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Intern  Joined: 09 Feb 2012
Posts: 47
In last examination Roger scored marks in each of 5 subjects  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 66% (02:23) correct 34% (02:20) wrong based on 274 sessions

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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!

Originally posted by NYC5648 on 04 Mar 2012, 07:34.
Last edited by Bunuel on 04 Mar 2012, 08:08, edited 1 time in total.
Edited the question and moved to PS subforum
Math Expert V
Joined: 02 Sep 2009
Posts: 59107

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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.

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/

No posting of PS/DS questions is allowed in the main Math forum.

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Intern  Joined: 09 Feb 2012
Posts: 47
Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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Many thanks!!!

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

Could you please explain it to me.

Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 59107
Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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NYC5648 wrote:
Many thanks!!!

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

Could you please explain it to me.

Thanks!

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.
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Manager  Joined: 18 Sep 2009
Posts: 231
Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 59107
Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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TomB wrote:
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

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.
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Intern  Joined: 08 Mar 2012
Posts: 3
Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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4
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.

Manager  Joined: 07 Dec 2011
Posts: 68
Location: India
Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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2
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.
Manager  B
Joined: 13 Mar 2012
Posts: 198
Concentration: Operations, Strategy
Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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NYC5648 wrote:
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!

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
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Math Expert V
Joined: 02 Sep 2009
Posts: 59107
Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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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

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Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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1
1
NYC5648 wrote:
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!

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
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Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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NYC5648 wrote:
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!

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 Intern  Joined: 05 Dec 2013
Posts: 12

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Bunuel wrote:
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.

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/

No posting of PS/DS questions is allowed in the main Math forum.

Bunuel - Could you walk me through how you reduced the fraction above (highlighted in blue)
Math Expert V
Joined: 02 Sep 2009
Posts: 59107

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1
bparrish89 wrote:
Bunuel wrote:
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.

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/

No posting of PS/DS questions is allowed in the main Math forum.

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

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

Hope it's clear.
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Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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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.

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Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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monalimishra wrote:
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.

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%
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Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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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.
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Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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[4x+5x+6x+7x+8x]/5 = 72
30x=360
x=12

4(12) = 48, which is below 50, thus we have 1 exam that he failed.
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Re: In last examination Roger scored marks in each of 5 subjects  [#permalink]

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_________________ Re: In last examination Roger scored marks in each of 5 subjects   [#permalink] 26 Sep 2019, 04:25
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