The ratio of boys to girls in the junior class is 2 to 3 respectively

Question

The ratio of boys to girls in the junior class is 2 to 3 respectively and the ratio of girls to boys in the senior class is 7 to 3 respectively. If there are 300 more students in the senior class than in the junior class and the combined ratio of boys to girls in both classes is 8 to 17 respectively, how many students are in the senior class?

(A) 100
(B) 300
(C) 375
(D) 400
(E) 500

(A) 100
(B) 300
(C) 375
(D) 400
(E) 500

gmatophobia · Answer

Junior Class

\frac{B}{G }= \frac{2x }{ 3x}

Senior Class

\frac{ G}{B }= \frac{7y }{ 3y}

( 7y + 3y ) - (2x + 3x) = 300

10y - 5x = 300

2y - x = 60 ----- (1)

\frac{2x + 3y }{ 3x + 7y} = \frac{8}{17}

Solving the equation we get

2x = y ----- (2)

Substituing (2) in (1)

4x - x = 60

x = 20

y = 40

Number of students in the senior class = 10y = 400

Option D

HWPO · Answer

The ratio in the junior class is  \frac{B}{G}  =  \frac{2x}{3x}  and together 5x.
So at the minimum x = 1 and so we have 5 students in the junior class.

Based on the above, the number of students in the senior class is at least 305. The ratio in the senior class is  \frac{B}{G}  =  \frac{3y}{7y}  and together 10y.
so, if at the minimum there are 5 students in the junior class, then y should at least be 31 (10*31 = 310). However, in the answer choices we've only got 375, 400, and 500.

375 is not possible because then y = 37.5 and we can't have half a boy/girl.

So basically you can start and check from 400.

If senior class = 400 students, then y = 40. Then it means that junior class = 100, x = 20. Plug in and check:

\frac{B}{G}  = (40+120)/(60+280) => 160/340 = 8z/17z ........... => Z/Z = 1 CORRECT.

Answer choice D

KarishmaB · Answer

We can use weighted averages here the way we use in mixtures.

Concentration of boys in junior class =  \frac{2}{5} = \frac{20}{50} 
Concentration of boys in senior class =  \frac{3}{10} = \frac{15}{50} 
Overall concentration of boys =  \frac{8}{25} = \frac{16}{50}

\frac{Ws}{Wj} = \frac{(20 - 16)}{(16 - 15)} = \frac{4}{1}

Students in senior class : Students in junior class = 4 : 1
The difference of 3 in ratio terms is 300 so multiplier is 100.
Number of students in senior class = 4 * 100 = 400

Answer (D

Postponemended · Answer

boys:girls:total
junior class: 2: 3: 5
senior class: 3: 7: 10
total : 8: 17: 25

either juniors are 6:9:15 but it does not give total 8: 17:25
or seniors 6:14:20 which gives us
so we know that 4j= j + 300
j=100
s= j+300 or s=4j = 400

ga821 · Answer

I think your logic for 375 is wrong. Because if JC minimum is 5 then SC is 370

Then y = 37 and answer should fit.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83067 Harsha GMAT-Club-Forum-09z60hw5.png

bumpbot · Answer

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The ratio of boys to girls in the junior class is 2 to 3 respectively

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The ratio of boys to girls in the junior class is 2 to 3 respectively

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