Having received his weekly allowance, John spent 3/5 of

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

Having received his weekly allowance, John spent 3/5 of

by Gmat_mission » Sat Mar 17, 2018 8:59 am

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

[spoiler]OA=B[/spoiler].

I am confused. What are the equations that I should set here? Can any expert give me some help? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sat Mar 17, 2018 8:59 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Mar 17, 2018 6:57 pm

Hi Gmat_mission,

We're told that John spent 3/5 of his allowance at the arcade, then spent one third of his remaining allowance at the toy store and then spent his last $0.80 at the candy store. We're asked for John's weekly allowance. This question can be solved by TESTing THE ANSWERS.

Let's start with the 'easiest' answer and TEST Answer B first:

Answer B: $3.00
IF.... John's allowance = $3.00
He spent (3/5)($3) at the arcade = $1.80 spent at the arcade, leaving $3.00 - $1.80 = $1.20
He then spent (1/3)($1.20) at the toy store = $0.40 spent at the toy store, leaving $1.20 - $0.40 = $0.80
This is an exact match for what we were told, so this must be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Having received his weekly allowance, John spent 3/5 of

by Brent@GMATPrepNow » Sun Mar 18, 2018 6:29 am

Gmat_mission 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

Let w = John's weekly allowance

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade
If 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 store
If 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 had $0.80 REMAINING
So (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 - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Wed Mar 21, 2018 3:25 pm

Gmat_mission 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

Jeffrey Miller
Head of GMAT Instruction
[email protected]