Look at the following example:

-------------------------------

Is x+y even?

(1)x-y is odd

(2)x

-------------------------------

^{2}-y^{2}is odd-------------------------------

Stop reading here and try
to find your answer option. Got it?, then proceed..

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.

x

^{2}-y^{2}= (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 x

^{2}-y^{2}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**.
(x

^{2}-y^{2}) = (x+y)(x-y) = 11 is odd. The fact here is**even if x**.^{2}-y^{2}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, x

^{2}-y^{2}= 3/4 * 4 = 3, an odd number.
So there exist x
and y such that

**even if x**.^{2}-y^{2}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.
Students should be correctly answer all the GMAT Preparation Questions before appear in test.

ReplyDeleteGMAT Data Sufficiency can be complete only by student interection.

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ReplyDeleteGMAT Data Sufficiency