Discussion Forum



Each of the questions given below consists of two statements numbered I and II given below it. Please read the questions carefully and decide whether the data provided in the statement(s) is / are sufficient to answer the given question.

1)

The cities X, Y and Z are on a straight line. City Z is between X and Y. The distance from X to Y is $100$ km. How far is X from Z ?

I. The distance from X to Y is $25\%$ more than the distance from Z to Y.

II. The distance from X to Z is $\frac{1}{4}$ of the distance Z to Y


A) I alone sufficient while II alone not sufficient to answer

B) II alone sufficient while I alone not sufficient to answer

C) Either I or II alone sufficient to answer

D) Both I and II are not sufficient to answer

E) Both I and II are necessary to answer

Answer:

Option C

Explanation:

.______.___________.
X   x    Z  (100 - x) Y

Let $XZ$ = $x$ km. Then, $ZY$ $=(100-x)$ km.

I. $XY-125\%$ of $ZY$

$\Leftrightarrow$ $100=\frac{125}{100}\times(100-x)$

$\Leftrightarrow 100-x$ $=\frac{100\times 100}{125}$ $=80$.

$\Leftrightarrow x=20$ km.

$\therefore XZ=20$ km.

Thus, I alone gives the answer.

II. $XZ=\frac{1}{4}ZY$

$\Leftrightarrow x=$ $\frac{1}{4}(100-x)$

$\Leftrightarrow$ $5x=100$ $\Leftrightarrow x=20$.

$\therefore XZ=20$ km.

Thus, II alone gives the answer.

$\therefore$ Correct answer is (C).