Data Interpretation questions typically have large amounts of data given in the form of tables, pie-charts, line graphs or some non-...

Data
Interpretation questions typically have large amounts of data given in the form
of tables, pie-charts, line graphs or some non-conventional data representation
format. The questions are calculation heavy and typically test your
approximation abilities. A very large number of these questions check your
ability to compare or calculate fractions and percentages. If you sit down to
actually calculate the answer, you would end up spending more time than
required. Here are few ideas that you can use for approximation.

**Funda 1 Calculating (Approximating) Fractions**

*When trying to calculate (approximate) a fraction p/q, add a value to the denominator and a corresponding value to the numerator before calculating (approximating).*

Example,

What is
the value of

*1789/762 ?*
First the
denominator. We can either take it close to 750 or to 800. Lets see how it
works in both cases. We know that the answer is between 2 and 3, so for adding
values / subtracting values from the denominator or the numerator, I will
consider a factor of 2.5.

**Case 1:**762 is 12 above 750, so I will subtract 12 from the denominator. Keeping the factor of 2.5 in mind, I will subtract 25 from the numerator.

My new
fraction is,

(

*1789 - 25) / (762 - 12) = 1763 / 750 = 1763 ? (4 / 3000 ) = 7.052 / 3 = 2.350666*
Actual
answer is 2.34776.

As you
can see, with very little effort involved in approximation, we arrived really
close to the actual answer.

**Case 2:**762 is 38 below 800, so I will add 38 to the denominator. Keeping the factor of 2.5 in mind, I will add 95 to the numerator.

My new
fraction is,

(

*1789 + 95) / (762 + 3**= 1884 / 800 = 2.355*
As you
can see, even this is close to the actual answer. The previous one was closer
because the magnitude of approximation done in the previous case was lesser.

**Funda 2 Comparing Fractions**

*If you add the same number to the numerator and denominator of a proper fraction, the value of the proper fraction increases.*

*If you add the same number to the numerator and denominator of an improper fraction, the value of the improper fraction decreases.*

Note: You
can remember this by keeping in mind that,

1/2 <
2/3 < 3/4 < 4/5 ...

and

3/2 >
4/3 > 5/4 > 6/5 ...

Example,

Arrange
the following in increasing order:

*117/229, 128/239, 223/449.*
Lets
first compare 117/229 & 128/239.

If we
added 11 to the numerator and the denominator of the first proper fraction, the
resulting proper fraction would be 128/240, which will be bigger in value than
the original (as per Funda 2).

We know
that 128/240 is smaller than 128/239, as the latter has a lower base.

So,
117/229 < 128/240 < 128/239

? 117/229
< 128/239

Now lets
compare 117/229 and 223/449.

If we
added 11 to the numerator and the denominator of the second proper fraction,
the resulting proper fraction would be 234/460, which will be bigger in value
than the original.

If we
doubled the numerator and denominator of the first proper fraction, the
resulting proper fraction would be 234/458.

We know
that 234/460 is smaller than 234/458, as the latter has a lower base.

So,
223/449 < 234/460< 234/458

? 223/449
< 117/229

Using the
above two results, we can say that 223/449 < 117/229 < 128/239

Note:
This question can be solved much simply by just looking at the numbers and
approximately comparing them with 12. I used this long explanation to
illustrate the funda given above.

Following
are a few other shortcuts that might come in handy during DI-related
calculations.

**Funda 3 Percentage Growth**

*If the percentage growth rate is r for a period of t years, the overall growth rate is approximately: rt + t * (t-1) * r*

^{2}/ 2
Note:
Derived from the Binomial theorem, this approximation technique works best when
the value of 'r' is small. If the rate is above 10%, then this approximation
technique yields bad results. Also, if the rate is 5% then r = 0.05; if the
rate is 7.2% then r = 0.072.

**Funda 4 Comparing Powers**

*Given two natural numbers a and b such that a > b > 1,*

*a*

^{b}will always be less than b^{a}
Note:
There are only two exceptions to this funda. I hope someone in the comments
will point them out (anyone?).

*The Author has taught Quantitative Aptitude at IMS for 4 years. An alumnus of IIT Kharagpur where he studied a dual-degree in computer science, he has also written*

__a book on business awareness__.