Are there more than five red chips on the table?

Statement 1:-
The probability of drawing a non red chip is given as :- 24/25=96/100.

Since it is given that there are 100 chips. Number of non-red chips =96.
Hence number of red chips= 4.
Statement 1 is sufficient.


Statement 2:-
Probability of drawing of red chip is 1/25. But we do not have any idea about the total number of chips.
Hence Statement 1 is insufficient.

Hence the solution is :- Option A.

Hi Bunuel,

How can answer be A, as we don't know how many piles will be on the table. If there will be only one pile of chips on the table, it is sufficient, otherwise, we won't be to tell.

Please clarify

Thanks

S1) P(Non-red) = \(\frac{24}{25}\)
=> P(Red) = \(\frac{1}{25}\)

Total chips = 100
=> No. of red chips = 4
Sufficient.

S2) P(Red) = \(\frac{1}{25}\)
We don't know the total number of chips
=> There could be 4 red chips, if total chips is 100
=> There could be 8 red chips, if total chips is 200

Insufficient.

A is the answer.

Hi

I agree that number of piles is not mentioned. But statement 1 says '.. from the pile of 100 chips..'. I think we can safely assume here that there is only one pile, which is being talked about. Had there been more piles, question would have mentioned something like 'Are there more than 5 red chips on the table where various piles of chips are kept.' or something like that.

@

Bunuel

Please confirm-I dont think we can assume that there are 100 chips. 1 only gives us the probability-we only go by what data is given-no assumptions
I think E should be the answer.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The last step of the VA method is to make the number of variables and the equations equal (from the whole question including the original condition, conditions 1) and 2) )

Assume r is the number of re chips and n is the number of non-red chips.
Since we have 2 variables and 0 equation, we need 2 equations.

Condition 1)
r + n = 100, r / ( r + n ) = 24/25
Since we have 2 equations in the condition 1), we can get n = 96.
Thus r = 4.
The answer is No.
This is sufficient by CMT (Common Mistake Type) 1.

Condition 2)
r / ( r + n ) = 1/25
r = 1, n = 24 / r = 10, n = 240.
This is not sufficient.

Therefore, the answer is A.

Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

Several people asked above about the wording: the wording of this question is very bad. You will never see a question written this way on the GMAT. For one thing, if a question is going to tell you the probability something will happen, it needs to tell you what you're doing. Statement 2 says "the probability of drawing a red chip is 1/25" -- when we do what? Pick one chip? Pick two chips with replacement? It doesn't even tell us we're drawing a chip from the table mentioned in the question. We could be doing anything. Statement 1 is problematic for the same reason, and when Statement 1 talks about "the pile of chips", I don't know what pile they're describing, since there's no "pile" mentioned anywhere. Is "the pile" the same collection of chips that is on the table? There's no way to guess.

So there isn't any reason to study this question - best to focus on problems that are properly worded, since that's what you'll always see on the real GMAT.