Question

Four friends Amrita, Deepa, Smita and Rhea complete their PhD in different number of years.
(K) The one who took maximum time took eight years to complete her PhD, while the one who took the least time took only three years to complete it.
(L) Rhea took more time only than Amrita and completed her PhD in five years.
(M) Smita did not take longer time than Deepa to complete her PhD.
Arrange the names of the friends in order from the minimum to the maximum number of years taken to complete their PhD.

• A. Amrita \(\rightarrow\) Rhea \(\rightarrow\) Smita \(\rightarrow\) Deepa
• B. Amrita \(\rightarrow\) Rhea \(\rightarrow\) Deepa \(\rightarrow\) Smita
• C. Smita \(\rightarrow\) Amrita \(\rightarrow\) Rhea \(\rightarrow\) Deepa
• D. Smita \(\rightarrow\) Amrita \(\rightarrow\) Deepa \(\rightarrow\) Rhea

Hint:

Pay close attention to the word "only" in statement L. "Rhea took more time ONLY than Amrita" means that except for Amrita, everyone else took more time than Rhea. This immediately places Amrita at the absolute bottom of the list and Rhea in the second position from the bottom.

Answer 1

The Correct Option is A

Step 1: Note the extremes.
The longest time is $8$ years and the shortest is $3$ years.
Step 2: Read clue (L).
Rhea took more time than only Amrita and finished in $5$ years; so Amrita took the least, $3$ years.
Step 3: Fix Amrita and Rhea.
Amrita $=3$ and Rhea $=5$, and everyone except Amrita took longer than Rhea.
Step 4: Place Smita and Deepa above Rhea.
Both Smita and Deepa took more than $5$ years, and one of them is the $8$-year maximum.
Step 5: Read clue (M).
Smita did not take longer than Deepa, so Smita $<$ Deepa, making Deepa the $8$-year maximum.
Step 6: Order minimum to maximum.
Amrita, Rhea, Smita, Deepa.
\[ \boxed{\text{Amrita} \rightarrow \text{Rhea} \rightarrow \text{Smita} \rightarrow \text{Deepa}} \]