If x and y are integers, is the value of x(y+1) even?
(1) x and y are prime numbers
(2) y>7
Can anyone help? TIA
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Should be (A).
From (A), we know that both x and y are prime numbers. Also, we already know that except number 2, all prime numbers are odd.
We have two cases now -
(i) Either both x and y are equal (not mentioned in the question so can not assume that they're not)
In this case, either both are 2, or non-2 prime numbers. In both the cases, x(y+1) = even.
(ii) Both x and y are not equal
In this case, if one is 2, then automatically x(y+1) = even. If both are non-2 prime numbers, then ODD*(ODD+1) = ODD*EVEN = EVEN.
Thus (a) is sufficient.
(b) is in sufficient because it doesn't tell anything about x.
Hope it helps.
From (A), we know that both x and y are prime numbers. Also, we already know that except number 2, all prime numbers are odd.
We have two cases now -
(i) Either both x and y are equal (not mentioned in the question so can not assume that they're not)
In this case, either both are 2, or non-2 prime numbers. In both the cases, x(y+1) = even.
(ii) Both x and y are not equal
In this case, if one is 2, then automatically x(y+1) = even. If both are non-2 prime numbers, then ODD*(ODD+1) = ODD*EVEN = EVEN.
Thus (a) is sufficient.
(b) is in sufficient because it doesn't tell anything about x.
Hope it helps.
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Hi atlantic,
First let us look at the problem statement.
x(y+1) is even or not?
We know that Even * Even = Even
or Even * odd = Even
So in this case we have the following conditions:
1) X is even and Y +1 is even
which means X is even and Y is odd
or
2) X is even and Y+1 is odd
which means X is even and Y is even
or
3) Y+1 is even and X is odd
which means Y is odd and X is odd
Coming to statement 1:
x & y are prime numbers.
All prime numbers are odd except 2.
So even if X is 2 and Y is any other odd number
or X&Y are both odd numbers, we know that X(Y+1) is even. Hence sufficient. AD
Statement 2:
y>7
Nothing abt x. Also we dont know whether y is even or odd.
Hence insufficient.
Answer (A).
Hope this is correct.
First let us look at the problem statement.
x(y+1) is even or not?
We know that Even * Even = Even
or Even * odd = Even
So in this case we have the following conditions:
1) X is even and Y +1 is even
which means X is even and Y is odd
or
2) X is even and Y+1 is odd
which means X is even and Y is even
or
3) Y+1 is even and X is odd
which means Y is odd and X is odd
Coming to statement 1:
x & y are prime numbers.
All prime numbers are odd except 2.
So even if X is 2 and Y is any other odd number
or X&Y are both odd numbers, we know that X(Y+1) is even. Hence sufficient. AD
Statement 2:
y>7
Nothing abt x. Also we dont know whether y is even or odd.
Hence insufficient.
Answer (A).
Hope this is correct.
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Is the answer C
a) x and y prime numbers
the product can be both even or odd
for even x= 2 y=3
for odd y=2 x=3
so not sufficient
b) y>7
for even x=2 y=8
for odd x =3 y=9
not sufficient
however combining both we can say the y+1 term is always going to be
even.
hence even*even =even
or odd*even = even
a) x and y prime numbers
the product can be both even or odd
for even x= 2 y=3
for odd y=2 x=3
so not sufficient
b) y>7
for even x=2 y=8
for odd x =3 y=9
not sufficient
however combining both we can say the y+1 term is always going to be
even.
hence even*even =even
or odd*even = even
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Yes, I think vinod_ece66 is right. I overlooked the case when y could be = 2 and x non-2 prime.
C it is.
C it is.
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OA is C.
Now I understand my mistakes. There is only one way that x(y+1) can be odd with prime numbers, and that is when x=3 and y=2. All the others are obviously even. GMAT can be tricky.
Thanks guys.
Now I understand my mistakes. There is only one way that x(y+1) can be odd with prime numbers, and that is when x=3 and y=2. All the others are obviously even. GMAT can be tricky.
Thanks guys.
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