When four fair dice are rolled simultaneously, in how many GMAT Problem-Solving

Question: When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?

    (A) 155
    (B) 625
    (C) 626
    (D) 671

Answer: D

Solution and Explanation:

Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with basic mathematics. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Due to the six possible outcomes of each dice. Hence, there are a total of 6 x 6 x 6 x 6 = 6⁴ potential possibilities.
Each die can produce one of five outcomes if no die will show the number 3.
∴
Amounts of results where the die does not indicate 3 = 5 × 5 × 5 × 5= 5⁴
the total number of possibilities that are possible if at least one die appears 3 is the sum of all possible outcomes minus the number of outcomes in which no die is shown. 3 = 6⁴ − 5⁴ = 671
Correct Answer: D

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
There were four dice totaled.
Each die has a result of 6.
Total number of results from four dice: (6)⁴.
⇒6×6×6×6 ⇒1296
preferably one or two
Two as a result of the overall outcome
If two outcomes don't occur, there are five outcomes that could happen.
(5)⁴
When at least one 2 is feasible, the outcome is 5*5*5*5 = 625.
(6)⁴ − (5)⁴
⇒1296−625 ⇒671
Correct Answer: D

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
First, we calculate the total number of outcomes when four fair dice are rolled, which is 6⁴ = 1296, since each die has six possible outcomes.
Next, we calculate the number of outcomes when none of the dice shows 3. There are five possible outcomes for each die that do not include 3, so the total number of outcomes when four dice are rolled without any 3s is 5⁴ = 625.
Therefore, the number of outcomes where at least one of the dice shows 3 is:
total number of outcomes - number of outcomes without any 3s
= 1296 - 625
= 671
So there are 671 outcomes when at least one of the dice shows 3.
Correct Answer: D

“When four fair dice are rolled simultaneously, in how many" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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