Math / GMAT Question (Fractions)?

Question

In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college. What fraction of the students in the senior class are male? Can you answer the previous question with the following information? - 75 percent of the students in the senior class have applied to college.
Please don't answer unless your are absolutely sure of your answer. Thank You.

The answer that CHESS wrote made sense to me except for the step from:
.72x + .8y / (x+y) = .75 to
.72x + .8y = .75 + .75
Wouldn't you multiply both sides by .75 which would result in a PRODUCT of .75 and .75 instead of a SUM?

Answer 1

Without anything to go by, you can't get a fraction with the first part of information. Apples and Oranges.
With the 75% thing,
x= male y=female (forget the chromasone (sp) thing)
(.72x + .8y)/(x+y) = .75
.72x + .8y = .75x +.75y
.05y = .03x
y= .6x
Now the fraction of the class that is male is:
x/(x+y)
from above, you can see y= .6x substitute
x/ (x+ .6x)
x/ 1.6x
fraction is 1/ 1.6 or .625 or 5/8 are male students in the senior class

Answer 2

addition and subtraction artwork the comparable way with fractions. looking the liquid crystal show with 3 fractions is slightly trickier, yet once you notice, 2, 4, and 5 all divide gently into 20. you could play around with the denominators to detect that or (the long yet optimistic way), multiply all 3 numbers at the same time to get 40 (2 x 4 x 5), and the fractions develop into (a hundred and eighty+a hundred and fifty-ninety six)/40, or 234/40 which simplifies right down to 117/20. bear in mind which you would be able to constantly constantly locate an elementary denominator via multiplying all denominators at the same time, in simple terms be optimistic you seem to simplify the top consequence if this is the path you opt for to take.

Answer 3

72 percent of the males and 80 percent of the females have applied to college. 75 percent of all the students have applied.

72M + 80F = 75 the average = 75%
M+F=1 so M=1-F the two percentages = 100%

72(1-F)+80F = 75 substitute 1-F for M
72-72F+80F=75 multiply 72 times 1-F
72+8F=75 ... -72F+80F=8F
8F=3
F=3/8 or 37.5%
M= 100 - 37.5% or 62.5%

Checking ...
Does 62.5% of 72 plus 37.5% of 80 = 75%?
0.625x72 = 45
0.375x80 = 30
30+45 does = 75

Therefore 62.5% of the class are males.

Answer 4

simple way to do this conver the percentage into fractions- 80 percent is 80/100 and 72/100. add the numbers to 152/200 and simplify to 19/25 i believe is the final number. check cuz im doin this in my head

Answer 5

Let x be the fraction of male student in class, we have:
0.72x + 0.8 (1-x) = 0.75
=> x = 5/8 = 0.625

Hence 62.5 percent of student are male ;)

Answer 6

You can't answer without the added information, you can get a lower limit with.
T = total class size, M=number males, F=females.
M+F = T
0.75 T = 0.72 M + 0.80 F
0.75 T = 0.72 M + 0.80 (T-M)
0.75 T = 0.72 M + 0.80T- 0.80M
0.75 T - 0.80T = 0.72 M - 0.80M
-0.05T = -0.08M
5T = 8M
M = 5/8T this is fraction of class that is male.

Answer 7

72% male = .72M
80% female = .80F
75% of all students = .75(M+F)
we get:
.72M + .80F = .75(M+F)
.72M + .80F = .75M + .75F
.05F = .03M
F = .03M/.05 = 3M/5
The total female population is equal to 3/5 of the male pop.
Total pop expressed in terms of males is:
M+F = M + 3M/5 = 8M/5
Percentage male = M divided by 8M/5 = 5/8 = 62.5%

Answer 8

wow, what "chess2226" wrote made a lot of sense to me.

Answer 9

73%