## Monday, 7 May 2012

### GMAT Preparation: Some traps in Data Sufficiency

Look at the following example:
-------------------------------
Is x+y even?
(1)x-y is odd
(2)x2-y2 is odd
-------------------------------

This example reminds me 'Snake and Ladder' game. Even if we escape at one snake-trap there exist a plenty of traps waiting to trick us.
The First Trap:
We know that, If x-y is even, x+y must also be even and vice versa. In that case, statement-1 seems sufficient to answer the question such that, we can narrow down the possible answer options to A or D.
That's the first trap..
The famous trap: "To assume the given numbers to be integers"
Is it mentioned that x and y are integers? Think for a while, there is a possibility that x-y can be even/odd even if x and y are not integers.
For example, if x = 2.3 and y= 0.3, then x-y = 2 is an even number, cool.
But, x+y = 2.6 is neither even nor odd, oh!
So here, as it is not exclusively mentioned that x and y are integers, statement-1 alone is not sufficient. So our possible answer options are now changed to B or C or E. What a shift!

The Second Trap:
Come to the second statement. It's a complicated one. It's an obvious trap. In fact it's a big snake-trap.
x2-y2 = (x+y)(x-y)
Yes, we know it, we have studied it several times, “The product of two odd numbers only, and no other combination can produce an odd number”.
"odd * odd = odd
odd * even = even
even * even = even", We all recited this several number of times.
No doubt. You also may know it. Then it definitely leads you to the trap.
“As x2-y2 is odd, both x+y and x-y are odd”. This leads to the sufficiency of statement-2 and ultimately deceits us to choose option B.
But don't get into that. Try to negate it, try for examples to prove insufficiency.
For example, consider x=3.6 and y=1.4.
Then x+y = 5 is odd and x-y = 2.2 is neither even nor odd.
(x2-y2) = (x+y)(x-y) = 11 is odd. The fact here is even if x2-y2 is odd, x-y is not odd.

Let us see one more example. Let us find x and y such that x+y = 3/4 and x-y = 4.
On solving, we can easily get the values of x and y as 19/8 and -13/8 respectively. But, x2-y2 = 3/4 * 4 = 3, an odd number.
So there exist x and y such that even if x2-y2 is odd, x+y is not odd.

A few Takeaways here:
"If not exclusively mentioned, don't assume the given numbers to be integers". They may be fractions and may push the sufficiency criteria of the statements to other end. GMAC can easily trick us here.
Indulging in critical thinking helps a lot in DS strategies. Don't jump on the obvious answer. Try to negate it. Try to find some examples to disprove it.