Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47946

Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
23 Mar 2015, 06:36
Question Stats:
81% (01:39) correct 19% (02:09) wrong based on 135 sessions
HideShow timer Statistics



Current Student
Joined: 23 May 2013
Posts: 189
Location: United States
Concentration: Technology, Healthcare
GPA: 3.5

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
23 Mar 2015, 07:58
Bunuel wrote: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?
A. $2.40 B. $3.00 C. $3.20 D. $3.60 E. $4.80
Kudos for a correct solution. Let's take a look at how much John spent. Let his allowance be A. Arcade: 3/5 * A Toy Store: 1/3 of his remaining allowance. This means he spent (1/3)*(2/5)*A. Candy Store: .8 The total amount spent has to add up to his allowance. Thus, \(\frac{3}{5}*A + \frac{1}{3}*\frac{2}{5}*A + .8 = A\) \(\frac{3}{5}*A + \frac{2}{15}*A + .8 = A\) \(\frac{9}{15} A + \frac{2}{15} A + .8 = A\) \(\frac{11}{15}A + .8 = A\) \(.8 = \frac{4}{5} = \frac{4}{15} A.\) \(A = \frac{4}{5}*\frac{15}{4} = \frac{15}{5} = 3.\) Therefore, John's total allowance is 3 dollars. Answer: B



Intern
Joined: 28 Jan 2015
Posts: 15
GPA: 3.35
WE: Marketing (Education)

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
23 Mar 2015, 08:01
Let A be John's total weekly allowance.
(3/5)A went to Arcade
"The next day he spent one third of his remaining allowance at the toy store" This is the tricky part because if you don't read the stem well, you will assume that 1/3(A) is spent on the toy store.
Rather, he spent the 1/3 of his remaining allowance, which is 1/3 of (2/5)A or (2/15)A
"and then spent his last $0.80 at the candy store" A  [ (1/3)A + (2/15)A ]= A  (11/15)A = (4/15)A
Therefore (4/15)A = .80 or 4/5 cents
A = $3.00



Intern
Joined: 20 Mar 2015
Posts: 18
Location: Italy
GPA: 3.7

Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
23 Mar 2015, 09:05
Allowance: \(x\)
\(x=\frac{3}{5}x+\frac{1}{3}(1\frac{3}{5})x+0.8\) \(\frac{2}{5}x=\frac{1}{3}\frac{2}{5}+0.8\) \(\frac{62}{15}x=0.8\Rightarrow x=\frac{15\cdot 0.8}{4}=3\)
The correct answer is B



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
24 Mar 2015, 02:46
Answer = B = 3 Let the opening balance = x (Salary) Spent at arcade = \(\frac{3x}{5}\); Balance = \(\frac{2x}{5}\) Spent at toy store \(= \frac{2x}{5} * \frac{1}{3} = \frac{2x}{15}\); Balance = \(\frac{4x}{15}\) Given that the final balance \(\frac{4x}{15} = 0.80\) x = 3
_________________
Kindly press "+1 Kudos" to appreciate



Current Student
Joined: 06 Mar 2014
Posts: 256
Location: India
GMAT Date: 04302015

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
24 Mar 2015, 15:52
Bunuel wrote: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?
A. $2.40 B. $3.00 C. $3.20 D. $3.60 E. $4.80
Kudos for a correct solution. Let the initial amount be x. He spends 3/5 of it. that leaves (2/5)*x He spends 1/3rd of (2/5)*x that leaves him with 2/3rd of (2/5)*x. It is mentioned that he has $0.8 remaining. So \((2/3)*(2/5)*x = 0.8\) \(x = 3.\) Answer: B



Director
Joined: 21 May 2013
Posts: 648

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
25 Mar 2015, 00:43
Bunuel wrote: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?
A. $2.40 B. $3.00 C. $3.20 D. $3.60 E. $4.80
Kudos for a correct solution. Total allowance=X Amount spent at the arcade=3/5X Amount Remaining=2/5X Amount Spent at the toy store=2/5*1/3X=2/15X Amount Remaining=2/5X2/15X=4/15X Now, 4/15X=$0.8 Therefore, X=$3.00. Answer B



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12185
Location: United States (CA)

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
25 Mar 2015, 21:32
Hi All, Since this question asks for John's weekly allowance, and the answers are numbers, we can TEST THE ANSWERS. Normally, when TESTing THE ANSWERS, it's best to start with Answer B or Answer D. Answer B looks like the easier answer to work with, so we'll start there... IF....John's allowance is $3.... First, John spent 3/5 of his allowance at the arcade.... (3/5)($3) = $1.80 $3  $1.80 = $1.20 Next, John spends 1/3 of his remaining allowance at the toy store... (1/3)($1.20) = $0.40 $1.20  $0.40 = $0.80 Then he spent his last 80 cents at the candy store.... In Answer B, John is left with 80 cents for the last "step", so this MUST be the answer. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 02 Jan 2014
Posts: 39

