Problem Solving

In a certain school, 40 more than 1/3 of all the students are taking a math course and 1/4 of those taking a math course are taking history course. If 1/8 of all the students in the school are taking history course, how many students are in the school?

A. 240
B. 300
C. 480
D. 720
E. 960


Much appreciated

The answer is 240 .

Thanks
Senthil

preciousrain7 wrote:In a certain school, 40 more than 1/3 of all the students are taking a math course and 1/4 of those taking a math course are taking history course. If 1/8 of all the students in the school are taking history course, how many students are in the school?

A. 240
B. 300
C. 480
D. 720
E. 960


Much appreciated

preciousrain7, Senthil is correct. I am adding the approach I used to solve the problem -
M = 40 + x/3
H = 1/4 * (40 + x/3)
But H = x/8
So if u solve the equ, 1/4 * (40 + x/3) = x/8; u will get x = 240. Got me?

preciousrain7 wrote:In a certain school, 40 more than 1/3 of all the students are taking a math course and 1/4 of those taking a math course are taking history course. If 1/8 of all the students in the school are taking history course, how many students are in the school?

A. 240
B. 300
C. 480
D. 720
E. 960


Much appreciated

Complicated story with numbers as answers - the little GMAT guy in your brain should be shouting "BACKSOLVING TIME!!"

Using the Kaplan method for backsolving, we start with either (B) or (D) - (B) looks easier, so let's pretend the answer is 300.

So, if we have 300 students, 140 of them take math (100 + 40).

1/4(140) = 35 take history.

1/8 of 300 are supposed to take history. 300 isn't even divisble by 8 (so we could have actually eliminated 300 from the get-go).

1/8(300) = 37.5.

So, we wanted 37.5 to take history, we only got 35. Now we need to decide if we need more students or fewer students to make the numbers balance.

If we added more students, then 1/4(1/3 + 40) = 1/12 + 10 wouldn't go up as quickly as 1/8 would. Therefore, we need fewer students.

Eliminate (C), (D) and (E): choose (A).

Maybe I'm misinterpreting the problem, but where in the problem does it say that 1/8 that takes history also takes math? That is why when solving it, I couldn't equate these 2 equations:

x/12+10 and x/8

Isn't there missing info?

xilef wrote:Maybe I'm misinterpreting the problem, but where in the problem does it say that 1/8 that takes history also takes math? That is why when solving it, I couldn't equate these 2 equations:

x/12+10 and x/8

Isn't there missing info?

we need to equate the nbr of students taking History.
from the math taking students (x/3 + 40), 1/4 take history.
& overall, x/8 take history.
equate them & there is your answer..

Ritz

xilef wrote:Maybe I'm misinterpreting the problem, but where in the problem does it say that 1/8 that takes history also takes math? That is why when solving it, I couldn't equate these 2 equations:

x/12+10 and x/8

Isn't there missing info?

we need to equate the nbr of students taking History.
from the math taking students (x/3 + 40), 1/4 take history.
& overall, x/8 take history.
equate them & there is your answer..

Ritz

xilef wrote:Maybe I'm misinterpreting the problem, but where in the problem does it say that 1/8 that takes history also takes math? That is why when solving it, I couldn't equate these 2 equations:

x/12+10 and x/8

Isn't there missing info?

It says that 1/8 of the total take history, and that 1/4 of those who take math also take history.

so:

1/4(1/3 x + 40) = (1/8)x

(1/12)x + 10 = (1/8)x

After getting a common denominator of 24 and isolating x:

10 = (3/24)x - (2/24)x

10 = (1/24)x

240 = x

It says that 1/8 of the total take history, and that 1/4 of those who take math also take history.

so:

1/4(1/3 x + 40) = (1/8)x

(1/12)x + 10 = (1/8)x

After getting a common denominator of 24 and isolating x:

10 = (3/24)x - (2/24)x

10 = (1/24)x

240 = x

Stuart,
I'm not having a problem with the algebra portion but rather with your assumption that 1/8 of the people who took history also took math. We know that some portion (x/12+10) took both math and history and 1/8 of the TOTAL took history - can't that 1/8 include both, students who took math+history and students who only took history (without math)?

can't we have the following scenario?

lets say you have 720 students in school:

1/4(720/3 + 40) = 70 students who take both math and history

720/8 = 90 students who take history; therefore, 70 take math +history and 20 take only history or history and some other subject.

Stuart,
I'm not having a problem with the algebra portion but rather with your assumption that 1/8 of the people who took history also took math. We know that some portion (x/12+10) took both math and history and 1/8 of the TOTAL took history - can't that 1/8 include both, students who took math+history and students who only took history (without math)?

Hmm... I guess I made that assumption because without it, the question is unanswerable.

You're right - the sentence "everyone who takes history also takes math" is missing from the problem.

thanks for clarifying.

Stuart Kovinsky wrote:

Stuart,
I'm not having a problem with the algebra portion but rather with your assumption that 1/8 of the people who took history also took math. We know that some portion (x/12+10) took both math and history and 1/8 of the TOTAL took history - can't that 1/8 include both, students who took math+history and students who only took history (without math)?

Hmm... I guess I made that assumption because without it, the question is unanswerable.

You're right - the sentence "everyone who takes history also takes math" is missing from the problem.

Actually the sentence "everyone who takes history also takes math" is not included in the problem. I got the problem from an official GMAT test but changed the words around. My issue with the question was exactly that... do we assume that 1/8 of the student who took history also took math....

hi guys, maybe my approach might shed some light.
x=whole class h=history and m = math

first off;

1/3x +40=math
1/4(1/3x +40)=history

1/8x=history class

SOooooo..

1/4(1/3x +40)=1/8x ==> 1/12x + 10 = 1/8x ===> x = 240


fun question.


so the question is going to be unanswerable?

will we come across techncal errors like this during the real thing?

preciousrain7 wrote:

Stuart Kovinsky wrote:

Stuart,
I'm not having a problem with the algebra portion but rather with your assumption that 1/8 of the people who took history also took math. We know that some portion (x/12+10) took both math and history and 1/8 of the TOTAL took history - can't that 1/8 include both, students who took math+history and students who only took history (without math)?

Hmm... I guess I made that assumption because without it, the question is unanswerable.

You're right - the sentence "everyone who takes history also takes math" is missing from the problem.

Actually the sentence "everyone who takes history also takes math" is not included in the problem. I got the problem from an official GMAT test but changed the words around. My issue with the question was exactly that... do we assume that 1/8 of the student who took history also took math....

Well, if you changed the words around, it's possible that the original language DID clarify the situtation.

The official GMAT questions are pretty thoroughly tested and it's very rare (but not unheard of) to get an erroneous question.

If such a question is found, then it's entirely removed from testing and treated as an unscored question.

Remember, 1/5 to 1/4 of the questions you see don't even count. It's possible that the question we're discussing was already unscored and just used for experimental purposes.

Ah! The nerve of these people, as if we don't have enough things to worry about.