Data Sufficiency

Of the students in the class, 55% of the females and 35% of the males passed the exam. Did more than half the students pass the exam?

1) More than half the students in the class are females
2) The number of female students is 20 more than the the number of male students.

IMO both are individually sufficient to answer the question.
D
See attached image for calcs.
Note: Pick numbers for which each of the boxes is a whole number since # students cant be fractions.

thanks...great way to solve....

but i have my doubts.

If i put in value of x as 20 and y as 80. the sum is 100 and the total passed are 51. Hence the percentage is more than 50%. Similarly as you have put in value of x as 20 and y as 40. the passing percentage is less than 50%.

Similarly for premise 2 i put in value of x as 1 and y 21 (as the question says that y is 20 more than x) the passing percentage is more than 50%. Also if i put the values as x as 1000 and y as 1020 then the passing percentage is less than 50%.

In my opinion the answer should be E as both statements are insufficient. unless i am missing something.

hjafferi wrote:Of the students in the class, 55% of the females and 35% of the males passed the exam. Did more than half the students pass the exam?

1) More than half the students in the class are females
2) The number of female students is 20 more than the the number of male students.

55% of the females passed the exam:
55/100 = 11/20.
Thus, 11/20 of the female students pass.
Implication:
The total number of female students must be a multiple of 20.

35% of the males passed the exam.
35/100 = 7/20.
Thus, 7/20 of the male students pass.
Implication:
The total number of male students must be a multiple of 20.

Statement 1: More than half the students in the class are females.

Try the LEAST POSSIBLE VALUES.
Case 1: Males = 20, Females = 40
Males who passed = 7/20 * 20 = 7.
Females who passed = 11/20 * 40 = 22.
Passed/total = (7+22)/(20+40) = 29/60.
Here, FEWER than half pass.

Try EXTREMES.
Case 2: Males = 20, Females = 80
Males who passed = 7/20 * 20 = 7.
Females who passed = 11/20 * 80 = 44.
Passed/total = (7+44)/(20+80) = 51/100.
Here, MORE than half pass.

Since FEWER than half pass in Case 1, but MORE than half pass in Case 2, INSUFFICIENT.

Statement 2: The number of female students is 20 more than the number of male students.

Try the LEAST POSSIBLE VALUES.
Case 1: Males = 20, Females = 40
Males who passed = 7/20 * 20 = 7.
Females who passed = 11/20 * 40 = 22.
Passed/total = (7+22)/(20+40) = 29/60.
Here, FEWER than half pass.

Try EXTREMES.
Case 3: Males = 100, Females = 120
Males who passed = 7/20 * 100 = 35.
Females who passed = 11/20 * 120 = 66.
Passed/total = (35+66)/(100+120) = 101/220.
Here, FEWER than half pass.

Case 3 illustrates that as the values INCREASE, the fraction who pass DECREASES.
Thus, the greatest possible fraction who pass = 29/60, which is LESS THAN 1/2.
SUFFICIENT.

The correct answer is B.