Percentage

[vipinsharma]

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.?

[Brent@GMATPrepNow]

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.?

When posting questions, please include the 5 answer choices. In many cases, the fastest approach involves using the answer choices to our advantage.
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.

Cheers,
Brent

[GMATGuruNY]

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.?

Increasing from 25% to 60% must yield a difference of 70 marks (from 30 BELOW passing to 40 ABOVE passing).
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.

[j_shreyans]

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

[[email protected]]

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

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

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???

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.

[GMATinsight]

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.?

Lets's say X = Total Marks

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