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4 friends A, B, C, and D appeared in a certain examination. The marks

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4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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New post Updated on: 12 Aug 2018, 23:36
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (02:49) correct 28% (03:11) wrong based on 150 sessions

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3 Major Concerns Students Face in Solving Percentage Problems - Exercise Question #3


4 friends A, B, C, and D appeared in a certain examination. The marks obtained by B is 33.3% less than A and 50% less than C. If the marks obtained by D is at least 2.5 times of the marks of B, then what is the maximum percentage by which the combined score of A and C is more than the score of D?

    A. 30%
    B. 35%
    C. 40%
    D. 45%
    E. 60%


To solve question 1: Question 1

To read the article: 3 Major Concerns Students Face in Solving Percentage Problems

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Originally posted by EgmatQuantExpert on 13 Jun 2018, 04:14.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:36, edited 3 times in total.
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Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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New post 13 Jun 2018, 04:56
1
Assume:
A =90 then
B=60 (90*1/3)
C=120 (60/0.5)
D= at least 150

A+C-D=90+120-150=60
(Percentage change/Value of D)*100 = (60/150)*100=40%

In MY opinion
Ans: C
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Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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New post 13 Jun 2018, 06:07
B = x
=>
A =1.5x
C =2x
D>= 2.5x

Q: Maximum of E= (A+C)/D
Emax <=> Dmin which we already got (2.5x)

=> E= 3.5x/2.5x = 1.4 => Answer: C: 40%
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Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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New post 13 Jun 2018, 06:48
Given:
B = 33.33% less than A = 50% less than C
D is atleast 2.5 times B.


Let's assume B = 100.
Then A = 150, C = 200 and D is atleast 250.
Maximum value of (A + C) - D = 350 - 250 = 100.
% \(= \frac{100}{250} * 100\) = 40%

Option C
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Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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New post 16 Jun 2018, 12:23

Solution



Given:
    • The marks obtained by B is 33.33% less than A
    • The marks obtained by B 50% less than C
    • The marks obtained by D is at least 2.5 times of the marks of B

To find:
    • The maximum percentage by which the combined score of A and C is more than the score of D

Approach and Working:
Let us assume the marks obtained by A, B, C, and D are a, b, c, and d respectively
    • As B got 33.3% less than A, we can write \(b = a – 33.3% of a = a – \frac{a}{3} = \frac{2a}{3}\)
    • As B got 50% less than C, we can write \(b = c – 50% of c = c – \frac{c}{2} = \frac{c}{2}\)
    • Hence, \(b = \frac{2a}{3} = \frac{c}{2}\)
      o Or, \(a = \frac{3b}{2}\) and \(c = 2b\)

    • Also, D got at least 2.5 times of B, therefore, we can write \(d = 2.5b = \frac{5b}{2}\)

Now, to maximise the percentage score of A and C over D, we need to minimise the score of D

The minimum score of D = 2.5b = \(\frac{5b}{2}\)
    • Therefore, the maximum percentage by which the combined score of A and C is more than the score of D = \(\frac{a + c – d}{d} * 100\) = \((\frac{3b}{2} + 2b – \frac{5b}{2})/ \frac{5b}{2} * 100\) = 40%

Hence, the correct answer is option C.

Answer: C
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Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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New post 14 Sep 2018, 22:42
LevanKhukhunashvili wrote:
Assume:
A =90 then
B=60 (90*1/3)
C=120 (60/0.5)
D= at least 150

A+C-D=90+120-150=60
(Percentage change/Value of D)*100 = (60/150)*100=40%

In MY opinion
Ans: C


Hi

if A = 90

B = (90*1/3) 30 not 60
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Re: 4 friends A, B, C, and D appeared in a certain examination. The marks   [#permalink] 14 Sep 2018, 22:42
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