Question: A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?

1. 37
2. 38
3. 39
4. 40
5. 41

Correct Answer: C
Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• A team contributes a total of $399 from its members.
• Each member contributed at least $10, and no one contributed $19.

Find out:

• The greatest number of members the club could have.

As per the conditions of the question, the team could not have 40 or more members.
Since the team contributes total of $399 from its members and each member contributed at least $10
Then we can say: If there are 40 members then $10*40=$400 > 399.

If 37 members contribute $10 each ($10*37=$370)
If the remaining two members contributed, for example, $11 and $18, respectively then the team would have is 37+1+1=39.

The greatest number of members the club could have = 39 members.

Approach Solution 2:
The problem statement implies that:

Given:

• A team contributes a total of $399 from its members.
• Each member contributed at least $10, and no one contributed $19.

Find out:

• The greatest number of members the club could have.

40 will be high since the product of 40 and 10 is greater than $399.
That is it implies 40*10 = $400 > $399

If there exist 37 members, then the total amount contributed = 37 * 10 = 370. However, we still need $29
If there exist 38 members, then the total amount contributed = 38 * 10 = 380. However, we still need $19. It is also stated in the question that no one contributed no more than $19.

Therefore, it leaves me to think, that the group of members can be 37 and 2 random people with any combination of $29. The contribution should be above $10 per person and less than $19 as per the conditions of the question.
If the remaining two members contributed, for example, $11 and $18, respectively then the team would have is 37+1+1=39.

The greatest number of members the club could have = 39 members.

Approach Solution 3:

The problem statement indicates that:

Given:

• A team contributes a total of $399 from its members.
• Each member contributed at least $10, and no one contributed $19.

Find out:

• The greatest number of members the club could have.

To solve the question, let us first divide = 399 by 10 (the minimum amount each member could contribute). Then we need to use the remainder to finish the problem.

Therefore, by dividing 399 by 10 we get:
399/10
Quotient =39, Remainder= 9

This implies that: 39 people x $10 + 1 person x $9 = $399
We see that if 39 members each contribute $10, someone would have to contribute the extra $9. It is required to note that, since each member contributed at least $10, the $9 could not have come from an additional member.
Therefore, the extra $9 must have been contributed by one (or more) of the existing 39 members.
Regardless of who contributed the extra $9, the maximum number of members the club could have is 39.
Therefore, the greatest number of members of the club could have 39 members.

“A team contributes total of $399 from its members”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must have a basic concept of arithmetic, algebra and geometry to calculate the sum properly. The candidates can follow GMAT Quant practice papers to analyse several sorts of questions that will enable them to improve their mathematical understanding.

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