### Directions

The following problem has a question and two statements which are labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge on mathematics and every day facts, choose:(1) If you can get the answer from (1) ALONE but not from (2) alone

(2) If you can get the answer from (2) ALONE but not from (1) alone

(3) If you can get the answer from BOTH (1) and (2) TOGETHER, but not from (1) alone or (2) alone

(4) If EITHER statement (1) ALONE or statement (2) ALONE suffices

(5) If you CANNOT get the answer from statements (1) and (2) TOGETHER, but need even more data

Question

A jar is filled with 60 marbles. All the marbles in the jar are either red or green. What is the smallest number of marbles that must be drawn from the jar in order to be certain that a red marble is drawn?

(1) The ratio of red marbles to green marbles is 2 : 1

(2) There are 20 green marbles in the jar

Correct Answer – Choice 4. Each statement is independently sufficient.

### Explanatory Answer

Information given in the question stem1. Total of 60 marbles.

2. Only red and green marbles.

**Statement 1**: Ratio of red to green marbles is 2 : 1.

There are 40 red marbles and 20 green marbles. The smallest number of marbles that must be drawn from the jar to be certain that a red marble is drawn is when you can be certain that if the all the marbles that you have drawn to that point are green and that there are no more green marbles.

i.e., the 21st marble will certainly be a red marble. Statement 1 provides us the required data.

__Statement 1 is SUFFICIENT__.

**: There are 20 green marbles in the jar.**

Statement 2

Statement 2

Statement 2 directly gives the number of green marbles. As explained in statement 1 this information is sufficient to answer the least number of marbles required to be certain that a red marble is drawn.

__Statement 2 is also SUFFICIENT__.

Choice (4) is the correct answer.

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