Question:
" Seven bags contain different number of balls. C contains more balls than F, but less than A. Two bags have more balls than B, but fewer than A. Two bags have more balls than B, but fewer than C. G has more balls than either A or B. F has more balls B and D.E doesn't have more balls than B. Which bag has a greater number of balls than exactly two bags?"
Doubt:
Which is the first clue that I am supposed to pick here? What are the steps that I am supposed to follow after the first statement as the problem unfolds? I always thought for, "two bags have more balls than .." as the starting statement but I am not able to comprehend till the end.
Usually with problems like this it is helpful to write down all your clues and try to combine them.
We have 7 bags A,B,C,D,E,F,G, now lets look at our hints \begin{gather} (1) A > C > F \\ (2) A > X_1 \geq X_2 > B, \text{ X_1, X_2 are unknown for now}\\ (3) C > X_3 \geq X_4 > B, \text{ X_3, X_4 are unknown for now} \\ (4) G \geq A > B \\ (5) F > D \text{ and } F > B \\ (6) B \geq E \end{gather}
Combining all our clues we have $G \geq A > C > F > D,B \geq E$ now note all clues except for (3) are satisfied, if we have $B > D$ this means $C > F > B$ but we need one more, this hows we need $D > B$ and therefore we have the sequence $G \geq A > C > F > D > B \geq E$.
Therefore the answer is $D$ because $D > B \geq E$.