Hi All,

This question is perfect for TESTing VALUES and you can keep the Values really small (which will make the 'math' really easy)...

We're told that, in a class, 1/4 of the number of girls is equal to 1/6 of the total number of students. We're asked for the ratio of the number of boys to the number of girls in the class.

IF....
Number of Girls = 4

We're told that (1/4)(4) = (1/6)(Total)

1 = (1/6)(Total)
Total students = 6

Number of Boys = 6-4= 2

The ratio of Boys:Girls is 2:4 = 1 to 2

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Assume; g = number of girls, b = number of boys

Total number of students = b + g

g / 4 = (b + g) /6

6g = 4(b + g) = 4b + 4g
2g = 4b
2/4 = b/g
b/g = 1/2

The answer is C. 1 to 2.

1/4 g = 1/6 t thus g = 2/3t

B= 1/3t
b/g = (1/3) / (2/3) = 1/2 ..C

C. Use real numbers. 1/4 of the number of girls is 10, so are 60 students. The number of girls is 4X10=40 and the number of boys is 60-40=20. 20/40 = 1/2

In a certain English Class, 1/4 of the number of girls is equal to 1/6 of the total number of students. What is the ratio of the number of boys to the number of girls in the class?
A) 1 to 4
B) 1 to 3
(C) 1 to 2
(D) 2 to 3
(E) 2 to 1

1/4 girls = 1/6 total
=> girls = 2/3 total

this implies, number of boys = 1/3 total

ratio of boys/girls = (1/3)/(2/3)
= 1/2

Answer : (C) 1 to 2

Consider a number with 4 and 6 as its factors- 24.

now 1/6 th of 24 = 1/4 th of girls------> 4=(1/4)g
So - Girls =16 and Boys=8
So ratio= 8/16 = 1/2

LCM\((4,6) = 12\). So, let the total number of students in the class be 12.

\(\frac{1}{6}(12) = 2 = \frac{1}{4}\)(number of girls). So, total number of girls in the class = \(4*2 = 8\).

Hence, the ratio of \(boys:girls = 4:8 = 1:2\). Ans (C).
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In a certain English class, 1/4 of the number of girls is equal to 1/6 of the total number of students. What is the ratio of the number of boys to the number of girls in the class?

A. 1 to 4
B. 1 to 3
C. 1 to 2
D. 2 to 3
E. 2 to 1

Here is the straightforward approach without testing numbers:

if 1/4 of girls = 1/6 of the class, then 4 * 1/4 of the girls = 4 * 1/6 of the glass

so all the girls represent 4/6, then the boys must be 2/6, and the ratio is 1:2

Attached is a visual that should help. I used the classic "algebra to simplify, plug in numbers to finish" method. Please ignore the 15 x 60...it is from another question.

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given
1/4 * g= 1/6*(b+g)
2g=4b
b/g = 1/2
IMO C

I'm really confusing myself -

Once we reduce it to 2G = 4B to 1G = 2B....why does that *not* mean that the ratio of boys to girls is 2:1?

Does 1G=2B not mean that for every one girl, there is 2 boys...

But also, when rearranged, I get that it can be re-written as 1/2=B/G. But I'm confused about why 1G=2B isn't a valid statement?

1/4 g = 1/6 t

thus g = 2/3t

B = 1/3t

b/g = (1/3) / (2/3)

IMO 1/2 ..C

Posted from my mobile device
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Hi,

I'm still confused how: 2g=4b turn out to be b/g = 1/2? can someone please help me out in a more easily way possible?

b = g/2 and so how we make b/g = 1/2?

Thank you.

Hi bonny1,

To start, most GMAT questions can be approached in more than one way - meaning that you don't have to take an Algebra approach to this question if you don't want to (you could very easily TEST VALUES instead). That having been said, the Algebra that you're asking about involves a couple of fairly standard 'math steps', so here's how you would work through those steps:

2G = 4B

When you have an equation, you can perform any 'math step' you want, as long as you perform it on BOTH sides of the equation. With this equation, since both sides are multiplied by an even number, we might want to start by dividing both sides by 2...

2G/2 = 4B/2
G = 2B

While you normally would not write a "1" in front of the G, that number is implied any time you have an individual variable...

1G = 2B

We can divide both sides by 2 again...

1G/2 = 2B/2
1G/2 = B

Finally, we divide both sides by G...

1G/2G = B/G

The "Gs" on the left side of the equation now 'cancel out'...

1/2 = B/G

GMAT assassins aren't born, they're made,
Rich
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This is very clear and makes perfect sense now.

Thank you so much