tags

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
_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Re: If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

### Show Tags

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.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58381
Re: If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

### Show Tags

24 Dec 2018, 01:36
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

_________________
Intern
Joined: 28 Aug 2018
Posts: 27
Location: India
Schools: LBS '21 (A)
GMAT 1: 650 Q49 V31
GPA: 3.16
Re: If x and y are positive integers, then what is the value of (–1)^x + (  [#permalink]

### Show Tags

28 Dec 2018, 06:21
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!!

Re: If x and y are positive integers, then what is the value of (–1)^x + (   [#permalink] 28 Dec 2018, 06:21
Display posts from previous: Sort by