Two problems on percentages

[knight247]

1)Mr. Tolstoy bought 100 CDs at $x and sold them at $y. Did Mr.Tolstoy profit from the
deal?
(1)40% of x > 30% of y
(2)30% of x > 40% of y

OA is B

2)Every item in an apparel shop has a tag that is either blue, green or yellow in color. The items with a blue tag are priced between $20 and $30. The items with a green tag are priced between $12 and $18 and the items with a yellow tag are priced between $5 and $10. Mary buys three items, each with a different color tag. Is the total discount on three items greater than 10%?
(1)The discount on the items with a blue tag is 20% and that on the items with a green tag is 25%.
(2)The discount on the items with a yellow tag is 40%.

OA is A

Detailed explanations would be appreciated

[Deepthi Subbu]

1. The question asks for this - Is y>x?

This can also mean - Is x/y < 1 ?

a. 0.4 x > 0.3 y

so x/y > .75 . The value can either be less than 1 or greater than 1. Insufficient.

b. 0.3 x > 0.4 y . So , x/y > 1.33 . The answer to the question is 'NO', hence sufficient .

OA B

[knight247]

Thanks Deepti! There's also a second one...Whats ur opinion on that?

[goalevan]

Problem 1

Is y greater than x?

Statement 1) (4/10)x > (3/10)y, or 4x > 3y.

y < (4/3)x

y could be equal to x, less than x or greater than x. Insufficient.

Statement 2) (3/10)x > (4/10)y, or 3x > 4y.

y < (3/4)x

If y is less than 3/4 of x, y is less than x. Sufficient.

B

Problem 2

B: $20 - $30
G: $12 - $18
Y: $5 - $10

Discount percentage = Discount / Total price
Discount = B*Br + G*Gr + Y*Yr
Total price = B + G + Y

Is the discount percentage of the three items, one of each tag, greater than 10%?

Statement 1) Br is given as 20% and Gr as 25%. Since these are both above 10%, let's try to minimize the total discount percentage and see whether it's possible to bring it below 10%.

To minimize the discount, we will minimize the price of the two items with B and G tags and assume a 0% discount for Y.

Minimum discount for B: $20 * 20% = $4
Minimum discount for G: $12 * 25% = $3
Minimum discount for Y: $0 (not given)

To minimize the discount percentage, we maximize the price of the Y tag to $10 to bring the discount percentage to:

($4 + $3) / ($20 + $12 + $10) = $7/$42 = 1/6 > 10%. It is not possible to bring the discount below 10%. Sufficient.

Statement 2) Yr is given as 40%. Since this is above 10%, let's try to again minimize the total discount percentage.

Minimum discount for B: $0 (not given)
Minimum discount for G: $0 (not given)
Minimum discount for Y: $5 * 40% = $2

We will maximize the price on the B and G tags to minimize the discount percentage again:

$2 / ($30 + $18 + $5) = $2/$52 = 1/26 < 10%. It is possible to bring the discount percentage below 10%, but depending on the rates for B and G, it's possible to keep above 10%. Insufficient.

A