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
25 Mar 2015, 21:57
3x/5 + (x3x/5)/3 + 0.8 = x, Solving for x , x= 3
Answer is B



Manager
Joined: 06 Jan 2014
Posts: 67

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
25 Mar 2015, 23:07
Let Allowance be x x (3/5x + 1/3(2/5x)) = 0.8 X= 3 Ans B
_________________
______________________________ Liked the Post !!!! KUDOs Plzzzzz



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
30 Mar 2015, 03:29
Bunuel wrote: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?
A. $2.40 B. $3.00 C. $3.20 D. $3.60 E. $4.80
Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:We know the following: 1. John spent 3/5 of his allowance at the arcade 2. The next day, John spent 1/3 of his remaining allowance at the toy store 3. Then he spent the remaining $0.80 at the candy store. Let's set John's allowance to A. Day One: John spent (3/5)A. This means he has A  (3/5)A in his pocket. That's (2/5)A. Day Two: He spent 1/3 of his remaining allowance, which was (2/5)A. So on day two, John spent (1/3)(2/5)A. So how much does he have left? At the beginning of day 2, he had (2/5)A. Then he spent (1/3)(2/5)A. Exactly like we did in day 1, we can count how much he has left by subtraction: (2/5)A  (1/3)(2/5)A = (2/3)(2/5)A If this is hard to understand immediately, then replace (2/5)A with x... x  (1/3)x = (2/3)x ...then look again at our previous calculation. So after the toy store, John has (2/3)(2/5)A. Finally: Then John spent all his money, $0.80, at the candy store. That means (2/3)(2/5)A = .80 Now we can do the math and solve for A. (2/3)(2/5)A = .80 (4/15)A = .80 4A = 12.00 A = 3.00
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 25 Nov 2014
Posts: 101
Concentration: Entrepreneurship, Technology
GPA: 4

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
30 Mar 2015, 10:24
Let total be x. John spent on day 1 : 3x/5. Rem 2x/5. Amt spent Next day: 2x/15. Lastly he spent remaining 0.8. Thus : 3x/5 + 2x/15 + .8 = x Solving for x we get x = 3. Alternately, we can plug in options. I always start by plugging in B, since the options are in increasing order. so let total be 3. Day 1 : 3*3/5 = 1.8 spent. Rem 1.2. Day 2 : 1.2/3 = .4 spent. Rem .8. Correct. Ans B.
_________________
Kudos!!



SVP
Joined: 06 Nov 2014
Posts: 1888

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
31 Mar 2015, 03:32
Bunuel wrote: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?
A. $2.40 B. $3.00 C. $3.20 D. $3.60 E. $4.80
Kudos for a correct solution. Let his allowance be x. Amount spent at arcade = 3x/5 Remaining = 2x/5 Amount spent at toy store = 1/3(2x/5) Last amount remaining = $0.80 Hence 3x/5 + 1/3(2x/5) + 0.80 = x So, x = 3 Hence option (B).  Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimusprep.com/gmatondemandcourse



CEO
Joined: 12 Sep 2015
Posts: 2703
Location: Canada

Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
18 Mar 2018, 07:33
Bunuel wrote: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?
A. $2.40 B. $3.00 C. $3.20 D. $3.60 E. $4.80
Kudos for a correct solution. Let w = John’s weekly allowance Having received his weekly allowance, John spent 3/5 of his allowance at the arcadeIf John spent 3/5 of his allowance, then he has 2/5 REMAINING So, ( 2/5)(w) = allowance REMAINING The next day he spent one third of his remaining allowance at the toy storeIf he spent 1/3, then he has 2/3 REMAINING So, ( 2/3)( 2/5)(w) = allowance REMAINING Once all of this is done, John has $0.80 REMAININGSo ( 2/3)( 2/5)(w) = 0.8 Simplify: (4/15)(w) = 0.8 Multiply both sides by 15 to get: 4w = 12 Divide both sides by 4 to get: w = 3 Answer: B Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2727

Re: Having received his weekly allowance, John spent 3/5 of his allowance
[#permalink]
Show Tags
21 Mar 2018, 16:20
Bunuel wrote: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?
A. $2.40 B. $3.00 C. $3.20 D. $3.60 E. $4.80 We can let n = the weekly allowance and create the equation: (3/5)n + 1/3(2/5)n + 0.8 = n 3n/5 + 2n/15 + 0.8 = n Multiplying by 15, we have: 9n + 2n + 12 = 15n 12 = 4n 3 = n Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Having received his weekly allowance, John spent 3/5 of his allowance &nbs
[#permalink]
21 Mar 2018, 16:20






