Crowan Throws 3 Dice and Records the Product of the Numbers GMAT Problem Solving

Question: Crowan throws 3 dice and records the product of the numbers appearing at the top of each die as the result of the attempt. What is the probability that the result of any attempt is an odd integer divisible by 25?

1. 7/216
2. 5/91
3. 13/88
4. 1/5
5. 3/8

Answer: A

Solution and Explanation

Approach Solution 1:

The total number of ways to throw 3 dice is 6 x 6 x 6 = 216

Only if two of the numbers are both 5s and the third number is an odd number can the product of the numbers on the top of three dice be an odd number that is divisible by 25. Well, here we are:
{1, 5, 5}, {5, 1, 5}, {5, 5, 1}, {3, 5, 5}, {5, 3, 5}, {5, 5, 3} and {5, 5, 5}
Thus the probability is 7/216.

Hence the correct answer is A.

Approach Solution 2:

As 555 can only happen in one manner in this situation, the nominator will have the following values:

551 - 515 - 155;
553 - 535 - 355;

555.

P(55O)= 7/216 (if you want to calculate as in previous case then:
P(55O)=P(551)+P(553)+P(555)=3!/2!∗1/6∗1/6∗1/6+3!/2!∗1/6∗1/6∗1/6+1/6∗1/6∗1/6=7/216)

Notice that the 16 scenarios listed above include all situations in which there are at least two 5s on a roll of three dice: 7 of these situations result in an odd sum, and 9 of them in an even amount.

Hence the correct answer is A.

Approach Solution 3:

The following strategy would be simpler
The number must contain the digit 25 in order to be a multiple of 25.
Thus, let there be three dashes:
Fix the first two dashes for 25, which is 5*5, which may be done in a variety of ways, including 1*1 = 1.
Let's insert the odd integers other than 5 in the last dash; the number of possible methods would be 2.
This arrangement's total permutations would be (1*1*2)*3!/2! (we must divide by 2! because two 5s are the same).
The likelihood of this is 6/216.
Probability of 555 = 1/16
As a result, the total problem of 7/216

Hence the correct answer is A.

“Crowan throws 3 dice and records the product of the numbers appearing at the top of each die as the result of the attempt.” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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