If a and b are positive integers, is a + b even?

FROM STATEMENT - I ( INSUFFICIENT )

5a - 1 = Odd
5a=even (as odd+1=even)
a=even/5 = even

We do not know the value of b so we can not comment on the value of a + b

FROM STATEMENT - II ( INSUFFICIENT )

ab = Even

We can have 3 Possibilities -

1. Both a and b are even
2. a is even & a is odd
3. b is even & a is Odd

FROM STATEMENT - I & II ( SUFFICIENT )

from statement I we know a=even
& From statement II b=even/even=even

Hence a=even and b=even
even + even = even

Answer should be C (Together both statements are sufficient to answer)

St 1: 5a-1 is odd or 5a is even or a is even. Nothing can be said about b. INSUFFICIENT
St 2: ab is even. that menas either a or b or both are even.INSUFFICIENT

St 1 & St 2: a is even. b can be even or odd. hence a +b can be even or odd. INSUFFICIENT

Option E

FROM STATEMENT - I ( INSUFFICIENT )

5a - 1 = Odd ; So, a must be Odd

We do not know , the value of b so we can not comment on the value of a + b


Hi,

I think from statement 1 it is clear that a is even, and not odd. since 5 multiplied with an even number will result in a number ending with 0 which in turn will give an odd number after subtracting 1.

If a and b are positive integers, is a + b even?

(1) 5a – 1 is odd
(2) ab is even

Statement 1 : 5a-1=odd, Rewrite this equation. 5a=odd+1, 5a=even.So a=even. This is insufficient to compute the value of a+b.
Statement 2: ab= even . 3 cases are possible.
1.a=even b=odd
2.a=odd b=even
3.a=even b=even.

Combine st1 and st2
We still have 2 choices 1 &3 from st 2 as we know a to be even from st1

Therefore the answer is E.

(1) 5a – 1 is odd
This is possible only when a is even.
However we have no information about b, which could be either odd or even.
If b is odd, a+b is not even whereas b being even means a+b is even
Insufficient.
(2) ab is even
This statement is true when :
1.a,b are both even
2.a is odd, b is even
3.a is even, b is odd.
Using condition1, a+b is even. However using condition2 and 3, a+b is odd.
Insufficient.

Combining both the statements,
a being even and b being odd, makes a+b odd.
On the contrary, b being even makes a+b even. Hence, insufficient(Option E)

We need to determine whether a + b is even, or whether a and b are both even or both odd.

Statement One Alone:

5a – 1 is odd

Since 5a - 1 is odd, a must be even. Here’s why:

5a - 1 = odd

5a = odd + 1

5a = even

Since adding 1 to any odd number gives us an even number, we know that 5a must be even. The only way for this to happen is if a is even. (Recall that odd x even = even.)

However, since we do not know anything about b, statement one alone is not sufficient to answer the question.

Statement Two Alone:

ab is even

Recall that even x even = even OR even x odd = even. Since ab is even, a and b could both be even OR one value could be even and the other odd. Thus, we cannot determine whether a + b is even. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we still do not have enough information to determine whether a + b is even. We know that a is even, but we still cannot determine whether b is even. If a is even and b is even, then a + b is even. However, if a is even and b is odd, then a + b is odd.

Answer: E

If a and b are positive integers, is a + b even?

(1) 5a – 1 is odd

This tells us that a is even. Let's check how:

5a - 1 = Odd

5a = Odd + 1

5a = Even

As, 5 * Even = Even

a is EVEN

With this we cannot determine if a and be is even as we do not know if b is even or odd.

Hence, (1) ===== is NOT SUFFICIENT

(2) ab is even

this is only possible when:

a - Even and b - Even

a - Odd and b - Even

a - Even and b - Odd

based on above scenarios a and b can be even or odd and hence not sufficient to determine if a + b is even

Hence, (2) ===== is NOT SUFFICIENT

Combining (1) & (2)

after combining we come to know that a will be even however, we are not sure on the value of b, b can either be odd or it can be even.

Hence we are still not able to determine if a + b = even

Hence, (1) & (2) ===== is NOT SUFFICIENT.


Hence, Answer is A

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I think the answer is E because from statement 1 we know that a is even and we have no information about b. And from statement 2, we know either a or b is even or both are even.

So even after combining b can be even or odd. So the answer is option E

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