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In last examination Roger scored marks in each of 5 subjects [#permalink]
04 Mar 2012, 06:34

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Difficulty:

45% (medium)

Question Stats:

72% (02:48) correct
28% (01:46) wrong based on 146 sessions

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?

Re: Ratio question [#permalink]
04 Mar 2012, 07:07

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Expert's post

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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%.

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
20 Mar 2012, 20:37

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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.

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
25 Jun 2013, 11:01

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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!

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 _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Re: Ratio question [#permalink]
08 Mar 2014, 08:03

1

This post received KUDOS

Expert's post

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%.

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
05 Mar 2012, 10:41

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

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
05 Mar 2012, 10:59

Expert's post

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

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
23 Mar 2012, 05:06

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 _________________

Practice Practice and practice...!!

If my reply /analysis is helpful-->please press KUDOS If there's a loophole in my analysis--> suggest measures to make it airtight.

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
03 Jan 2014, 07:03

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

Re: Ratio question [#permalink]
08 Mar 2014, 07:57

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%.

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
08 Mar 2014, 09:24

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.

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
09 Mar 2014, 02:26

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.

Answer A.

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% _________________

Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
01 May 2015, 13:39

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Re: In last examination Roger scored marks in each of 5 subjects [#permalink]
24 May 2015, 01:10

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.

gmatclubot

Re: In last examination Roger scored marks in each of 5 subjects
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