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Comment on Students at ABC Academy
I did it in a different way.
That's a fantastic solution.
That's a fantastic solution. Great work!
Option C (72) is divisible by
But thank you for the alternative approach.
Another great solution. The
Another great solution. The great thing about GMAT math questions is that they can typically be solved in more than one way!
56 divided by 7 is 8, so 56
Perfect!
Perfect!
Hi Brent, could you kindly
We are told that the ratio of
We are told that the ratio of girls to boys is 5 to 3.
So, some possible scenarios include:
5 girls and 3 boys (for a total of 8 students in the school)
10 girls and 6 boys (for a total of 16 students in the school)
15 girls and 9 boys (for a total of 24 students in the school)
20 girls and 12 boys (for a total of 32 students in the school)
etc
Notice that the total number of students in the school is always divisible by 8.
This is because the two components of the ratio 5 to 3 add up to 8.
Since the total number of students must be divisible by 8, we can eliminate B and D because those answer choices are not divisible by 8.
Once the 20 boys and 20 girls leave, the new ratio of boys to girls is 2 to 5.
We can apply the same logic to conclude that the new total number of students must be divisible by 7 (the sum of 2 and 5)
So, we can take the remaining three answer choices (A, C and E), and subtract 40 (the number of students who left) to see if the number of students remaining is divisible by 7.
A) 56 - 40 = 16
So, if there are presently 56 students in the school, then there would be 16 students remaining after 40 of them left.
Since 16 is not divisible by 7, we can eliminate answer choice A since it does not meet the conditions of the question.
C) 72 - 40 = 32
Since 32 is not divisible by 7, we can eliminate answer choice C since it does not meet the conditions of the question.
E) 96 - 40 = 56
Since 56 IS divisible by 7, it must be the correct answer
Brilliant and great
Isn't this way easier?
(5x-20)/(3x-20) = 2/5, cross multiply find x
I found the video method too complicated, or is it just me?
Your 1-variable solution
Your 1-variable solution works too. I find that some students have trouble keeping track of what x represents. So, for this question type, I typically use 2 variables to avoid any difficulties.
well, my thought about the
Agreed!
Agreed!
can you show the rest of your
Let 5x = the ORIGINAL number
Let 5x = the ORIGINAL number of girls
And let 3x = the ORIGINAL number of boys
ASIDE: This ensures that the ratio of girls/boys = 5x/3x = 5/3
So, 5x - 20 = the number of girls AFTER 20 girls leave
And 3x - 20 = the number of boys AFTER 20 boys leave
AFTER some children leave, the ratio of girls/boys = 5/2
So, we can write: (5x - 20)/(3x - 20) = 5/2
Cross multiply to get: 5(3x - 20) = 2(5x - 20)
Expand: 15x - 100 = 10x - 40
Add 100 to both sides to get: 15x = 10x + 60
Subtract 10x from both sides to get: 5x = 60
Solve: x = 12
So, the ORIGINAL number of girls = 5x = 5(12) = 60
And the ORIGINAL number of boys = 3x = 3(12) = 36
TOTAL number of children = 60 + 36 = 96
Cheers,
Brent
It should be equal to 5/2
What part of the solution are
What part of the solution are you referring to?
i feel the correct ans. is 56
This is a bit of a Sentence
This is a bit of a Sentence Correction question. The second sentence is a hypothetical scenario that DID NOT occur. So, at the end, when we ask "How many children attend ABC Academy?", we cannot factor in the hypothetical information.
Consider this similar example: Joe has some apples. IF Joe were to give 9 apples to Sue, then Joe would have 1 apple. How many apples does Joe have?
As the question is worded, the answer is 10 (the number of apples he presently has)
Thank you I was almost asking
Hi Brent, I also solved the
That's correct.
That's correct.
Here's another example:
IF Joe's height were doubled, he WOULD be 12 feet tall.
How tall IS Joe?
The "IF Joe's height were doubled..." part is a hypothetical situation that does not actually happen. So, when we're asked "How tall IS Joe?" we can use the hypothetical information to determine that Joe is 6 feet tall.
The same applies to the video question above. We're told "IF 20 boys and 20 girls WERE to leave, the ratio of the number of boys to the number of girls WOULD be...."
In the question at https://gmatclub.com/forum/in-a-certain-district-the-ratio-of-the-number..., there is no hypothetical situation. We're told that "After 600 additional Republicans and 500 additional Democrats registered,..."
So, those 1100 additional registrations actually happened. Also, for further clarification, we're asked "AFTER THESE REGISTRATIONS, there were how many more voters in the district registered as Democrats than as Republicans?"
Does that help?
Cheers,
Brent
It's clear now, thanks!
thanks for clarifying my
Hi Brent, what if the new
For example, you have 5B=3G and new ratio after subtracting 20 students is 4/7 and you have (7B-20)=(4G-20)
or this will never be the case with gmat since they expect you to solve this under 2 mins and they will always give situations like above?
You can get both kinds of
You can get both kinds of systems of equations. That is, you can get nice convenient systems where both equations have the same expressions (e.g., 5B), and you can get less convenient systems.
Let's continue with your example...
If the new ratio were 4/7, we'd get: (B-20)/(G-20) = 4/7
Cross multiply to get: 7(B-20) = 4(G-20)
Expand to get: 7B - 140 = 4G - 80
Rearrange to get: 7B - 4G = 60
So, we have the system
5B = 3G
7B - 4G = 60
From here, we'd have to solve the system the same way we solve other systems of equations (covered here https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...)
Cheers,
Brent
Hi Brent, I started doing as
Thanks for sharing! Yes, I
Thanks for sharing! Yes, I worded the question like that to make students aware of the order in which the values appear in a ratio.
Cheers,
Brent
I did it a different way.
(5x-20)/(3x-20)= 5y/2y
My reasoning is that we know Y is a different number than X. For me it is easier than just using 5/2.
Okay, but you are
Okay, but you are unnecessarily adding a variable, when one is not needed (since 5y/2y = 5/2).
How do you handle the resulting equation?
Cheers,
Brent
Hi Brent, question asked how
Isn't the question a bit ambiguious that is it referring to total number of children before or after those 20 boys and girls leaving the Academy? Any tips of how to differentiate from this type of question as I calculated total number using after leave so is 56. Thanks Brent
PRESENTLY the ratio of girls
PRESENTLY the ratio of girls to boys is 5 to 3.
The word IF starts a HYPOTHETICAL situation in which 20 boys and 20 girls leave the academy.
Keep in mind that this HYPOTHETICAL situation never actually happens.
The question asks "How many children attend the academy?"
Since the word ATTEND is present tense, the question is asking how many students PRESENTLY attend the academy.
There's a similar question:
Felix the cat weighs x pound. IF Felix WERE to gain 3 pounds, then it WOULD weigh 10 pounds.
How much does Felix weigh?
In this example, the HYPOTHETICAL situation is Felix gaining 3 pounds.
The question "How much does Felix weigh?" is in the present tense, which means we want to know Felix's weight BEFORE the hypothetical weight gain of three pounds.
Does that help?
Crystal clear now. Noted