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e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2871
4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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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

_________________

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.
Senior Manager  G
Joined: 13 Feb 2018
Posts: 270
GMAT 1: 640 Q48 V28 Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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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
Intern  Joined: 10 Jun 2018
Posts: 12
Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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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%
Manager  S
Joined: 11 Apr 2018
Posts: 128
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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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
e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2871
Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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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
_________________
Manager  S
Joined: 16 Jan 2018
Posts: 91
Location: New Zealand
Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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

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