There were 250 seniors and 200 juniors in an auditorium. While the 250

Question

There were 250 seniors and 200 juniors in an auditorium. While the 250 seniors and 200 juniors were in the auditorium, another group of students consisting of only juniors and seniors entered the auditorium. Once this new group of students entered the auditorium, the ratio of the number of seniors to the number of juniors in the auditorium was 7 to 5.

In the table, select a number of Seniors who entered the auditorium and a number of Juniors who entered the auditorium that are jointly consistent with the information given. Make only two selections, one in each column.

HarshavardhanR · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=83677 Harsha GMAT-Club-Forum-8llzk3u5.png

AVMachine · Answer

Let say A seniors and B junior were added then new ratio would be: (250 + A) / (200 + B) = 7/5

Solving this would provide you with the equation: A = 30 + 1.4B;

Now, Check the options and get the answer.

Gem165 · Answer

Before forming equations, we can simply put the values given in options for seniors or juniors and see whether they are divisible by 7 or 5 respectively, while doing this we get the value 58 for Seniors and 20 for juniors. 250+58 = 308 which is divisible by 7 with a multiplier of 44, and in turn multiply it with 5 we get 220, which is just 20 more juniors.

GmatTest2026 · Answer

Solution: We set up the equation for this 250+S/200+J = 7/5
 
 1250 + 5S = 1400 + 7J

S = 150+7J/5

We got this above equation, now we look for the values for Junior and Senior that fit into this equation. The only value that fits for Senior is 58 and for Junior is 20. So, Number of Seniors enter into auditorium is 58 and Juniors is 20.

Bismuth83 · Answer

1. The question asks us to  find the number of seniors and juniors, who entered the auditorium . Let these values be x and y, respectively.

2. Our final ratio is equal to  \frac{7}{5} = \frac{# \ of \ seniors}{# \ of \ juniors} = \frac{# \ of \ original \ seniors + # \ of \ seniors \ who \ joined}{# \ of \ original \ juniors + # \ of \ juniors \ who \ joined} = \frac{250 + x}{200 + y} .

3. This can be simplified,  \frac{7}{5} = \frac{250 + x}{200 + y} \rightarrow 1400 + 7y = 1250 + 5x \rightarrow 150 = 5x - 7y .

4. We can plug in the answer choices and see (knowing that y must divisible by 5 can help) that x = 58 and y = 20.

5. Our answer will be:   Seniors - 58 and Juniors - 20  .

Advait01 · Answer

Let say A seniors and B junior were added then new ratio would be: (250 + A) / (200 + B) = 7/5

Solving this would provide you with the equation: A = 30 + 1.4B;

Now, Check the options and get the answer.

There were 250 seniors and 200 juniors in an auditorium. While the 250

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