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Jack and Lily are playing quiz. They start with 50 chocolates each

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Joined: 17 Jan 2017
Posts: 61
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Jack and Lily are playing quiz. They start with 50 chocolates each  [#permalink]

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New post 07 Apr 2018, 02:45
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

86% (01:27) correct 14% (02:52) wrong based on 14 sessions

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Jack and Lily are playing quiz. They start with 50 chocolates each and Jack asks questions. For each correct answer, Jack gives Lily 4 chocolates and for each incorrect answer, Lily gives three chocolates to Jack. If at the end of the quiz, Lily gave only one-third answers correct and is left with 36 chocolates, how many questions did Jack ask her?

A. 7
B. 14
C. 21
D. 36
E. 43

Source: ExpertsGlobal
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Joined: 31 Oct 2013
Posts: 376
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Jack and Lily are playing quiz. They start with 50 chocolates each  [#permalink]

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New post 07 Apr 2018, 05:44
benejo wrote:
Jack and Lily are playing quiz. They start with 50 chocolates each and Jack asks questions. For each correct answer, Jack gives Lily 4 chocolates and for each incorrect answer, Lily gives three chocolates to Jack. If at the end of the quiz, Lily gave only one-third answers correct and is left with 36 chocolates, how many questions did Jack ask her?

A. 7
B. 14
C. 21
D. 36
E. 43

Source: ExpertsGlobal


In my opinion , Back solving is perfect for this question. Notice that Lily gives 1/3 of the questions were correct. thus total no. of question must be divisible by 3. we are left with only C and D.

start with C, total question 21.
(1/3)*21=7 =correctly answered by lily
so, incorrect answer=21-7=14

Now , lily has 50 chocolates.
for correct answer she gets 4 chocolates. so total no. of chocolates she get is =7*4=8
for incorrect answer she provides = 14*3=42
so, 50-42+28=36= no of chocolates lily left with.

Thus, correct answer will be 21 as it meets our condition.
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Jack and Lily are playing quiz. They start with 50 chocolates each  [#permalink]

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New post 09 Apr 2018, 15:41
benejo wrote:
Jack and Lily are playing quiz. They start with 50 chocolates each and Jack asks questions. For each correct answer, Jack gives Lily 4 chocolates and for each incorrect answer, Lily gives three chocolates to Jack. If at the end of the quiz, Lily gave only one-third answers correct and is left with 36 chocolates, how many questions did Jack ask her?

A. 7
B. 14
C. 21
D. 36
E. 43

Source: ExpertsGlobal

Lily started with 50 chocolates. She ends up with 36, i.e., a net loss of chocolates, which we can also call "points"

(36-50) = -14 = the SUM of her points from the questions

A weighted average accounts for the net loss. There are twice as many negative values as there are positive values.

Let \(x\) = the number of questions

\(\frac{1}{3}\)x were correct
Each correct answer = +4 chocolates to Lily

\(\frac{2}{3}\)x were incorrect
Each incorrect answer = -3 chocolates from Lily

Call -3 and +4 "point value"

She had a net loss of chocolates: (36 - 50) = -14

(weight of incorrect answers)* (point value) +
(weight of correct answers) * (point value)
must sum to -14

\((\frac{2}{3}x * -3) + \frac{1}{3}x * 4 = -14\)
\(-\frac{6}{3}x + \frac{4}{3}x = -14\)
\(-6x + 4x = -42\)
\(-2x = -42\)
\(x = 21\)


Answer C

Thinking in terms of deficits is odd. I'd check this answer.
21 questions: 7 correct, 14 incorrect
(7) * (4) = +28 chocolates
(14) * (-3) = -42 chocolates

(50 + 28 - 42) = 36 chocolates. That works

_________________

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that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Jack and Lily are playing quiz. They start with 50 chocolates each &nbs [#permalink] 09 Apr 2018, 15:41
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