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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2201
4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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Updated on: 12 Aug 2018, 22:36
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:54) correct 30% (03:05) wrong based on 119 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, 03:14.
Last edited by EgmatQuantExpert on 12 Aug 2018, 22:36, edited 3 times in total.
Manager
Joined: 13 Feb 2018
Posts: 135
Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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13 Jun 2018, 03:56
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
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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13 Jun 2018, 05:07
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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Joined: 11 Apr 2018
Posts: 120
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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13 Jun 2018, 05:48
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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2201
Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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16 Jun 2018, 11:23

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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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

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Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

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Manager
Joined: 16 Jan 2018
Posts: 90
Location: New Zealand
Re: 4 friends A, B, C, and D appeared in a certain examination. The marks  [#permalink]

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14 Sep 2018, 21:42
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
Re: 4 friends A, B, C, and D appeared in a certain examination. The marks &nbs [#permalink] 14 Sep 2018, 21:42
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# 4 friends A, B, C, and D appeared in a certain examination. The marks

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