The question below consists of a question and two statements numbered I and II…
2023
The question below consists of a question and two statements numbered I and II are given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
Point X is in which direction with respect to Y?
I. Point Z is at equal distance from both point X and point Y.
II. Walking 5 km to the East of point X and taking two consecutive right turns after walking 5kms before each turn leads to point Y
- A.
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.
- B.
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.
- C.
if the data in Statement I alone or in Statement II alone are sufficient to answer the question,
- D.
if the data in both the Statements I and II are not sufficient to answer the question.
Show answer & explanation
Correct answer: B
In direction-sense data sufficiency, a statement is sufficient only when it fixes a single, unambiguous relative direction between the two points asked about; distances alone, or relationships that hold for many different layouts, are not enough — each statement must be checked independently by literally tracing what it describes.
Statement I: Z being equidistant from X and Y only places Z on the perpendicular bisector of XY — countless different positions of X relative to Y are consistent with this, so no direction can be fixed. Statement I alone is insufficient.
Statement II: Start at X and walk 5 km East to reach a point A.
Facing East, the first right turn faces South; walking 5 km reaches a point B, 5 km South of A.
Facing South, the second right turn faces West; walking 5 km reaches Y, 5 km West of B.
Net displacement from X: the 5 km East leg and the 5 km West leg cancel exactly, leaving only 5 km South. So Y is exactly 5 km due South of X, i.e., X is due North of Y.
Plotting on a grid with East as +x and North as +y: X = (0, 0) → (5, 0) → (5, −5) → Y = (0, −5). The vector from X to Y is (0, −5), confirming X lies due North of Y purely from Statement II, independent of Statement I.
Since Statement II alone fixes the direction while Statement I alone does not, the data in Statement II alone are sufficient, and Statement I alone is not.