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Percentage

by Soumita Ghosh » Fri Jan 25, 2013 11:08 pm
Did at least 15 percent of the children in Springfield suffer adverse effects after taking a certain vaccination?

(1) Among the Springfield children, 20 percent of the girls and more than 10 percent of the boys suffered adverse effects after taking the vaccination.

(2) Among the Springfield children, 20 percent of the boys and more than 15 percent of the girls suffered adverse effects after taking that vaccination.

A)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
B)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;
D)EACH statement ALONE is sufficient to answer the question asked;
E)statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Can anyone solve it through any easy method???

OA B
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by hemant_rajput » Sat Jan 26, 2013 2:07 am
Soumita Ghosh wrote:Did at least 15 percent of the children in Springfield suffer adverse effects after taking a certain vaccination?

(1) Among the Springfield children, 20 percent of the girls and more than 10 percent of the boys suffered adverse effects after taking the vaccination.

(2) Among the Springfield children, 20 percent of the boys and more than 15 percent of the girls suffered adverse effects after taking that vaccination.

A)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
B)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;
D)EACH statement ALONE is sufficient to answer the question asked;
E)statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Can anyone solve it through any easy method???

OA B

Statement 1:- we know 20% of G and (10+)% of boys are affected. Now in order to find whether it is at least equal to 15% of total population we need to know total no. of boys and girls. Hence, not sufficient.


statement 2:- we know (15+)% of G and 20% of boys are affected. Now because whatever might be the population of boys and girls, we know for sure that the total combination will be greater than 15%.

say only 15% of girls are affected.

so now we have 15% of G and 20% of B. So for total population value will lie between 15 to 20%. Hence, we can say that at least 15 percent of the children have adverse effect.

statement 2 is sufficient.

answer b
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by GMATGuruNY » Sat Jan 26, 2013 4:34 am
Soumita Ghosh wrote:Did at least 15 percent of the children in Springfield suffer adverse effects after taking a certain vaccination?

(1) Among the Springfield children, 20 percent of the girls and more than 10 percent of the boys suffered adverse effects after taking the vaccination.

(2) Among the Springfield children, 20 percent of the boys and more than 15 percent of the girls suffered adverse effects after taking that vaccination.

OA B
Use REASON.

Statement 1:
MORE THAN 10% of the BOYS suffered adverse effects.
20% OF THE GIRLS suffered adverse effects.
This means that the percentage of the ALL THE CHILDREN who suffered adverse effects must be SOMEWHERE BETWEEN 10% AND 20%.
Thus, it's possible that less than 15%, exactly 15%, or more than 15% of the children suffered adverse effects.
INSUFFICIENT.

Statement 2:
MORE THAN 15% OF THE GIRLS suffered adverse effects.
20% OF THE BOYS suffered adverse effects.
This means that the percentage of the ALL THE CHILDREN who suffered adverse effects must be SOMEWHERE BETWEEN 15% AND 20%.
Thus, at least of the children 15% suffered adverse effects.
SUFFICIENT.

The correct answer is B.
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by Soumita Ghosh » Sat Jan 26, 2013 10:44 am
can we solve this by plugging number anyway..??
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by hemant_rajput » Sat Jan 26, 2013 10:55 am
Soumita Ghosh wrote:can we solve this by plugging number anyway..??
Obviously not, because if you plugged the value then you are eliminating unknowns from here, which are the deciding factors here. Although, remember one thing the motive here is to tell whether we can solve this problem using some combination of given statement or not. We really don't need to solve this question.
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by jp78 » Mon Sep 15, 2014 12:04 pm
Can't we use weighted average concept?

if so, Option 1 wouldn't be sufficient?
(1) 20% girls and more than 10% boys : so the weighted average will be always near to the greatest percentage, then shouldn't be atleast 15%?
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by GMATGuruNY » Mon Sep 15, 2014 12:19 pm
jp78 wrote:Can't we use weighted average concept?

if so, Option 1 wouldn't be sufficient?
(1) 20% girls and more than 10% boys : so the weighted average will be always near to the greatest percentage, then shouldn't be atleast 15%?
Statement 1: Among the Springfield children, 20 percent of the girls and more than 10 percent of the boys suffered adverse effects after taking the vaccination.
Test EXTREME cases.

Case 1: total girls = 25, total boys = 75, total students = 100.
Percent suffering adverse effects = (20% of the 25 girls + 12% of the 75 boys)/100 = (5+9)/100 = 14%.

Case 2: total girls = 75, total boys = 25, total students = 100.
Percent suffering adverse effects = (20% of the 75 girls + 12% of the 25 boys)/100 = (15+3)/100 = 18%.

Since the percent is less than 15% in Case 1 but greater than 15% in Case 2, INSUFFICIENT.

Take-away:
Since we don't know the ratio of girls to boys, we cannot determine whether the percentage for all the students is closer to the girls' percentage (20%) or to the boys' percentage (more than 10%).
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by [email protected] » Mon Sep 15, 2014 1:28 pm
Hi jp78,

The concept that you're thinking about works ONLY when we have the same number of boys as girls. As Mitch points out in his examples, if there are considerably more boys OR more girls, then the percentages can vary significantly.

Ratios and Percents shows up a number of times on the GMAT, so if you want to score at a high level, then you have to be clear on all of them. It would not surprise me if you saw a question that tested this exact concept on Test Day.

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