Is a two digit positive integer xy, where x is the tens digit and y is

Question

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

M36-35

Bunuel · Accepted Answer

Official Solution:

Is a two digit positive integer  xy , where  x  is the tens digit and  y  is the units digits, even? 
 
Notice that the question asks whether  y , the units digit of a two digit positive integer  xy , is even.
 
(1)  x  is an even number. Clearly insufficient.
 
(2) The greatest common factor of  x  and  y  is 1
 
Also, insufficient. For example, consider 12 and 13.
 
(1)+(2) Both  x  and  y  cannot be even because in this case the greatest common factor of  x  and  y  would not be 1 (as given in the second statement), thus  y  is odd. Sufficient.

Answer: C

NCRanjan · Answer

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

Shrey9 · Answer

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

gvij2017 · Answer

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

Statement 1
X is even no. 
We don't know about Y.

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.

C is answer.

Bunuel · Answer

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

GMATin · Answer

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

Rocknrolla21 · Answer

Hi, I have a doubt here.

Does this question ask if x+y is even, or if xy as a two digit number is even?

Thanks!

Bunuel · Answer

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

There is no x + y there.

Rocknrolla21 · Answer

Thank you,  Bunuel !

Then, I don't understand why isn't statement 2 alone sufficient?

The GCF of X and Y is 1, and this means that they are co primes. All the prime numbers except 2 are odd. So, xy will be odd. Ex - 23, 25, 73. These all are odd numbers.

Please help me understand where I am going wrong.

Thanks!

Bunuel · Answer

xy could be even in many cases. For example, 12, 14, 16, 18, 32, 34, 38, 52, 54, 56, 58, 72, 74, 76, 78, 92, 94, 98.

Rocknrolla21 · Answer

Thanks,  Bunuel !

I think what I missed was the scenarios that hold true when the GCF of two integers is 1. I only considered co primes. I didn't consider the other two cases, which are:

- one of the integers, x or y, can be 1
- one of the integers, x or y, could be odd or even

Thanks a bunch!

Archit3110 · Answer

target is 10x+y an even number possible when y is even
#1
x is even
x=2,4,6,8
no info about y insufficient
#2
GCF of x & y is 1
means both x & y are consecutive numbers
value of x is not known insufficient
from 1 &2
since x is even so y has to be odd 
sufficient to say that 10x+y is odd

option C

Is a two digit positive integer xy, where x is the tens digit and y is

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Is a two digit positive integer xy, where x is the tens digit and y is

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