If a and b are integers, is ab odd? (1) b = a + 2 (2) b/a is an odd is

for question to be yes both a & b have to be odd

stmnt 1: b and a are integers value 2 units far , so it can even or odd , not sufficient

smtnt 2: b/a can again be even or odd not sufficient


combining both statements; only for b= 3 and a=1 we get relation right ,hence sufficient ... C is right..

Here a and b are integers. It is not mentioned that they are only positive integers.
so in addition to pair a= 1 and b=3, you can take b=1 and a=-1 which satisfy both statement.
But we are asked whether ab is odd.
In both cases 1*3 or -1*1 are odd.
C is correct choice.

a * b = odd

b = a + 2

if a = 2 then no it is not odd.

if a = 1 then b = 3 yes it is odd.

Insufficient.

Statement 2)

b/a = odd

6/2 = 3 >> here b = 6 and a = 2 so no it is not odd.

15/3 = 5 >> here b = 15 and a = 3 so it is odd.

Insufficient.

Combined.

(a+2)/a = odd

1 + 2/a = odd

means a = 1 and b = 3

yes it is odd.

Answer choice C

Hi,

Is a*b is odd ?

If product of two numbers(a*b) has to be odd means, then both the numbers has to be odd.

i.e., ODD * ODD = ODD.

So, answer to the question is YES, if both the numbers “a” and “b” are odd.

Otherwise, the answer to the question would be “NO”

We can quickly plug in values and check the statement and the question.

Also, knowing the below rules will help,

EVEN + EVEN = EVEN

EVEN + ODD = ODD

ODD + ODD = EVEN

Statement I is insufficient:

b = a + 2

Let’s take, a = 1(ODD)

Then b = 3(ODD). Because (b= 1(ODD) +2(EVEN) = ODD)

Answer to the question is YES,

a * b = 1(ODD) * 3(ODD) = 3

But if,

Let’s take, a = 2(EVEN)

Then b = 4(EVEN). Because (b= 2(EVEN) +2(EVEN) = EVEN)

Answer to the question is NO,

a * b = 2(EVEN) * 4(EVEN) = 8.

Statement II is insufficient:

b/a is an odd integer.

Let’s take, a = 1(ODD) and b = 3(ODD).

Then, 3/1 = 3(ODD)

Answer to the question is YES,

a * b = 1(ODD) * 3(ODD) = 3

But if,

Let’s take, a = 2(EVEN) and b = 6(EVEN).

Then, 6/2 = 3(ODD)

Answer to the question is NO,

a * b = 2(EVEN) * 6(EVEN) = 12.

Together it is sufficient.

b = a+2

b/a is an odd integer,

(a+2)/a = 1 + (2/a) = ODD

Then (2/a) has to be an even integer,

2/a + 1(ODD) = ODD

So, 2/a has to be EVEN.

So, “a” can be either 1 or -1

So if a = 1, then b = 3, then answer to the question is YES

Similarly, if a = -1, then b = 1, then answer to the question is still YES

So the answer is C.

Hope this helps.

b/a is an odd integer
let say b/a = 2p +1 (where p is an integer 0,1,2......)
b = 2ap + a

b =2 + a
2ap +a = 2 +a
ap =1
as a is an integer and p #0 (it became undefined), thus a can be only 1 so b =3