Xavier Aptitude Test 2023 Paper

Question : 54 of 102

Marks: +1, -0

. The problem below consists of a question and two statements numbered

1 & 2

.
You have to decide whether the data provided in the statements are sufficient to answer the question. In a cricket match, three slip fielders are positioned on a straight line. The distance between 1st slip and 2nd slip is the same as the distance between 2nd slip and the 3rd slip. The player X , who is not on the same line of slip fielders, throws a ball to the 3rd slip and the ball takes 5 seconds to reach the player at the 3rd slip. If he had thrown the ball at the same speed to the 1st slip or to the 2 nd slip, it would have taken 3 seconds or 4 seconds, respectively. What is the distance between the 2nd slip and the player X?
1. The ball travels at a speed of

3.6 {\km} \/

hour.
2. The distance between the 1 st slip and the 3rd slip is 2 meters.

Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient.
Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficien
Each statement alone is sufficient
Both statements together are sufficient, but neither of them alone is sufficient
Statements 1 & 2 together are not sufficient

Validate

Solution:

Let players at slips 1,2 and 3 be a, b, and c, respectively.
Let the speed of the ball be

m

.
The trajectory of the ball is not specified in the question. But let's take it as straight line.

The distance between the 1st and 2nd slips is the same as the distance between the 2nd and 3rd slips.
The length of '

a b

' = The length of '

b c

'. It implies Xb is the median of triangle Xac.
It takes

3 {\ sec}, 4 {\ sec}

and 5 sec for the ball to reach

{\a}, {\b}

and c , respectively.
Hence,

{\Xa}=3 {\m}, {\Xb}=4 {\m}

and

{\Xc}=5 {\m}

.
Using Apollonius's theorem,

\;2 × ((4 m)^2+(a b)^2) =(3 m)^2+(5 m)^2

\;16 m^2+(a b)^2=17 m^2

\;a b=m

Hence,

a c=2 m

Using the properties of triangle, the sum of two sides should be greater than the third side,

\;\;\text " But, Xa "\;+ \;\text " ac "\;=\;\text " Xc "\;

\;3 {\m}+2 {\m}=5 {\m} .

Hence, this arrangement is not possible.
As this question has ambiguity, XAT officials awarded full marks to all candidates for this question.

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