Quantitative Aptitude

Syllabus: Quantitative Aptitude: Data interpretation - data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables; numerical computation and estimation - ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series; mensuration and geometry; elementary statistics and probability.

Percentages, ratios, profit and loss

Convert every percentage to a fraction ( $12.5\%=1/8$ , $16\tfrac23\%=1/6$ ) and most of the arithmetic disappears. Profit and discount are always on different bases — profit on cost price, discount on marked price — and mixing them is the usual trap.

$\text{net of two changes}=a+b+\dfrac{ab}{100}\ \%$
signs included; a 20% rise then a 20% fall nets $-4\%$

Interest, averages and mixtures

Alligation answers every mixture question in one line and is worth practising until it is reflexive: the ratio of quantities is the inverse ratio of the distances from the mean.

$SI=\dfrac{PRT}{100},\qquad A=P\left(1+\dfrac{r}{100}\right)^n$

Time, speed, distance and work

Work problems are speed problems in disguise: rate $\times$ time = job. Take the job as the LCM of the individual times and the fractions vanish.

$\dfrac{1}{t}=\dfrac{1}{a}+\dfrac{1}{b}\ \Rightarrow\ t=\dfrac{ab}{a+b}$

Permutations, combinations and probability

Ask one question first: does order matter? If yes it is a permutation, if no a combination. Then ask whether repetition is allowed. Nearly every mistake in this topic is an answer to the wrong one of those two questions.

$^nP_r=\dfrac{n!}{(n-r)!},\qquad ^nC_r=\dfrac{n!}{r!(n-r)!}$

Series, powers, exponents and logarithms

Number-series questions are solved by looking at differences, then ratios, then the differences of the differences. If none works, check for squares, cubes and primes before anything more exotic.

$\text{AP: }a_n=a+(n-1)d,\ \ S_n=\dfrac{n}{2}[2a+(n-1)d]$

Mensuration and geometry

Know the solids cold — the questions are rarely hard, only quick. Remember that scaling a linear dimension by $k$ scales area by $k^2$ and volume by $k^3$ ; a surprising number of questions are exactly that fact.

$\text{sphere: }V=\tfrac43\pi r^3,\ S=4\pi r^2$

Data interpretation and elementary statistics

Read the axis units and the footnotes before the numbers — a chart in lakhs against a question in crores is a deliberate trap. For pie charts convert degrees to percentages once ( $1\%=3.6^\circ$ ) and reuse it. Estimate first: the options are often far enough apart that a rounded calculation decides the answer.

$1\%=3.6^\circ\ \text{of a pie chart}$

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