Question

A, B, C, D are four points in a straight line. Distance from A to B is 10, B to C is 5, C to D is 4 and A to D is 1. Which one of the following is the correct sequence of the points ?

• A. A- B - C - D
• B. A - C - B - D
• C. A - D - C - B
• D. A - C - D - B

Answer 1

Answer: (C)

A - D - C - B

Given:$A,B,C,D$ are four points in a staraight line

Distance from $A$ to $B$ is $AB=10$ units

Distance from $B$ to $C$ is $BC=5$ units

Distance from $C$ to $D$ is $CD=4$ units

Distance from $A$ to $D$ is $AD=1$ unit

Here $10>5>4>1\Rightarrow AB>BC>CD>DA$

$AB$ is the longest line,the sequence is $A-B$

$\Rightarrow BC>CD\Rightarrow C$ lies between $A$ and $B$

$\therefore$the sequence is $A-C-B$

$AC=5$ units then $CB=5$ units

Now,$D$ may lie between $AC$ or $AB$

$\because CD<AC,CD<BC$

Since $AD$ starts from $A$ and lies between $A$ and $C$

and $AD=1$ unit

$\therefore D$ cannot lie between $B$ and $C$

Hence $D$ lies between $A$ and $C$

The correct sequence is $A-D-C-B$