Data Interpretation and Data Sufficiency — Quick Revision

Every method from Tables, Bar and Line Graphs, Pie Charts and Data Sufficiency on one page, for the last week before Prelims Paper II.

Before Any DI Set

Step	What to check
Title	What is measured, for whom
Units	Thousand tonnes, ₹ crore, per cent, degrees
Rows / columns	Which is category, which is time
Footnotes	The base of any percentage
Totals	Add each column once if not given; reuse

Core Formulas

$$\boxed{\text{Growth} = \frac{\text{Later} - \text{Earlier}}{\text{Earlier}}\times 100}$$$$\boxed{\text{Share} = \frac{\text{Item}}{\text{Total}}\times 100} \qquad \boxed{\text{Average} = \frac{\text{Sum}}{\text{Count}}}$$$$\boxed{\text{Percentage-point change} = \text{New \%} - \text{Old \%}}$$

Speed Methods

Method	How
1% block	Find 1% of the base, count how many blocks fit (342 of 1,900: 1% = 19, \( 342 \div 19 = 18\% \))
Cross-multiply	\( \frac{a}{b} \) vs \( \frac{c}{d} \): compare \( ad \) with \( bc \)
Benchmarks	\( \frac{1}{4} = 25\% \), \( \frac{1}{5} = 20\% \), \( \frac{1}{6} \approx 16.7\% \), \( \frac{1}{8} = 12.5\% \)
Small base first	The smallest starting value often has the highest growth rate
Weighted, not simple	Combine percentages via counts, never by averaging

Graphs

Graph	Key fact
Simple bar	One series; read values to the nearest gridline
Grouped bar	Series side by side; ratio questions
Stacked bar	Height = total; segment ÷ height = share
100% stacked bar	Shows shares only, not amounts
Line slope	Absolute change, not growth rate
Two lines	Vertical gap = difference; crossing = order swaps
Y-axis	Check whether it starts at zero

Pie Charts

$$\boxed{360° = 100\%,\quad 1\% = 3.6°} \qquad \boxed{\text{Amount} = \frac{\text{Degrees}}{360}\times\text{Total}}$$

Degrees	%	Degrees	%	Degrees	%
18°	5	60°	\( 16\frac{2}{3} \)	120°	\( 33\frac{1}{3} \)
36°	10	72°	20	144°	40
45°	12.5	90°	25	180°	50
54°	15	108°	30	270°	75

• Within one pie: ratio of amounts = ratio of angles.
• Across two pies: multiply each share by its own total.
• Share unchanged ⇒ amount grows at the same rate as the total.

Data Sufficiency

Choice	Meaning
I alone	I works, II does not
II alone	II works, I does not
Either	Each works alone
Both	Only together
Neither	Not even together

Rule	Detail
Order	I alone → II alone → together
“What” stem	Needs one unique value
“Is” stem	Definite yes or definite no
Equations	\( n \) independent equations for \( n \) unknowns
Ratios	A ratio alone never gives actual numbers
Assumptions	No positivity/whole numbers unless stated

Don’t Confuse

This	vs	That
Increase (subtract)		Percentage increase (subtract, then divide by earlier value)
Percentage points (75% − 60% = 15 points)		Percent change (\( \frac{15}{60} = 25\% \))
Degree difference (48°)		Percentage difference (\( \frac{48}{3.6} \approx 13.3 \) points)
Either (each alone)		Both (only together)
Simple average of pass rates		Overall pass rate (total passed ÷ total appeared)