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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Mary buys several pencils that cost 30 cents and 24 cents. How many of  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 65% (01:29) correct 35% (01:15) wrong based on 52 sessions

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Mary buys several pencils that cost 30 cents and 24 cents. How many of 30 cent pencils did he buy?

1) Total cost is \$1.02
2) He buys 4 pencils in total

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Senior Manager  G
Joined: 06 Jul 2016
Posts: 358
Location: Singapore
Concentration: Strategy, Finance
Re: Mary buys several pencils that cost 30 cents and 24 cents. How many of  [#permalink]

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MathRevolution wrote:
Mary buys several pencils that cost 30 cents and 24 cents. How many of 30 cent pencils did he buy?

1) Total cost is \$1.02
2) He buys 4 pencils in total

x = 0.30
y = 0.24

1) 0.30x + 0.24y = 1.02
x = 1, y = 3
These are the only values x and y can take.
Sufficient.

2) x+y = 4
x = 2, y = 2
x = 1, y = 3
Insufficient.

A is the answer.
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Intern  B
Joined: 06 Feb 2016
Posts: 47
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41 GPA: 3.5
Re: Mary buys several pencils that cost 30 cents and 24 cents. How many of  [#permalink]

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St 1: 30*x+24y=102 Only one value of x and one value of y fits the equation:
30*x+24*3=102 Sufficient

St 2: Not sufficient
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Mary buys several pencils that cost 30 cents and 24 cents. How many of  [#permalink]

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==> In the original condition, it is a 2 by 2 question that appears most frequently on current gmat math.

Attachment: 7.27.png [ 19.21 KiB | Viewed 620 times ]

According to the table above, there are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get 30x+24y=102, 5x+4y=17 and x+y=4, so you get x=1 and y=3. The answer is C. However, this question is an integer question, one of the key questions, so you use CMT 4 (A: if you get C too easily, consider A and B). For con 1), from 5x+4y=17, 5 and 4 are mutually exclusive and x and y are positive integers, you only get x=1, y=3, hence it is unique and sufficient.

Therefore, the answer is A, not C.
_________________ Re: Mary buys several pencils that cost 30 cents and 24 cents. How many of   [#permalink] 27 Jul 2017, 01:08
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