Population

[greenwich]

In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is

(A) 1 to 2
(B) 1 to 3
(C) 1 to 4
(D) 2 to 3
(E) 3 to 4

[Brent@GMATPrepNow]

In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is

(A) 1 to 2
(B) 1 to 3
(C) 1 to 4
(D) 2 to 3
(E) 3 to 4

A quick approach is to choose some numbers that meet the given conditions.

So, let's say that there is 1 person over twenty-one.

If there are 3 times as many people aged twenty-one or under as there are people over twenty-one, then there must be 3 people aged twenty-one or under.

This means the TOTAL population = 1 + 3 = 4

The ratio of those twenty-one or under to the total population = 3 to 4

Answer: E

Cheers,
Brent

[greenwich]

In the following question:

In Mr. Smith's class, what is the ratio of the number of boys to the number of girls?

(1) There are 3 times as many girls as boys in Mr. Smith's class.
(2) The number of boys is 1/4 of the total number of boys and girls in Mr. Smith's class.

It seems that the wording in (1) is similar to the question that I posted earlier. But (1) G=3B.

Am I missing something?

[ganeshrkamath]

In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is

(A) 1 to 2
(B) 1 to 3
(C) 1 to 4
(D) 2 to 3
(E) 3 to 4

U = n(age<=21)
O = n(age>21)
U = 3O

U/(U+O) = 3O/(3O + O)
= 3/4

Choose E

In the following question:

In Mr. Smith's class, what is the ratio of the number of boys to the number of girls?

(1) There are 3 times as many girls as boys in Mr. Smith's class.
(2) The number of boys is 1/4 of the total number of boys and girls in Mr. Smith's class.

It seems that the wording in (1) is similar to the question that I posted earlier. But (1) G=3B.

Am I missing something?

Statement 1: G = 3B (you are right. The wording is similar and so are the underlined parts)
B/G = 1/3
Sufficient.

Statement 2: B = (B+G)/4
3B/4 = G/4
B/G = 1/3
Sufficient.

Choose D

Cheers

[greenwich]

I am missing something here. Why it's not B=3G in the second question as the wording in the second one is similar to the first question?

[ganeshrkamath]

I am missing something here. Why it's not B=3G in the second question as the wording in the second one is similar to the first question?

3 times as many people aged twenty-one or under as there are people over twenty-one

U = 3O

3 times as many girls as boys in Mr. Smith's class.

G = 3B

Hope this helps.

Cheers

[Mathsbuddy]

In the United Kingdom, we try not to write ratios as fractions - as it can lead to misconceptions. Instead we use a colon. I would answer the population question using a grid like this:

<=21 : > 21 : Total
3 : 1 : 4

So, the answer is simply 3:4 (which means 3 to 4).

Similarly, with the boy/girl question. However, the 2nd clue is redundant.
From clue 1, the girls:boys ratio is 3:1. Therefore the boys:girls ratio is simply reversed = 1:3.

To show that the 2 questions are identical:

Girls : Boys : Total
3 : 1 : 4 which is no different to the population question above.

Although fractions are equivalent to ratios, they can confuse. Just leave ratios as integers with colons and the job is done quickly without algebra or fractions. Dead easy.

[GMATGuruNY]

Just leave ratios as integers with colons and the job is done quickly without algebra or fractions. Dead easy.

Don't limit yourself to one approach.
Sometimes treating ratios as fractions can make a problem easier.
For an example, check my post here:

https://www.beatthegmat.com/ratio-and-pr ... 69870.html

[Mathsbuddy]

Thanks for that. I like the simplicity of cancelling them all down, just like when finding the resultant gear ratio in a chain of gears or cog wheels. Yes I agree, one needs to be flexible, particularly for that higher level question. I tried to do it without fractions, but it ultimately came down to the same thing really. I've published it nonetheless as cosmetic alternative. Thanks again.

