Percentage
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- vipinsharma
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A student scores 25% and failed by 30 marks while another student who scores 60% get 40 marks more than minimum required marks to pass. find the maximum marks in the exam.?
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- Brent@GMATPrepNow
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When posting questions, please include the 5 answer choices. In many cases, the fastest approach involves using the answer choices to our advantage.vipinsharma wrote:A student scores 25% and failed by 30 marks while another student who scores 60% gets 40 marks more than minimum required marks to pass. find the maximum marks in the exam.?
Here's one approach:
Let T = the TOTAL number of marks the test is out of (i.e., the maximum score)
Let P = the number of marks required to PASS the test
A student scores 25% and failed by 30 marks
In other words, getting 25% of the total possible marks results in a score that's 30 marks LESS THAN the number of marks required to pass.
We can write: 0.25T = P - 30
Rewrite as 0.25T + 30 = P
A student who scores 60% gets 40 marks more than minimum required marks to pass
In other words, getting 60% of the total possible marks results in a score that's 40 marks MORE THAN the number of marks required to pass.
We can write: 0.60T = P + 40
Rewrite as 0.60T - 40 = P
Since the red and blue equations are set equal to P, we can write...
0.25T + 30 = 0.60T - 40
Rearrange to get: 70 = 0.35T
Solve to get: T = 200
So, the test is out of 200 marks. So, the maximum score is 200.
ASIDE: If the answer choices had been included, it might have been faster to just start testing the answer choices.
ASIDE: If we solve for P, we see that the PASSING score for this test was 80 marks. I mention this because some students might assume that 50% was the passing score for the test.
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Brent
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Increasing from 25% to 60% must yield a difference of 70 marks (from 30 BELOW passing to 40 ABOVE passing).vipinsharma wrote:A student scores 25% and failed by 30 marks while another student who scores 60% get 40 marks more than minimum required marks to pass. find the maximum marks in the exam.?
If there are a total of 100 possible marks, the difference between 60% and 25% = 60-25 = 35.
Since the required difference of 70 marks is TWICE AS GREAT, the total number of marks must be TWICE AS GREAT as 100:
2*100 = 200.
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Hi All ,
I got stuck in the last step. Please advise.
Let Minimum be M and Total be T
So 25T/100=M-30
from this we got T=(M-30)100/25 .....(|)
And 60T/100=M+40
From this we got T=(M+40)100/60 .....(||)
now we can equate these two
(M-30)100/25=(M+40)100/60
So we will get M=80
now what???
please advise.
Thanks
Shreyans
I got stuck in the last step. Please advise.
Let Minimum be M and Total be T
So 25T/100=M-30
from this we got T=(M-30)100/25 .....(|)
And 60T/100=M+40
From this we got T=(M+40)100/60 .....(||)
now we can equate these two
(M-30)100/25=(M+40)100/60
So we will get M=80
now what???
please advise.
Thanks
Shreyans
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Hi j_shreyans,
Now that you know that M = 80, you can plug THAT value back into either of the two original equations that you wrote and get the value of T.
Using the first equation....
T = (80-30)(100)/25
T = (50)(4)/1
T = 200
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Now that you know that M = 80, you can plug THAT value back into either of the two original equations that you wrote and get the value of T.
Using the first equation....
T = (80-30)(100)/25
T = (50)(4)/1
T = 200
GMAT assassins aren't born, they're made,
Rich
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You've got it all there - once you discover that M = 80, plug into the equation in green, or (1/4)T = M - 30, and you're set.j_shreyans wrote:Hi All ,
I got stuck in the last step. Please advise.
Let Minimum be M and Total be T
So 25T/100=M-30
So we will get M=80
now what???
- GMATinsight
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Lets's say X = Total Marksvipinsharma wrote:A student scores 25% and failed by 30 marks while another student who scores 60% get 40 marks more than minimum required marks to pass. find the maximum marks in the exam.?
Passing Marks = 0.25 X + 30 [as per first statement of question]
Passing Marks = 0.60 X - 40 [as per first statement of question]
Both are the same therefore
0.25 X + 30 = 0.60 X - 40
i.e. 0.35 X = 30 + 40
i.e. X = 70/0.35 = 200
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