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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Apr 21, 2014 9:41 am
What fraction of this year's graduation students at a certain college are males?

(1) Of this year's graduation students, 35% of male and 20% of female transferred from another college.
(2) Of this year's graduation students, 25% transferred from another college.
Let M = ALL male graduates
Let F = ALL female graduates

Target question: What fraction of this year's graduation students at a certain college are male?
In other words, we want the value of M/(M+F), so we can rephrase the target question...

REPHRASED target question: What is the value of M/(M+F)?

Statement 1:Of this year's graduation students, 35% of male and 20% of female transferred from another college.
In other words, the TOTAL number of graduates who transferred = 0.35M + 0.2F
This info is not enough to find the value of M/(M+F)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Of this year's graduation students, 25% transferred from another college.
Total number of graduates who transferred = 0.25(M+F)
This info is not enough to find the value of M/(M+F)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the total number of graduates who transferred = 0.35M + 0.2F
Statement 2 tells us that the total number of graduates who transferred = 0.25(M+F)
So, we can conclude that 0.35M + 0.2F = 0.25(M+F)
Expand: 0.35M + 0.2F = 0.25M + 0.25F
Rearrange to get: 0.10M = 0.05F (Perfect)
Multiply both sides by 20 to get 2M = F
From here, we can find the value of M/(M+F)
Since 2M = F, we can replace F with 2M to get:
M/(M+F) = M/(M+2M)
= M/3M
= 1/3
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

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Brent
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by GMATGuruNY » Mon Apr 21, 2014 10:50 am
What fraction of this year's graduating students at a certain college are males?

1) Of this year's graduating students, 33% of the males and the 20% of the females transferred from another college.

2) Of this year's graduating students, 25% transferred from another college.
Neither statement alone is sufficient to determine males/total.
When the statements are combined, the result is a WEIGHTED AVERAGE/MIXTURE problem:
Of all the men, the percentage who transferred from another college = 33%.
Of all the women, the percentage who transferred from another college = 20%.
Of all the students -- the MIXTURE of men and women -- the percentage who transferred from another college = 25%.

We can use ALLIGATION to determine males/total.

Step 1: Plot the 3 percentages on a number line, with the percentage for the men and women (33% and 20%) on the ends and the percentage for all the students (25%) in the middle.
M 33---------25----------20 W

Step 2: Calculate the distances between the percentages.
M 33----8----25----5-----20 W

Step 3: Determine the ratio in the mixture.
The ratio of men to women is the RECIPROCAL of the distances in red.
M:W = 5:8.

Since 5+8=13, of every 13 students, 5 are men and 8 are women.
Thus, males/total = 5/13.
SUFFICIENT.

The correct answer is C.

Please note the following:
Almost NO MATH is needed here if we understand how WEIGHTED AVERAGES work.
Statement 1 indicates the percentages for the two INGREDIENTS (the men and the women).
Statement 2 indicates the percentage for the MIXTURE (the men and women combined).
If we know the percentages for the two ingredients and the percentage for the mixture, we can ALWAYS determine the RATIO of the two ingredients (in this case, M:W).

Thus -- without doing any math -- we can see that the two statements combined are SUFFICIENT to determine males/total.

Other alligation problems:
https://www.beatthegmat.com/mixture-prob ... tml#593241
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by sanju09 » Mon Apr 21, 2014 10:27 pm
[spoiler]Posting the screen shot of a GMAT PREP is an offence. So avoid it and take pain of typing it out carefully.[/spoiler]

Let there be m males and f females graduating in the college this year.

Target Question: What is the value of m/ (m + f)?

(1) 0.33m + 0.20f = # of students transferred from other college. Evidently [spoiler]insufficient[/spoiler] to answer the value of m/ (m + f).

(2) 0.25 (m + f) = # of students transferred from other college. Evidently [spoiler]insufficient[/spoiler] to answer the value of m/ (m + f).

Combining, 0.33m + 0.20f = 0.25 (m + f) will give us a direct relation in m and f, which is [spoiler]sufficient[/spoiler] to answer the value of m/ (m + f).

[spoiler]Choose C[/spoiler]
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