This is an excellent question which not only tests you on your probability concepts but also on your ability to conjure up numbers to fit a particular situation. It’s only fair that this is classified as a 700 level question.
In case you are not able to figure out how to interpret the statements given, you can take smaller values for the number of marbles, establish a pattern and apply it to the values given in the statements.
For example, if we assume 5 red marbles, 4 white marbles and 3 blue marbles – remember, all three values have to be distinct since it’s clearly mentioned that x>y>z – let’s see what happens with statement I and statement II.
To ensure that at least one marble of each color is removed from the jar, we have to remove a minimum of (5+4+1) = 10 marbles.
But what if we did the other way round – (3+4+1) = 8 marbles? Remember that you have to ensure that you have 1 marble of each color. You can take out 5 of red and 3 of blue and still have 8 marbles. But this way, you don’t have 1 marble of all colors. So, if we have to ensure 1 marble of each color, we have to exhaust the red and white because they are higher in number. Exhausting them will automatically ensure the next one is blue. Sounds right?
Similarly, to ensure that a red marble is removed from the jar, we have to remove a minimum of (3+4+1) = 8 marbles.
We can now adopt a similar approach to interpret the data given in the statements.
From statement I alone, we can say x + y + 1 = 55, which leads us to x + y = 54. Since x and y are different, x can be 28 and y can be 26; or x can be 29 and y can be 25 and so on. Clearly, this is not sufficient to find the number of red marbles in the jar uniquely. Options A and D can be eliminated. Possible answers are B, C or E.
From statement II alone, we can say 1 + y + z = 51, which gives us y + z = 50. Again, y and z can be different values. But, whatever they are, we have no information about x from this statement. Hence, this is insufficient. Option B can be eliminated.
Combining both statements I and II, we have x + y = 54 and y + z = 50. Solving these equations, we get x – z = 4. Also, x>y>z. The only set of values to satisfy all the above conditions, is {x=28, y=26, z= 24}.
Therefore, the correct answer option is C.
Getting this question right, definitely depends on whether you were able to get the equations right. But, more importantly, it also depends on how you used the inequality – x>y>z.
This is a question which can take about 2 minutes to solve, considering the difficulty level and also because you need to try values.
Hope this helps!
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