[[email protected]]

Hi Mathsbuddy,

The GMAT will test you several times on your ability to convert information from one "format" to another, so be prepared for this eventuality. In addition, it's sometimes beneficial to convert data to another format, as it decreases the amount of time needed to solve the given question.

As far as ratios are concerned, there are a variety of "formats", including....

2:5 - standard ratio
2/5 - fraction
2 to 5 - text
40% - percent (based on part/part ratio)
.4 - decimal (based on part/part ratio)

GMAT assassins aren't born, they're made,
Rich

[greenwich]

In the United Kingdom, we try not to write ratios as fractions - as it can lead to misconceptions. Instead we use a colon. I would answer the population question using a grid like this:

<=21 : > 21 : Total
3 : 1 : 4

So, the answer is simply 3:4 (which means 3 to 4).

Similarly, with the boy/girl question. However, the 2nd clue is redundant.
From clue 1, the girls:boys ratio is 3:1. Therefore the boys:girls ratio is simply reversed = 1:3.

To show that the 2 questions are identical:

Girls : Boys : Total
3 : 1 : 4 which is no different to the population question above.

Although fractions are equivalent to ratios, they can confuse. Just leave ratios as integers with colons and the job is done quickly without algebra or fractions. Dead easy.

I don't follow this part - the 2nd clue is redundant.
From clue 1, the girls:boys ratio is 3:1. Therefore the boys:girls ratio is simply reversed = 1:3.

How the boys:girls ratio is simply reversed and the 2nd clue is redundant?

[Abhishek009]

Below 21 = 3A

Above 21 = A

Total Population is 4A

Ratio of Population of below 21 to entire population is nothing but - 3A/4A => 3 : 4

[greenwich]

Below 21 = 3A

Above 21 = A

Total Population is 4A

Ratio of Population of below 21 to entire population is nothing but - 3A/4A => 3 : 4

The wording in this question is similar to the second question that I posted above. But on the second question (1) G=3B. Why not B=3G?

What am I missing here?

[Abhishek009]

In the following question:

In Mr. Smith's class, what is the ratio of the number of boys to the number of girls?

(1) There are 3 times as many girls as boys in Mr. Smith's class.
(2) The number of boys is 1/4 of the total number of boys and girls in Mr. Smith's class.

It seems that the wording in (1) is similar to the question that I posted earlier. But (1) G=3B.

Am I missing something?

Consider in this case total population ( P ) consists of Girls ( G ) and Boys ( B )

So , P = G + B

According to statement 1-

There are 3 times as many girls as boys in Mr. Smith's class.

So, G = 3B

We already know that P = G + B { Replace G with 3B here }

So, P = G + 3G =>4G


Statement 2 -

The number of boys is 1/4 of the total number of boys and girls in Mr. Smith's class.


The red highlighted part here simply refers to the total population of boys and girls

P = B + G ( Form of total population )

1/4 of the total number of boys and girls = 1/4 of P

Plug in any value of P , say 4 here

So Boys come out to 1/4 of P = 1 , therefore total number of girls = 3


So, Girls = 3 times the number of Boys here as well....

The wording in this question is similar to the second question that I posted above. But on the second question (1) G=3B. Why not B=3G?

What am I missing here?

To be precise -

There are 3 times as many girls as boys in Mr. Smith's class.

The question states explicitly Girls = Certain times Boys....

You need to find out the number of girls given the number of boys , it means for each boy there are three times girls present in the class...

[Mathsbuddy]

Somebody asked why the second boy/girl clue is redundant.
Basically, clue 1 gives us a girls:boys ratio of 3:1.
Therefore the boys:girls ratio is 1:3.
Therefore the second clue is not required, as we have just solved the question without it.

Alternatively we could have worked out the answer from the second clue, which would make the first clue redundant.

Redundant just means "Exceeding what is necessary... superfluous." Either one clue or the other can be used to solve this question. The extra clue just gives us something to check our answer against.

I hope that helps.