How many multiples of 4 are there between 12 and 96, inclusive? GMAT Problem Solving

Question: How many multiples of 4 are there between 12 and 96, inclusive?

(A) 21
(B) 22
(C) 23
(D) 24
(E) 25

Answer: B

Solution and Explanation:

Approach Solution 1:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to number theory. Because of how the options are set up, it is hard to choose the best one. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
It is asked in the question to find out the count of numbers which are multiples of 4 and are between 12 and 96.
Number of multiples of x in range = (last multiple of x in the range - first multiple of range)/x + 1
In the given case: (96 - 12) / 4 + 1 = 22
Some examples:
How many multiples of 5 are there between the range of -7 and 35, inclusively?
The range's last multiple of five is thirty; its first multiple of five is five;
(30−(−5))/ 5+1 = 8
OR: Count the number of 7-digit multiples that fall between -28 and -1, inclusive.
The range's last multiple of seven is seven, while its first multiple of seven is twenty-one.
(−7−(−21)) / 7 + 1 = 3
Correct option: B

Approach Solution 2:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to number theory. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
It is asked in the question to find out the count of numbers which are multiples of 4 and are between 12 and 96.
All multiples of 4 between 12 and 96, inclusive, are required of us (meaning we have to include the 12 and the 96).
There are 25 positive multiples of 4 when working with all positive integers from 1 to 100 since (4)(25) = 100.
When dealing with all positive integers from 1 to 96, inclusive, there are 24 positive multiples of 4 since (4)(24) = 96.
The multiples of 4 that do not fall inside the specified range must now be eliminated.
The two are 4 and 8.
Total multiples of 4 = (24 - 2) = 22
Correct option: B

Approach Solution 3:
To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
It is asked in the question to find out the count of numbers which are multiples of 4 and are between 12 and 96.
All the numbers will be in the AP
So the first number will be 12 and the last will be 96.
An = a+(n-1)d (general term in an AP)
12+(n-1)4 = 96
N-1 = 21
N = 22
We get total multiples of 4 as 22
Correct option: B

“How many multiples of 4 are there between 12 and 96, inclusive?" - 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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