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A bakery bakes two kinds of bread, X and Y...

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by swerve » Sat Jan 06, 2018 1:37 pm
A bakery bakes two kinds of bread X and Y. With the same amount of money, you can afford either 2/3 pounds of bread X or 1 1/4 of bread Y. How many pounds can I afford of bread Y, with the same amount can I buy 1 1/2 of X?

$$A.\ \ \frac{5}{4}$$
$$B.\ 1\ \frac{1}{4}$$
$$C.\ 2\ \frac{13}{16}$$
$$D.\ 3\ \frac{3}{7}$$
$$E.\ 5\ \frac{1}{4}$$

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I'm not sure about my solution. I need your help. Thanks.
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by GMATGuruNY » Sat Jan 06, 2018 3:37 pm
swerve wrote:A bakery bakes two kinds of bread X and Y. With the same amount of money, you can afford either 2/3 pounds of bread X or 1 1/4 of bread Y. How many pounds can I afford of bread Y, with the same amount can I buy 1 1/2 of X?

$$A.\ \ \frac{5}{4}$$
$$B.\ 1\ \frac{1}{4}$$
$$C.\ 2\ \frac{13}{16}$$
$$D.\ 3\ \frac{3}{7}$$
$$E.\ 5\ \frac{1}{4}$$
You can afford either 2/3 pounds of bread X or 1 1/4 of bread Y.
(2/3)X = (5/4)Y
X = (3/2)(5/4)Y
X = (15/8)Y.

How many pounds can I afford of bread Y, with the same amount can I buy 1 1/2 of X?
(3/2)X = (3/2)(15/8)Y = (45/16)Y = 2 and 13/16 Y.

The correct answer is C.
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by Scott@TargetTestPrep » Mon Aug 12, 2019 5:42 pm
swerve wrote:A bakery bakes two kinds of bread X and Y. With the same amount of money, you can afford either 2/3 pounds of bread X or 1 1/4 of bread Y. How many pounds can I afford of bread Y, with the same amount can I buy 1 1/2 of X?

$$A.\ \ \frac{5}{4}$$
$$B.\ 1\ \frac{1}{4}$$
$$C.\ 2\ \frac{13}{16}$$
$$D.\ 3\ \frac{3}{7}$$
$$E.\ 5\ \frac{1}{4}$$

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I'm not sure about my solution. I need your help. Thanks.
Let 2/3 lbs of bread X cost n dollars. Then, one pound of bread X costs n/(2/3) = 3n/2 dollars.

Since 2/3 lbs of bread X costs n dollars, 1 1/4 = 5/4 lbs of bread Y also costs n dollars and hence, one pound of bread Y costs n/(5/4) = 4n/5 dollars.

1 1/2 = 3/2 lbs of bread X costs 3/2 * 3n/2 = 9n/4 dollars. With 9n/4 dollars, one can buy (9n/4)/(4n/5) = (9n/4)*(5/4n) = 45/16 = 2 13/16 lbs of bread Y.

Answer: C

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