Question: In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, those whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Maths. How many opt for none of the three subjects?
- 19
- 21
- 26
- 41
- 57
“In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics”- is the topic from the GMAT Quantitative problem set. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1
As mentioned in the question, the total strength of the class is 120. Therefore, based on the question, it can be said that;
Total number of students that study physics are; 120/2 = 60
Total number of students that study chemistry are; 120/5 = 24
Total number of students that study maths are; 120/7 = 17
Now, considering the question, we need to calculate the number of students that study all the three subjects. Therefore, LCM (2, 5, 7) = 70x = 1.
Students that study only Physics and Chemistry; LCM (2,5) = 10x = 12 - 1(students who study all 3) = 11
Students who study only Physics and Maths = LCM(2, 7) = 14x = 8 - 1 = 7
Students who study only Chemistry and Maths = LCM(5, 7) = 35x = 3 - 1 = 2
Now replacing the value of x in each of the equations, we can find the number of students studying each subject.
Students who study only Physics = 60 - 11 - 7 - 1 = 41
Students who study only Chemistry = 24 - 11 - 2 - 1 = 10
Students who study only Maths = 17 - 7 - 2 - 1 = 7
Now evaluating the total number of students that study only one subject; 1 + 11 + 7 + 2 + 41 + 10 + 7 = 79
Thus, in order to calculate the number of students that study none of the subjects;
Total - Total who study at least one subject = 120 - 79 = 41.
Therefore, 41 students study none of the three subjects.
Correct Answer: D
Approach Solution 2
The total number of students as mentioned in the question are 120.
Even probability can be highlighted as 60 -> Odd= 60
Considering division by 5: 120/5= 24, however, it is mentioned that half of them are odd=12.
Now, consider divisibility by 7, we get; 120/7= 17.
The number of odd numbers is either 8 or 9. To check, multiply 17*7. Since the product is odd, we know that the number of odd numbers is 9.
Divisible by both 7 and 5: 35,70,105. We only want the number of odd numbers=2.
Thus, evaluating based on the above mentioned situation we get;
Odd numbers=60
Odd numbers that are divisible by 5=12
Odd numbers that are divisible by 7=9
Odd numbers that are divisible by 7 and 5=2
Number of people who did not take any of the 3 classes=60-12-9+2=41
Correct Answer: D
Approach Solution 3
There are 120 students overall, according to the question.
It is possible to emphasise the following: Odd=60, Even=60.
120 divided by 5 equals 24, however it is noted that half of these are odd, therefore the answer is 12.
When we divide 120 by 7, we obtain the result 17 (120/7).
There are either 8 or 9 odd numbers. Multiply 17*7 to verify. We know there are nine odd numbers since the product is odd.
35,70,105 is divisible by both 7 and 5. Only odd numbers, i.e. 2, will do.
In light of the above circumstance, we can evaluate as follows:
In light of the above circumstance, we can evaluate as follows:
Odd integers that divide by 5 equal 12
Odd integers that divide by 7 equal 9
Odd integers that may be divided by 7 and 5 equal two
60-12-9+2=41 persons did not join in any of the three classes.
Correct Answer: D
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