Data Sufficiency Question 61
Directions : Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements sufficient to answer the question. Read both the statements and
(Bank of Maharashtra PO Exam, 26.10.2016)
Give answer (1) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
Give answer (2) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
Give answer (3) if the data in statement I alone or in statement II alone are sufficient to answer the question.
Give answer (4) if the data in both the statements I and II are not sufficient to answer the question.
Give answer (5) if the data in both the statements I and II together are necessary to answer the question.
- In an election, only two candidates (A and B) contested. 20% of the registered voters did not cast their votes and 160 votes cast were declared invalid. What is the number of registered voters?
I. Number of votes received by B is 864 which is 672 less than the number of votes received by $A$.
II. A got 672 votes more than B. Number of votes received by $A$ is equal to $48 %$ of the number of registered voters.
Show Answer
Correct Answer: 61. (3)
Solution: 61. (3) From statement I,
Let total registered voters be $x$.
$\therefore$ Total valid votes $=\frac{4 x}{5}-160$
$\therefore \frac{4 x}{5}-160=864+864+672$
$\Rightarrow \frac{4 x}{5}-160=2400$
$\Rightarrow \frac{4 x}{5}=2400+160=2560$
$\Rightarrow x=\frac{2560 \times 5}{4}=3200$
From statement II,
Total registered votes $=x$
$\therefore$ Votes got by $\mathrm{A}=\frac{48 x}{100}$
Total valid votes $=\frac{4 x}{5}-160$
$\therefore$ Votes got by $\mathrm{B}$
$=\frac{4 x}{5}-\frac{48 x}{100}-160$
$\therefore$ Difference
$=\frac{48 x}{100}-\left(\frac{4 x}{5}-\frac{48 x}{100}-160\right)$
$=\frac{48 x}{100}-\frac{4 x}{5}+\frac{48 x}{100}+160$
$=\frac{96 x}{100}-\frac{80 x}{100}+160$
$=\frac{16 x}{100}+160$
$\therefore \frac{16 x}{100}+160=672$
$\Rightarrow \frac{16 x}{100}=672-160=512$
$\Rightarrow x=\frac{512 \times 100}{16}=3200$
BETA
