Mrs. Jones divided $120 evenly among her children. Tom, the

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Mrs. Jones divided $120 evenly among her children. Tom, the

by AAPL » Fri May 25, 2018 7:44 am

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Mrs. Jones divided $120 evenly among her children. Tom, the eldest, decided to give each of his brothers and sisters $6 of his share. Eventually, Tom ended up with $12. How many children does Mrs. Jones?

A. 4
B. 5
C. 6
D. 8
E. 10

The OA is A.

Is there a strategic approach to solve this PS question? Can anyone help, please? Thanks!

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Source: Beat The GMAT — Problem Solving | Fri May 25, 2018 7:44 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

Tom

by GMATGuruNY » Fri May 25, 2018 8:19 am

AAPL wrote:Mrs. Jones divided $120 evenly among her children. Tom, the eldest, decided to give each of his brothers and sisters $6 of his share. Eventually, Tom ended up with $12. How many children does Mrs. Jones?

A. 4
B. 5
C. 6
D. 8
E. 10

We can PLUG IN THE ANSWERS, which represent the total number of children.
When the correct answer is plugged in, Tom's resulting amount = $12.

B: 5 children, implying that the original share per child = 120/5 = 24
After Tom gives $6 to each of his 4 siblings, Tom's resulting amount = 24 - (4*6) = 0.
Tom resulting amount is too small.
For Tom's resulting amount to be greater, there must be FEWER CHILDREN, so that each child receives a greater portion of the $120 and fewer siblings are given $6 of Tom's allotment.

The correct answer is A.

A: 4 children, implying that the original share per child = 120/4 = 30
After Tom gives $6 to each of his 3 siblings, Tom's resulting amount = 30 - (3*6) = 12.
Success!

Last edited by GMATGuruNY on Tue May 29, 2018 8:48 am, edited 1 time in total.

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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 » Fri May 25, 2018 8:46 am

AAPL wrote:Mrs. Jones divided $120 evenly among her children. Tom, the eldest, decided to give each of his brothers and sisters $6 of his share. Eventually, Tom ended up with $12. How many children does Mrs. Jones?

A. 4
B. 5
C. 6
D. 8
E. 10

Let x = # children that Mrs. Jones has
This means x-1 = # of Tom's siblings.
If Tom gives each sibling $6, the total amount that Tom gave to siblings = 6(x - 1)
AFTER giving $6 to each sibling, Tom had $12 remaining.
So, BEFORE he gave away the money, the amount Tom had = 12 + 6(x - 1) = 12 + 6x - 6 = 6x + 6

Since each child originally received the SAME amount, we know that EACH child received 6x + 6 dollars
Since there are x children, the TOTAL amount the children received = (x)(6x + 6)
Since the x children received a TOTAL of $120, we can write: (x)(6x + 6) = 120
Expand equation: 6xÂ² + 6x = 120
Subtract 120 from both sides: 6xÂ² + 6x - 120 = 0
Divide both sides by 6 to get: xÂ² + x - 20 = 0
Factor to get: (x + 5)(x - 4) = 0
So, EITHER x = -5 OR x = 4
Since x cannot be negative, we can rule out x = -5, which means x must equal 4

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue May 29, 2018 8:30 am

AAPL wrote:Mrs. Jones divided $120 evenly among her children. Tom, the eldest, decided to give each of his brothers and sisters $6 of his share. Eventually, Tom ended up with $12. How many children does Mrs. Jones?

A. 4
B. 5
C. 6
D. 8
E. 10

Let x = the number of children Mrs. Jones has. Since Tom is one of the children, he has (x - 1) siblings. Tom receives 120/x dollars and he gives 6 dollars to each of his (x - 1) siblings and he has 12 dollars left.

We can create the equation:

120/x - 6(x - 1) = 12

120 - 6x(x - 1) = 12x

120 - 6x^2 + 6x = 12x

-6x^2 - 6x + 120 = 0

Dividing both sides by -6, we have:

x^2 + x - 20 = 0

(x + 5)(x - 4) = 0

x = -5 or x = 4

Since x can't be negative, x must be 4.

Answer: A

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