did > 1/2 class pass?

[CrackXam]

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.

SPOILER: Official Answer - E
IMO - B

[lsr]

I agree with the Official Answer.

CrackXam, how can you solve the question with the second statement?

[givemeanid]

E for me

[CrackXam]

Supp there are 100 students, 60 F and 40 M.
55&#37; of 60 +35%of 40 < 50

suppose there are 140 students, 80F and 60 M
55% of 80 +35% of 60 < 70

In all cases it ill be lesser than 1/2!

[lsr]

Supp there are 100 students, 60 F and 40 M.
55&#37; of 60 +35%of 40 < 50

suppose there are 140 students, 80F and 60 M
55% of 80 +35% of 60 < 70

In all cases it ill be lesser than 1/2!

You are absolutely right!!! (I totaly missed it....)


From the question stem:

55%F = (55/100)F = (11/20)F
therefore F=20f; where f is a positivie integer.

35%M = (35/100)M = (7/20)M
therefore M=20m; where m is a positive integer.

Is (55%F+35%M)/(F+M)>1/2?
which simplyfies to:
F>3M?

First Statement:
F>M
not sufficient.

Second Statement:
F=M+20
subtitute into the question stem,

M+20>3M ?
M<10.

since M=20m, and m is a positive integer.
the smallest value of M is 20.

Therefore Sufficient.

Answer is B.

GOOD CATCH CrackXam!!!

[DJValentino]

Good question CrackXam!!

[ibo]

My answer is E too

[Gmater-1]

Can anybody help me in understanding LSR's explanation? tnx

[cesar82]

I dont know if this will help you in understanding, but this is one way of looking at it (fast)

if at all, the second statement would be insufficient at lower values of boys and girls.

at higher values, like 100, 1000 boys etc.. the respective percentages wont add up to 50&#37; of the total

at the least possible value which is 20 boys (35% * 20 has to be an integer) we still have <50%

so it would seem that b is sufficient

[bose]

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