We can let t = the total number of geese before migration; thus, the number of male geese = 0.3t and the number of female geese = 0.7t. If we let the number of migrating geese = m, then the number of male migrating geese = 0.2m and the number of female migrating geese = 0.8m.

Thus, the migration rate for the male geese is 0.2m/0.3t = 2m/3t and the migration rate for the female geese is 0.8m/0.7t = 8m/7t.

Thus, the ratio of male migration rate to female migration rate is:

(2m/3t)/(8m/7t) = (7t x 2m)/(3t x 8m) = (14mt)/(24mt) = 14/24 = 7/12.

Answer: B
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Let there be g geese, of which 0.3g are male and 0.7g are female
Lets say m geese migrated, 0.2m are male and 0.8m are female

Migration Rate Male = 0.2m / 0.3g = (2/3)*(m/g)
Migration Rate Female = 0.8m / 0.7g = (8/7)*(m/g)

Ratio of migration rates = (2/3) / (8/7) = 7/12

Answer is (b)
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Let' take the Number of geese to be 100.

Male = 30. Female = 70.

Now the second part of the Q, Let's take the Number migrated to be 20.

So we have 20 geese that migrated and out of that 20% are male i.e 20/100 *20 = 4 Geese (Males)

And now we know out of the total 20 geese , 4 are male , then 16 have to be female.

Now the ratio part , Male Geese Ratios = 4/30 = 2/15. - A

Female Geese Ratios =16/70=8/35 - B

Cross Multiply Equations A and B and you get =7/12 .

Ans B

Hi all,

i too tried the same method and its taking more than 3 Mins.

Please tell if there is any fast solution method.

Regards,
Rrsnathan

say 100 are geese.. 30% means 30 are male and 70 are female.

Now x geese migrates,
Therefore \(\frac{x}{5}\) are male (since 20% of migrating geeses are male) and hence \(\frac{4x}{5}\) are female

Therefore \(\frac{Migration rate male}{Migration rate female}\) = {(x/5)/30} / {(4x/5)/70}

Solving we get, 7/12 as answer.

Consider Kudos if the post helped.

If we use the formula they give us

Isnt the migration rate the following:

Males = # geese migrating / total # of geese in sex = 0.2 (0.3x) / 0.3
Females = 0.8 * 0.7 / 0.7

Can someone help please explain why it is not the above?

0.2 * (0.3x) is a problem. The questions says that 20% of the geese migrating were males. It doesn't say that 20% of males migrated.

Sp if there were 100 geese in all, 30 were males. The question does NOT say that 20% of these 30 migrated.

Say, if half the total geese migrated, 50 migrated. Out of these 50, 20% were male i.e. 10 were male.

SO we need to take 20% of migrated geese, not the 20% of male population.

Does this sort out your problem?
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Taking 100 as the number of geese in the study, 30 are male and 70 are female. Setting the number of geese that migrate as 5x, the number of male geese migrating is x (20%), and the number of female geese migrating is 4x (80%).

Ratio = (x/30)/(4x/70) = 70x/120x = 7/12

Kudos if you agree!

Please reply if you have a better solution.

You could use the same method, but with simpler numbers.

30 males

70 females

Any 20/80 ratio for males migrating to females migrating will work. So, you could use the following.

10 males migrated

40 females migrated

male migration ratio: 10/30 = 1/3

female migration ratio: 40/70 = 4/7

(1/3)/(4/7) = 7/12

Choose B, and you are on to the next question.

Enjoy the GAME!
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Great explanation! Can someone quickly point out why you divide (1/3) by (4/7) in order to take the ratio of those?

Thanks

[/quote]
[Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
the migration rate for the male geese = 1/3
the migration rate for the female geese=4/7
BUT we have to find RATIO of these rates:-
"theratio of the migration rate for the male geese to the migration rate for the female geese?"

That is why we divide 1/3 by 4/7

Hope it helps
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This can be solved easily using a Double Matrix Method. Refer the attached pic.

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Im surprised to see that this question is 700 level. I'm saying this not because I found it easy (I actually got it wrong) but more of it can be solved by just deeper comprehension and no sophisticated formula or deep math number theory necessary. I noticed that this is one of my weaknesses, the PERCENT within another PERCENT type of questions.

Hi Bunuel ,

Would you know some good practice questions that tests this PERCENT within a PERCENT type of question?

Thanks.

We don't have a specific sub-tag for such questions but you can search here: https://gmatclub.com/forum/search.php?s ... tag_id=191
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Hi All,

We're told that 30 percent of a group of geese were male and that SOME of the geese migrated during the study (with 20 percent of that subgroup of migrating geese being male). We're asked for the RATIO of the migration rate for the MALE geese to the migration rate for the FEMALE geese. This question can be solved rather easily by TESTing VALUES (although you have to stay organized and label your work).

Since we're dealing with percents, let's TEST 100.

