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Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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23 Mar 2015, 06:36
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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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23 Mar 2015, 07:58
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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



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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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23 Mar 2015, 08:01
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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



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Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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23 Mar 2015, 09:05
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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



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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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24 Mar 2015, 02:46
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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
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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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24 Mar 2015, 15:52
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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



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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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25 Mar 2015, 00:43
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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



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



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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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25 Mar 2015, 23:07
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Let Allowance be x x (3/5x + 1/3(2/5x)) = 0.8 X= 3 Ans B
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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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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
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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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30 Mar 2015, 10:24
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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.
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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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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



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Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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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
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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]
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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
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