GATE2012 AE: GA-7

Question

The total runs scored by four cricketers $P,Q,R$ and $S$ in years $2009$ and $2010$ are given in the following table;

$$\begin{array}{|c|c|c|} \hline \textbf{Player} & \textbf{2009} & \textbf{2010} \\\hline \textbf{P} & \text{802} &\text{1008} \\\hline \textbf{Q} & \text{765} &\text{912} \\\hline \textbf{R} & \text{429} &\text{619} \\\hline \textbf{S} & \text{501} &\text{701} \\\hline \end{array}$$

The player with the lowest percentage increase in total runs is 

• A. $P$
• B. $Q$
• C. $R$
• D. $S$

Answer 1

$\%$ increase is defined as: $ \left(\dfrac{\text{final value - initial value}}{\text{initial value}}\right)\times 100$

$p=\dfrac{206}{802}\times 100=25.68 \%$

$q=\dfrac{147}{765}\times 100=19.21$

$r=\dfrac{190}{429}\times 100=44.28$

$s=\dfrac{200}{501}\times 100=39.42$

So, the lowest increase is for Q.

B is the answer

Comments

no need to  calculate total run...

Answer 2

These are the type of questions we we often have to solve in real world without using a pen and paper and an approx answer is all that is required. Here is a technique I find useful which can given approximate answers. If you need to the point correct answer then there might be a need to use the pen and paper.

Player	2009	2010	Approx Difference
P	802	1008	200
Q	765	912	150
R	429	619	200
S	501	701	200

Now the idea is to, divide the original number by some quantitiy to make close to 100, and use the same number for difference. That will give you an approximate percentage.

$ 1.\; \frac{802}{8} \approx 100 \;, \frac{200}{8} \approx 25\%$

$ 2.\; \frac{765}{8} \approx 100 $

ideally this will be 7.65,  so we can be sure ans is between, $\frac{150}{7} \approx 21\% \;and\;  \frac{150}{8} \approx 18\%$

$ 3.\; \frac{429}{4} \approx 100 \;, \frac{200}{4} \approx 50\%$

$ 4.\; \frac{501}{5} \approx 100 \;, \frac{200}{5} \approx 40\%$

Hence the answer is B.

Disclaimer: As there are too many approximations involved, this works when there is sufficient amount of gap in the answers. If the answers is too close then pen and paper is required. This also requires certain level of comfort-ness with doing maths in mind.

Answer 3

Lowest percentage increase is for Q

and highest percentage increase for R

 

so here answer is Q Option B