Total geese = 100
30% are male = 30 male geese
the rest are female = 70 female geese

Some of these 100 geese migrated - and we're told that 20% of this sub-group are male. This means that the number of migrating birds MUST be a multiple of 5. For the sake of continuing to use "round numbers", let's choose 50

50 migrating geese
20% are male = 10 male migrating geese
the rest are female = 40 female migrating geese

We're asked for the RATIO of male migration RATE to female migration RATE

Male rate = 10/30 = 1/3
Female rate = 40/70 = 4/7

(Male rate)/(Female rate) = (1/3)/(4/7) = 7/12

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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IMO this is less of a Percents and Interests problem, and more of a Ratio problem.

Total (T) | Male (M) | Female (F) |
Total # of geese | \(\frac{3}{10}\) T = M | \(\frac{7}{10}\) T = F
x = total # geese migrating | \(\frac{2}{10}\) x = M | \(\frac{8}{10}\) x = F

The part that is tricky is understanding that 1) the percent of the # of migrating male geese given has no amount basis/relation to the total number of geese given, so this is NOT a successive/multiple percent change problem where we combine \(\frac{3}{10} T * \frac{2}{10}\), and 2) these two different ratios can be joined together to answer the ratio in the question stem. Migration rate of geese is # of geese of that sex migrating / total # of geese of that sex.

Therefore Male migration rate/Female migration rate is:
\(\frac{2}{10} x / \frac{3}{10} T\) / \(\frac{8}{10} x / \frac{7}{10} T\)

Answer is B. \(\frac{7}{12}\)

The question is tricky as it employs some typical Official GMAT traps.

1. The quantities are all given in terms of percentages. No actual numbers are specified.
2. After being given the percentages of group members (male geese, female geese), we are then told that a certain percentage of these group members have migrated.
3. The final quantity asked is a ratio of two other ratios.

The second point may lead to a trap. We might assume that once we have actual numbers of the members, we will then be able to calculate the actual numbers of the members that migrated. The latter point is incorrect. We are not told that a certain percentage of the initial group members migrated. We are only given percentages of the group members that migrated of the total (unknown) number of members that migrated. Once we identify these traps, we can watch for them.

Since we are only given percentages and asked to find a ratio, we can safely assume a number like '100' for the initial total number of geese.

We are told that 30% of the initial number of geese were male. So, we have male geese = 30 and female geese = 70.

Now, we are told that an unknown number of these geese migrated. We can denote the number that migrated by the variable "x".

We are told that 20% of the migrating geese were male. So, we have male geese that migrated = 0.2x and female geese that migrated = 0.8x

We are asked to find the ratio of two migration rates. According to the formula given, we have:

Migration rate for male geese = Number of male geese that migrated/Number of male geese = 0.2x/30

Migration rate for female geese = Number of female geese that migrated/Number of female geese = 0.8x/70

Taking the ratio of these rates, we get the answer:

(0.2x/30)/(0.8x/70) = 7/12

ANSWER: (B)

A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]

Approach #1:

Let the no of geese included in the study plan be g. Then the no of males geese included is .3g and female geese will be .7g.

Also, let's say the no of geese migrated during study be m and the no of males would be .2m and females would be .8m.

migration rate for the male geese = .2m/.3g = 2m/3g

migration rate for the female geese = .8m/.7g = 8m/7g

The ratio of the migration rate for the male geese to the migration rate for the female geese = (2m/3g)/(8m/7g) = (2/3) *(7/8) =7/12

Option B is the answer.

Approach #2:
Assume that no of geese included in the study plan be 100 .
No of males geese = 30% 100 = 30
No of female geese = 100- 30 = 70

Assume that the no of geese migrated during study be 10. ( Here you can assume any no where you can easily find 20 % of it)
No of males geese migrated = 20% 10 = 2
No of female geese = 10- 2 = 8

migration rate for the male geese = 2/30

migration rate for the female geese =8/70

The ratio of the migration rate for the male geese to the migration rate for the female geese = (2/30) /(8/70) = (2/30) *(70/8) = 7/12

Option B is the answer.

Thanks,
Clifin J Francis,
GMAT SME
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We can skip algebra and just find some values that satisfy the given information.

A total of 30 percent of the geese included in a certain migration study were male.
So, it could be the case that there where 100 geese in the STUDY, which means 30 were male and 70 were female.

Some of the geese migrated during the study and 20 percent of the migrating geese were male
So it could be the case 10 geese from the study migrated, which means 2 were male and 8 were female.

What was the ratio of the migration rate for the male geese to the migration rate for the female geese?
The migration rate for the males = 2/30 = 1/15
The migration rate for the females = 8/70 = 4/35

So, the ratio of the migration rate for the male geese to the migration rate for the female geese = (1/15)/(4/35)
= (1/15)(35/4)
= 35/60
= 7/12

Answer: B
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