Data Sufficiency Question 22
Directions : In each of the following questions, a question and three statements following it have been given. You are required to study the question and statements and decide that the information given in which statement(s) is necessary to answer the question?
(Corporation Bank Specialist Officer (Marketing) Exam 22.02.2014)
- What will be the area of a 2 metre wide boundary around a rectangular field?
I. The breadth of the field is one-fourth of its length. Area of the field is 144 sq. metre.
II. The ratio of the length and breadth is respectively $3: 2$.
III. Area of the field is 216 sq. metre.
(1) I, II, and III
(2) only I, II, and III
(3) I and II.
(4) Any one of the three statements
(5) None of these
Show Answer
Correct Answer: 22. (2)
Solution: 22. (2) From statement II,
If length $=x$ metre and breadth $=y$ metre, then
$y=\frac{1 \times 2}{4}(x+y)$
$\Rightarrow 2 y=x+y \Rightarrow y=x$
$\therefore x^{2}=144$
$\Rightarrow x=\sqrt{144}=12$ metres
Area of field $=(16)^{2}-(12)^{2}$
$=256-144$
$=112$ sq. metre
From statements II and III,
Length $=3\ \text{m}$
Breadth $=2 x$ metre
$\therefore 3x \times 2x=216$
$\Rightarrow x^{2}=\frac{216}{3 \times 2}=36$
$\Rightarrow x=6$
$\therefore$ Length $=18$ metre, Breadth $=$ 12 metre
Area of the field with boundary line
$=(18+2 \times 2)(12+2 \times 2)$
$=22 \times 16=352$ sq. metre
$\therefore$ Area of boundary $=352-216$
$=136$ sq. $\mathrm{m}$.
BETA
