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Math Expert V
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If a and b are positive integers, is a + b even?  [#permalink]

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Question Stats: 83% (01:12) correct 17% (01:16) wrong based on 130 sessions

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

(1) 5a – 1 is odd
(2) ab is even

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Re: If a and b are positive integers, is a + b even?  [#permalink]

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E
the value of a can be odd or even but we can't specify the vale of b it can be odd or even too
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Re: If a and b are positive integers, is a + b even?  [#permalink]

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

(1) 5a – 1 is odd
(2) ab is even

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

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 ( INSUFFICIENT )

Since we do not have a unique value of b , this statement is insufficient...

Thus, Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed, asnwer will be (E)

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If a and b are positive integers, is a + b even?  [#permalink]

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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

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Re: If a and b are positive integers, is a + b even?  [#permalink]

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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
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If a and b are positive integers, is a + b even?  [#permalink]

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Abhishek009 wrote:
Bunuel wrote:
If a and b are positive integers, is a + b even?

(1) 5a – 1 is odd
(2) ab is even

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.
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Re: If a and b are positive integers, is a + b even?  [#permalink]

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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

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If a and b are positive integers, is a + b even?  [#permalink]

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(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)
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Re: If a and b are positive integers, is a + b even?  [#permalink]

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

(1) 5a – 1 is odd
(2) ab is even

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.

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Re: If a and b are positive integers, is a + b even?  [#permalink]

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

(1) 5a – 1 is odd
(2) ab is even

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.

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Re: If a and b are positive integers, is a + b even?  [#permalink]

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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

Sent from my Lenovo K33a42 using GMAT Club Forum mobile app Re: If a and b are positive integers, is a + b even?   [#permalink] 11 Jul 2017, 08:23

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