Mary buys several pencils that cost 30 cents and 24 cents. How many of

Question

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

akshayk · Answer

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.

Devbek · Answer

Answer A.

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

MathRevolution · Answer

==> 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 2876 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.
Answer: A

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