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

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Manager
Joined: 17 Jan 2017
Posts: 61

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07 Apr 2018, 01:45
00:00

Difficulty:

35% (medium)

Question Stats:

78% (02:29) correct 22% (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
Director
Joined: 31 Oct 2013
Posts: 876
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)

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07 Apr 2018, 04:44
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.

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.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2204

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09 Apr 2018, 14:41
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

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

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
Jack and Lily are playing quiz. They start with 50 chocolates each &nbs [#permalink] 09 Apr 2018, 14:41
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