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# There are five sales agents in a certain real estate office. One month

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There are five sales agents in a certain real estate office. One month [#permalink]
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There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen

Anyone could help me finding my mistake and why?
I assumed that Andy = 100 in the first place, then I started

based on the given info.
Andy=2Ellen
Bob+3 = Ellen
Cary = 2 Bob
Dora = Bob+Ellen

Andy =100
Ellen 50
Bob =47
Cary=94
Dora=97

I know it is a mistake but way!!
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Re: There are five sales agents in a certain real estate office. One month [#permalink]
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mohd_int wrote:
There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen

Anyone could help me finding my mistake and why?
I assumed that Andy = 100 in the first place, then I started

based on the given info.
Andy=2Ellen
Bob+3 = Ellen
Cary = 2 Bob
Dora = Bob+Ellen

Andy =100
Ellen 50
Bob =47
Cary=94
Dora=97

I know it is a mistake but way!!

Andy sold twice as many properties as Ellen: Andy = 2*Ellen;

Bob sold 3 more than Ellen: Bob = Ellen + 3;

Cary sold twice as many as Bob: Cary = 2*Bob;

Dora sold as many as Bob and Ellen together: Dora = Bob + Ellen,

If Andy = 100, then;

Ellen = 50;

Bob = 53;

Cary = 106;

Dora = 53 + 50 = 103.

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Re: There are five sales agents in a certain real estate office. One month [#permalink]
Bunuel wrote:
mohd_int wrote:
There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen

Anyone could help me finding my mistake and why?
I assumed that Andy = 100 in the first place, then I started

based on the given info.
Andy=2Ellen
Bob+3 = Ellen
Cary = 2 Bob
Dora = Bob+Ellen

Andy =100
Ellen 50
Bob =47
Cary=94
Dora=97

I know it is a mistake but way!!

Andy sold twice as many properties as Ellen: Andy = 2*Ellen;

Bob sold 3 more than Ellen: Bob = Ellen + 3;

Cary sold twice as many as Bob: Cary = 2*Bob;

Dora sold as many as Bob and Ellen together: Dora = Bob + Ellen,

If Andy = 100, then;

Ellen = 50;

Bob = 53;

Cary = 106;

Dora = 53 + 50 = 103.

Thank you so much for your post. I see now my mistake!
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There are five sales agents in a certain real estate office. One month [#permalink]
2
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nycgirl212 wrote:
Official Guide for GMAT Quant Review 2016
Practice Question
Question No.:9
Page: 63
Difficulty:

There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen

A = 2E
B = E + 3
C = 2B
D = B + E
E

In problems such as this one, if you can make one variable equal to 100, it makes things simple.

(Here, the base variable does not have to be 100 because there are no percentages involved. I use 100 consistently because it's versatile.)

Once written out as above:
1) every variable is defined by B and/or E; but
2) B is defined by E

Let E = 100
A = 2E = 200
B = E + 3 = 103
C = 2B = 206
D = B + E = 203

C, Cary, sold the most properties.

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Re: There are five sales agents in a certain real estate office. One month [#permalink]
nycgirl212 wrote:

There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen

We can create the following equations:

A = 2E

B = E + 3

C = 2B

D = B + E

Looking at our equations, Ellen is not the person who sold the most properties because at least Bob sold more than she did. We also see that Dora sold more than Bob, so Bob is not the person who sold the most properties. Since B = E + 3 (so B > E), we see that Dora sold more than Andy (D > B since B + E > E + E). So Andy is not the person who sold the most properties and we are left with Cary and Dora. Since B > E, we see that Cary sold more than Dora (C > D since B + B > B + E). Thus, Cary sold the most properties.

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Re: There are five sales agents in a certain real estate office. One month [#permalink]
nycgirl212 wrote:
Official Guide for GMAT Quant Review 2016
Practice Question
Question No.:9
Page: 63
Difficulty:

There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen

let Ellen sold sold X properties
then Andy = 2x
Bob = x+3
Carry = 2(x+9)
Dora 2(x+3) +2x

now i summed up all these properties

x+2x+x+3+2(x+9) +2(x+3) +2x

so i get 9x+27

9x=-27

x = -3

so why my solution is such long and incorrect ?

anyone?
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Re: There are five sales agents in a certain real estate office. One month [#permalink]
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Lets plugin simple numbers

No of properties sold by ellen : 1
Andy (Twice as ellen) : 2
Bob (3 More than ellen) : 4
Cary(Twice as many as ellen): 8
Dora(Bob + Ellen) : 5

Cary has sold the highest number of properties

Ans: C
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There are five sales agents in a certain real estate office. One month [#permalink]
dave13 wrote:
nycgirl212 wrote:
Official Guide for GMAT Quant Review 2016
Practice Question
Question No.:9
Page: 63
Difficulty:

There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen

let Ellen sold sold X properties
then Andy = 2x
Bob = x+3
Carry = 2(x+9) is incorrect it should be Carry = 2 (x+3) = 2x + 6
Dora 2(x+3) +2x if Dora is Bob + Ellen then the equation should be like this Dora = x + 3 + x = 2x + 3

now i summed up all these properties

x+2x+x+3+2(x+9) +2(x+3) +2x

so i get 9x+27

9x=-27

x = -3

so why my solution is such long and incorrect ?

anyone?

You started correctly by assuming x for Ellen.

We are just comparing the values. There is no need to sum any of the them.

If Ellen = x

Then Andy = 2x

Bob = x + 3

Carry = 2*Bob = 2 (x+3) = 2x + 6

Dora = Bob + Ellen = x+3 +x = 2x + 3

For whatever substituted value of x (as long as the x value is an integer > 0). Because they cannot sell in negative nor in fractions :D.

Carry have sold more than anyone else.

I hope this helps.
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Re: There are five sales agents in a certain real estate office. One month [#permalink]

Ellen = X
Andy = 2X
Bob = 3X
Carry = 2 * 3X = 6X
Dora = 3X+X = 4X

Carry sold more real estate than anyone else at office
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There are five sales agents in a certain real estate office. One month [#permalink]
[1] Create Equations

A = 2E
B = E + 3
C = 2B
D = B+E

[2] Set E = 10 and Solve

A = 2(10) ... A = 20
B = 10 + 3 ... B = 13
C = 2(13) ... C = 26
D = 13 + 10 ... D = 23

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Re: There are five sales agents in a certain real estate office. One month [#permalink]
nycgirl212 wrote:
Official Guide for GMAT Quant Review 2016
Practice Question
Question No.:9
Page: 63
Difficulty:

There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?

a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen

Given:
1. There are five sales agents in a certain real estate office.
2. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together.

Asked: Who sold the most properties that month?

Let properties sold by Andy, Ellen, Bob, Cary & Dora be a, e, b, c, d respectively

a = 2e (1)
b = 3 + e (2)
c = 2b (3)
d = b + e (4)

Since properties sold are positive integers

a = 2e; a>e
b = 3 + e; b>e
c = 2b = 6 + 2e; c>b>e
d = b + e = 3 + 2e; c>d>{a,b}>e

Cary (c) sold the most properties in the month.

IMO C
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Re: There are five sales agents in a certain real estate office. One month [#permalink]
say,Ellen sold =x
So, Bob=x+3
Andy=2x
Cary= 2(x+3)=2x+6
Dora = x+x+3=2x+3
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Re: There are five sales agents in a certain real estate office. One month [#permalink]
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Re: There are five sales agents in a certain real estate office. One month [#permalink]
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