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# Each of the 30 first graders in a class bought one of three

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Manager
Joined: 10 Feb 2011
Posts: 112

Kudos [?]: 370 [0], given: 10

Each of the 30 first graders in a class bought one of three [#permalink]

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09 Mar 2011, 15:04
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50% (00:00) correct 50% (00:40) wrong based on 3 sessions

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269. Each of the 30 first graders in a class bought one of three kinds of dictionaries, pocket edition, at price of \$15; compact edition, at price of \$18; and ordinary edition, at price of \$20. How many students bought the compact edition?
(1) The total cost of all dictionaries bought by the students is 540 dollars.
(2) The students who bought pocket edition are twice as many as the students who bought the compact edition.

Kudos [?]: 370 [0], given: 10

Intern
Status: Sophomore
Affiliations: President of Student Associoation
Joined: 09 Dec 2010
Posts: 37

Kudos [?]: 1 [0], given: 11

Schools: HBS 2+2, IESE YTP
Re: 269. Each of the 30 first graders in a class bought one of t [#permalink]

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09 Mar 2011, 16:57
banksy wrote:
269. Each of the 30 first graders in a class bought one of three kinds of dictionaries, pocket edition, at price of \$15; compact edition, at price of \$18; and ordinary edition, at price of \$20. How many students bought the compact edition?
(1) The total cost of all dictionaries bought by the students is 540 dollars.
(2) The students who bought pocket edition are twice as many as the students who bought the compact edition.

(2) let the number of students who bought the compact ed.=x,
the number of students who bought pocket ed.=2x
(1) 15*2x+18*x+20*y=540 and 2x+x+y=30 => 3x+y=30
y=15, x=5

Kudos [?]: 1 [0], given: 11

TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1602

Kudos [?]: 599 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Re: 269. Each of the 30 first graders in a class bought one of t [#permalink]

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09 Mar 2011, 21:13
PE + CE + OE = 30

15 * PE + 18 * CE + 20 * OE = 540

From (1)

15 (30 - CE - OE) + 18 * CE + 20 * OE = 540

450 - 15CE - 15OE + 18CE + 20OE = 540

5OE + 3CE = 90

5 * 15 + 3 * 5 = 90, so PE = 10 and Total = 15* 10 + 18 * 5 + 20 * 15 = 150 + 90 + 300 = 540

5 * 9 + 3 * 15 = 90, so PE = 6 and Total = 15 * 6 + 18 * 15 + 9 * 20 = 90 + 270 + 180 = 540

Not enough

From (2)

PE = 2CE

2CE + CE + OE = 30

=> 3CE + OE = 30

CE can be 3, OE = 21, PE = 6

or CE can be 1, OE = 27, PE = 2

Noe enough

From 1 and 2 :

5OE + 3CE = 90
3CE + OE = 30

so OE = 15 CE = 5, and PE = 10

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Kudos [?]: 599 [0], given: 40

Re: 269. Each of the 30 first graders in a class bought one of t   [#permalink] 09 Mar 2011, 21:13
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# Each of the 30 first graders in a class bought one of three

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