Hi All,
Ratio questions can be solved in variety of ways and in a variety of "formats" (fractions, decimals, percents, etc.). If you're not great with ratios yet, then that's okay - a bit of "brute force" and TESTing VALUES can still get you the correct answer.
In this prompt, we're told that the ratio of males:females is 4:5. This does NOT tell us how many actual people there are. It DOES tell us that for every 4 males there will be 5 females. Furthermore, we know that the number of males MUST be a multiple of 4, the number of females MUST be an equivalent multiple of 5 and the total number of people MUST be an equivalent multiple of 9. The question asks how many males there are.
Fact 1: If the number of girls increased by 20%, then males would constitute 40% of this larger student body.
Let's TEST VALUES....
IF the original number of...
Males = 4
Females = 5
20% more females = +1
Males:Females is now 4:6 which is 4/10 of the total and equals 40%
The answer to the question is 4
IF the original number of...
Males = 8
Females = 10
20% more females = +2
Males:Females is now 8:12 which is 8/20 of the total and equals 40%
The answer to the question is 8
Fact 1 is INSUFFICIENT
Fact 2: If 10 more male students joined the school, the new ratio of males to females would be 9:10.
With the original ratio of males to females, we could have....
4 males and 5 females
8 males and 10 females
12 males and 15 females
Etc.
Adding 10 more males to each of these options would yield DIFFERENT results.....
4 males and 5 females becomes 14 males and 5 females = 14:5
8 males and 10 females becomes 18 males and 10 females = 18:10
12 males and 15 females becomes 22 males and 15 females = 22:15
Recognizing this, we will EVENTUALLY get to the ONE answer that creates a 9:10 ratio. It ends up being....
80 males and 100 females becomes 90 males and 100 females = 9:10
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich