A class of boys and girls has more girls than boys, with a total of 50

Question

A class of boys and girls has more girls than boys, with a total of 50 students. On a particular day, 20 students were absent, leaving more boys than girls present.

Select for  Maximum  the maximum possible number of girls that could have been in the original class of 50 students, and select for  Minimum  the minimum possible number of girls who could have been absent on that day. These two values could correspond to separate scenarios and are not necessarily consistent with each other. Make only two selections, one in each column.

ManifestDreamMBA · Answer

Original
G+B = 50
G>B
Min G = 26

Absent
g+b = 30
b>g
Min b = 16
Max g = 14

Now 
26-min = max
26-min = 14
 min = 12 (absent)

Max G = 14+20 = 34

Bunuel · Answer

Official Solution: Given that the total number of students is 50, we have: G + B = 50 To determine the maximum possible number of girls in the original class , we need to ensure that after 20 students were absent, the number of boys present was greater than the number of girls present. If there were 49 girls and 1 boy, even if all 20 absent students were girls, the remaining students would be 29 girls and 1 boy, meaning boys would not outnumber girls. Therefore, we need to find the highest possible G such that G - 20 < B, while still satisfying G + B = 50. Substituting B = 50 - G into G - 20 < B, we get G - 20 < 50 - G, which simplifies to 2G < 70, or G < 35. Thus, the maximum possible G is 34. For example, if G = 35, then B = 15. Even if all 20 absent students were girls, the remaining students would be 15 girls and 15 boys, meaning boys would not outnumber girls. Therefore, the number of girls must be less than 35, making 34 the maximum possible. To minimize the number of girls who could have been absent on the day when the number of boys exceeded the number of girls, we should start with the smallest possible number of girls, which is 26. Since 20 students were absent, 30 students were present in the class that day. To achieve the smallest possible number of absent girls, we need to distribute the 30 students as evenly as possible while ensuring that the number of boys exceeds the number of girls. This approach maximizes the number of girls present, minimizing the difference between 26 (the initial number of girls) and the number of girls present. The closest distribution that meets this condition is 16 boys and 14 girls, meaning the minimum number of girls who could have been absent is 26 - 14 = 12. Correct answer: Maximum "34" Minimum "12" GMAT-Club-Forum-ixz9f7p9.png

egmat · Answer

Hi there,

Great question! Let's set up the constraints and work through both parts.

Define: G = total girls, B = total boys. We know:
- G + B = 50
- G > B, so G >= 26 (since students are whole numbers)
- 20 absent, 30 present
- Among those present, boys > girls

Let g = girls absent. Then boys absent = 20 - g.
- Girls present = G - g
- Boys present = (50 - G) - (20 - g) = 30 - G + g

Key Insight: The key constraint (more boys than girls present) gives us:
30 - G + g > G - g
30 + 2g > 2G
g > G - 15

Part 1: Maximum (max girls in the class):
We need at least one valid value of g to exist. Since g <= 20 (only 20 absent total), we need G - 15 < 20, which means G < 35, so G <= 34.

Check G = 34: g must be > 34 - 15 = 19, so g = 20. That means all 20 absentees are girls. Girls present = 34 - 20 = 14, boys present = 16. Indeed 16 > 14. Works!

Check G = 35: g must be > 20, but g can't exceed 20 (only 20 absent). Impossible!

Therefore, maximum girls in the class = 34.

Part 2: Minimum (min girls absent):
We need g > G - 15, meaning g >= G - 14 (since g must be a whole number). To make g as small as possible, we minimize G. The smallest G can be is 26.

At G = 26: g >= 26 - 14 = 12.

Check g = 12: Girls present = 26 - 12 = 14, boys present = 24 - 8 = 16. Indeed 16 > 14. Works!

Check g = 11: Girls present = 15, boys present = 15. Not more boys than girls. Fails!

Therefore, minimum girls absent = 12.

The correct pair: 34 for Maximum, 12 for Minimum.

Answer: 4A (34), 3B (12)

A class of boys and girls has more girls than boys, with a total of 50

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GMAT Two-part Analysis (TPA) Questions

A class of boys and girls has more girls than boys, with a total of 50

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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Perfect 805 Score Debrief by Julia

My Rewards