GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2018, 18:45

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

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

Show Tags

07 Apr 2018, 02:45
00:00

Difficulty:

35% (medium)

Question Stats:

78% (02:29) correct 22% (02:52) wrong based on 14 sessions

HideShow timer Statistics

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: 651
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Jack and Lily are playing quiz. They start with 50 chocolates each  [#permalink]

Show Tags

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.

(1/3)*21=7 =correctly answered by lily

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: 2037
Jack and Lily are playing quiz. They start with 50 chocolates each  [#permalink]

Show Tags

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

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

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

_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.