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Math Expert V
Joined: 02 Sep 2009
Posts: 60644
Is a two digit positive integer xy, where x is the tens digit and y is  [#permalink]

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Difficulty:   15% (low)

Question Stats: 76% (01:03) correct 24% (01:15) wrong based on 157 sessions

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Is a two digit positive integer xy, where x is the tens digit and y is the units digits, even?

(1) x is an even number
(2) The greatest common factor of x and y is 1

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Intern  B
Joined: 10 Sep 2018
Posts: 43
Re: Is a two digit positive integer xy, where x is the tens digit and y is  [#permalink]

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1
Question is XY even
i.e is y = 0,2,4,6,8

stmt1 : X is even . Tells nothing about Y . Not sufficient. it can be 21 22 23 etc

stmt 2 : X and Y . GCF is 1 . They are consecutive numbers or co primes. 23 , 34 etc Not sufficient

Combined if X is even then y is definitely odd and hence XY is not even . Sufficient
Manager  S
Joined: 23 Apr 2018
Posts: 164
Is a two digit positive integer xy, where x is the tens digit and y is  [#permalink]

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NCRanjan wrote:
Question is XY even
i.e is y = 0,2,4,6,8

stmt1 : X is even . Tells nothing about Y . Not sufficient. it can be 21 22 23 etc

stmt 2 : X and Y . GCF is 1 . They are consecutive numbers or co primes. 23 , 34 etc Not sufficient

Combined if X is even then y is definitely odd and hence XY is not even . Sufficient

Posted from my mobile device

Hello sir,
I wanted to point out a typing error you made in the post.

"Combined if X is even then y is definitely odd and hence XY is not even"

It should be 'if X is even and Y is definitely odd, then XY is even'

Either way the statement is sufficient, but the error might confuse new members.

Thanks
Director  P
Joined: 09 Aug 2017
Posts: 679
Re: Is a two digit positive integer xy, where x is the tens digit and y is  [#permalink]

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1
X and y are positive integer
10x+y= even or odd?

Statement 1
X is even no.

Statement 2
The greatest common factor of x and y is 1
Means x and y are prime no.
for (2,3), 10x+y is odd.
for (3,5), 10x+y is even

Statement 1+2
2,3 is only pair

10x+y is Odd.

Math Expert V
Joined: 02 Sep 2009
Posts: 60644
Re: Is a two digit positive integer xy, where x is the tens digit and y is  [#permalink]

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Bunuel wrote:
Is a two digit positive integer xy, where x is the tens digit and y is the units digits, even?

(1) x is an even number
(2) The greatest common factor of x and y is 1

_________________
Manager  G
Joined: 24 Dec 2018
Posts: 107
Concentration: Entrepreneurship, Finance
GMAT 1: 710 Q47 V40
Is a two digit positive integer xy, where x is the tens digit and y is  [#permalink]

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1
For xy to be even, y has to be either 0, 2, 4, 6 or 8 (basically y has to be even)

1) Given x is even doesn't help us draw any conclusions for value of y.
For eg: x=2. y=3 results in 23 which is odd
Or x=2 and y=4 results in 24 which is even

So, this statement is insufficient

2) GCF of x and y is 1 goes to show either of the following 3 cases: 1) One of the two x & y is odd and other is even, 2) x and y are distinct prime numbers, 3) at least one of the numbers x and y is 1.

Going by any of the cases we can prove that we cannot draw any conclusive inferences for value of y. Hence, this statement is insufficient

Combining 1 & 2, clearly x is even. Let's try putting this constraint on three cases we have mentioned in statement 2

Case 1: x is even. So, clearly y is odd. Thus, xy is odd

Case 2: x is even and prime so x=2. So, clearly y is any other prime number other than 2. All prime numbers except 2 are odd. Hence xy is odd

Case 3: x is even so x cannot be 1. Hence, y=1. Hence xy is odd

This shows that answer is C Is a two digit positive integer xy, where x is the tens digit and y is   [#permalink] 31 Dec 2018, 03:54
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