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Do we need actual numbers here? Why can't percents be enough

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by neerabhu » Sat Aug 02, 2014 10:26 pm
What percent of Jefferson high school students study German?
Of the male students enrolled at Jefferson high school 20 percent study German.
Of the female students enrolled at Jefferson high school 35 percent study German.
A
Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient.
B
Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient.
C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D
EACH statement ALONE is sufficient.
E
Statements 1 and 2 TOGETHER are not sufficient.
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by sapuna » Sun Aug 03, 2014 12:39 am
The correct answer is E. While answers 1) and 2 ) tell us about the percent of male and female respectedly , we do not know what percent of the total students are male and what female.
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by GMATGuruNY » Sun Aug 03, 2014 3:10 am
neerabhu wrote:What percent of Jefferson high school students study German?
Of the male students enrolled at Jefferson high school 20 percent study German.
Of the female students enrolled at Jefferson high school 35 percent study German.
Clearly, neither statement alone is sufficient.

Statements combined:
Case 1: total male students = 20, total female students = 80, for a total of 100 students
In this case:
Number of male students who study German = 20% of 20 = 4.
Number of female students who study German = 35% of 80 = 28.
Of the 100 students, the percentage who study German = 4+28 = 32%.

Case 2: total male students = 80, total female students = 20, for a total of 100 students
In this case:
Number of male students who study German = 20% of 80 = 16.
Number of female students who study German = 35% of 20 = 7.
Of the 100 students, the percentage who study German = 16+7 = 23%.

Since the percentage who study German can be different values, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by GMATinsight » Sun Aug 03, 2014 4:03 am
neerabhu wrote:What percent of Jefferson high school students study German?
Of the male students enrolled at Jefferson high school 20 percent study German.
Of the female students enrolled at Jefferson high school 35 percent study German.
A
Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient.
B
Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient.
C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D
EACH statement ALONE is sufficient.
E
Statements 1 and 2 TOGETHER are not sufficient.
If Total Male = X
If Total Female = Y
Then Total Students = X + Y

Question : German Students / (X+Y) = ?

Statement 1) Of the male students enrolled at Jefferson high school 20 percent study German.

Image

Total German as fraction of Total Students is unknown
INSUFFICIENT

Statement 2) Of the female students enrolled at Jefferson high school 35 percent study German.

Image

Total German as fraction of Total Students is unknown
INSUFFICIENT

Combining the Two statement

Image

(0.2X + 0.35 Y) / (X+Y) Still doesn't give us total German Students / (X+Y)

INSUFFICIENT

Answer: Option E
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by Brent@GMATPrepNow » Sun Aug 03, 2014 6:03 am
I thought I'd point out that Bhoopendra approach is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- male or female
- study German or doesn't study German

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Sun Aug 03, 2014 11:35 am
HI neerabhu,

This DS question can be handled in the same way that you'd handle a "mixture" question. To know the exact answer, you'd either need to know the exact number of male students and female students OR you'd need to know the ratio of male students to female students.

If 20% of the males and 35% of the females speak German, then the "mixture" would lead to a TOTAL percentage that is between 20% and 35%. If there were LOTS more males, then the percentage would be lower (closer to 20%); if there were LOTS more females, then the percentage would be higher (closer to 35%).

In this case, we're never given enough information to determine that relationship. Mitch provides a couple of examples that prove that the answer changes depending on the number of students.

Final Answer: E

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