In last examination Roger scored marks in each of 5 subjects

Question

In last examination Roger scored marks in each of 5 subjects in the following ratio 4:5:6:7:8 and got an overall score of 72%. If 50% of the maximum marks is passing and the maximum marks of each subject is the same, in how many subjects did Roger fail?

A. 1
B. 2
C. 3
D. 4
E. 5

Many thanks.
Have a great Sunday!

A. 1
B. 2
C. 3
D. 4
E. 5

Many thanks. 
Have a great Sunday!

Bunuel · Accepted Answer

In last examination Roger scored marks in each of 5 subjects in the following ratio 4:5:6:7:8 and got an overall score of 72%. If 50% of the maximum marks is passing and the maximum marks of each subject is the same, in how many subjects did Roger fail?

A. 1
B. 2
C. 3
D. 4
E. 5

Given: A:B:C:D:E=4x:5x:6x:7x:8x, for some multiple x. Assume the maximum marks of each subject to be y, so the the maximum marks of ALL 5 subjects will be 5y.

So, we have that \(4x+5x+6x+7x+8x=\frac{72}{100}*5y\) --> \(30x=\frac{72*5}{100}*y\) --> \(x=\frac{12}{100}*y\). \(4x=\frac{48}{100}*y\) and \(5x=\frac{60}{100}*y\), so in subject A Roger scored 48% (less than 50%) and in subject B 60% (more than 50%). Obviously in all other subjects Rogers scores will be higher than 50%.

Roger failed in only one subject A.

Answer: A.

P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

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monalimishra · Answer

I did this by picking numbers. 
Say the max mark in each subject is 100.
Then I can directly know that Roger scored 40,50,60,70,80. 
Since passing mark is 50% of max mark => passing mark = 50.
Thus Roger failed in only 1 subject, where he scored 40.

Answer A.

NYC5648 · Answer

Many thanks!!!

But I dont really get the step, to multiply with 5y

Could you please explain it to me.

Thanks!

Bunuel · Answer

We are told that "the maximum marks of each subject is the same", say it's y, then the sum of the marks in all 5 subjects will be y+y+y+y+y=5y.

Hope it's clear.

TomB · Answer

Hi bunnel

can you suggest any material for ratio and proportions. I have completed ratio and proportions in manhattan word translations, but still i need some extra practice

Thanks

Bunuel · Answer

I can think of no material on this subject though below are some questions to practice: PS questions on Fractions/Ratios/Decimals: search.php?search_id=tag&tag_id=36 DS questions on Fractions/Ratios/Decimals: search.php?search_id=tag&tag_id=57 Hope it helps.

karun0109 · Answer

took x as a percentage of score in an exam

(4x+5x+6x+7x+8x)5 =72 = avg percentage
6x=72
x = 12

therefore marks are 48%, 60% and so on and only the one value 48% is below the passing threshold of 50%. Hence, A.

kraizada84 · Answer

LET MAX MARKS BE Y

then (4+5+6+7+8)x=0.72*5y
=> 30x=3.6y
=> x=36y/300=3y/25
hence

4x= 4*3y/25=12y/25--> fail
5x--> pass
as all other scores are greater than 5x hence he passed in all

hence failed in 1 subject

option A

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=36
All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57

WoundedTiger · Answer

For ratio and proportion questions, We can always check at first for plugging in values.

Let us assume that for each exam the max score is 100. So total max score in 5 exams is 500 
where as Roger scored 72% of 500 which is 360

360 is total marks scored by Roger which is nothing but some of sum of his scores in all subjects

so we have 4a+5a+6a+7a+8a = 360 where "a" is any positive integer, solving for "a", we get 30a= 360 ----> a=12

4a= 48 < 50 and in rest all exams he passed so ans should be A

jlgdr · Answer

Total sum of scores is 30x Total sum of scores is also 720 720/30 = 12 = x So then, we can start with the first and it will give 48, fail Next is obviously 60 pass, so only 1 fail Hence A Hope it helps! Cheers J

bparrish89 · Answer

Bunuel - Could you walk me through how you reduced the fraction above (highlighted in blue)

Bunuel · Answer

30x=\frac{72*5}{100}*y=\frac{(6*12)*5}{100}*y  --> reduce by 30=6*5:  x=\frac{12}{100}*y  --> multiply by 4:  4x=\frac{48}{100}*y .

Hope it's clear.

AKG1593 · Answer

Option A.
Let the marks be 4x,5x,6x,7x and 8x.
Total=30x
Avg.=6x
Now 6x=72
X=12
On calculating Subject marks,we get 48,60,72,84 & 96.
Only one subject is <50.

Posted from my mobile device

PareshGmat · Answer

Though the answer A is correct, the calculations are wrong

If we consider 40,50,60,70,80 as the scores, then the average comes up 60%

shallow9323 · Answer

Hi, 
Is my logic correct.

what i understood was 72% score implies, 72% of max that is 100%
and since he got 72% in the ratios 4 5 6 7 8 therefore he got 48% of max marks in A. which is less that 50% if max marks.
hence he failed in 1 subject.

law258 · Answer

/5 = 72
30x=360
x=12

4(12) = 48, which is below 50, thus we have 1 exam that he failed.

Archit3110 · Answer

let each subject be max 100 marks 
so total marks max ; 500
and passing marks ; 50 marks for each subject
he scored ; 500* .72 ; 360 marks
so his avg per subject must be 360/30 ; 12 marks
4:5:6:7:8 ; we see that at 4*12 ; 48 marks is 1 subject where he has scored <50 % 
OPTION A ; 1

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In last examination Roger scored marks in each of 5 subjects

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