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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

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

by BTGmoderatorDC » Mon Nov 25, 2019 4:37 pm

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

OA B

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Mon Nov 25, 2019 4:37 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Nov 25, 2019 10:09 pm

BTGmoderatorDC 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

OA B

Source: Magoosh

Say John's weekly allowance was $x. Thus, he spent $3x/5 at the arcade. The remaining sum = x - 3x/5 = $2x/5. Then he spent 1/3 of 2x/5 = $2x/15 at the toy store. Remaining now = 2x/5 - 2x/15 = $4x/15

=> 4x/15 = 0.80 => x = $3.00

The correct answer: B

Hope this helps!

-Jay
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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

by Brent@GMATPrepNow » Tue Nov 26, 2019 6:36 am

BTGmoderatorDC 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

OA B

Source: Magoosh

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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[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] » Tue Nov 26, 2019 12:34 pm

Hi All,

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Nov 27, 2019 10:51 am

BTGmoderatorDC 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

OA B

Source: Magoosh

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]