Pg 153, MGMAT # Properties, Confusing Answer,Doubt btw A & D

[farukh_a]

Hi,
Below is a question on Page 153 of MGMAT Number Properties Strategy Guide. I solved it and got an answer different from the answer given in the answer key.

4) If c and d are integers is c-3d even?
(1) c and d are odd.
(2) c-2d is odd.
Solution
The question is asking us if c-3d is even. Simplifying the requirement, we are actually being asked:

if c and d are both even
of
if c and d are both odd

Stem-1

c and d are odd

Therefore odd * (3)(odd) will always be odd. So the answer is "YES"-"SUFFICIENT"

Stem-2
c-2d is odd
Therefore C is definitely odd and d can be even or odd but since d is being multiplied by 2 so the answer for 2d would always be even.

Now have a look at the table below:

Here we are sure that c would only be Odd and d can be either Odd or Even.

if c=Odd and d=Odd then 3d=Odd, therefore c-3d=Odd-Odd=Odd
if c=O and d=Even then 3d-Even, therefore c-3d=Odd-Even=Odd

Therefore the answer to the question is "NO" - Sufficient.

Therefore the answer to this question should be "D".

But the answer key says that the answer is "A".

Can anyone please elaborate and let me know where I am making a mistake.

Regards
Farukh

[gokul_nair1984]

Dude...Let's plug in some values and disprove the second statement...

If c and d are integers is c-3d even?
(1) c and d are odd.
(2) c-2d is odd....

c=1,d=2....=>c-2d=-3(Odd)

Therefore, c-3d=-5(Not Even)...So, NO for this Case

Moving on, Take c=1,d=1....=>c-2d=-1(Odd)

Therefore, c-3d=-2(Even)...So, YES for this case


This is where you went wrong,

In Line with your post,
if c=Odd and d=Odd then 3d=Odd, therefore c-3d=Odd-Odd=Odd
....
Let's plug in some numbers to disprove your statement..
5-3=2(Even)
Odd - Odd = Even(Always)...Therefore, for your case there can be odd and even...Thus only A suffices


PS:Make sure you consider negative scenarios unless expicitly mentioned otherwise

[tim]

exactly. OP assumed odd-odd=odd, which is clearly not true..