Every item in an apparel shop has a tag that is either blue, green or

Question

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%.

(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%.

Bunuel · Answer

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%.

(1) The discount on the items with a blue tag is 20% and that on the items with a green tag is 25%.

The least discount on a blue-tagged item = 20*0.2 = $4;
The least discount on a green-tagged item = 12*0.25 = $3;

Even if Mary bought an yellow-tagged item at the full price of $10, the discount = (4 + 3)/(20 + 12 + 10) = 7/42 = 1/6 > 10%. Sufficient.

(2) The discount on the items with a yellow tag is 40%.

If Mary bought a blue-tagged item and a green-tagged item with 100% discount, then the overall discount would be more than 10%.
If Mary bought a blue-tagged item and a green-tagged item with 0% discount and an yellow-tagged item with 40% discount, then the overall discount would be less than 10%.

Not sufficient.

Answer: A.

Hope it's clear.

sambeetmallick · Answer

k781119 · Answer

I also got A but for the denominator, why did you use (20+12+10) instead of (30+18+10)? I got that 7/58 was still greater than 10%

godblessme · Answer

20 and 12 are used because we are examining the case when least discount is provided because it is obvious that if 30 and 12 are used the discount will be higher

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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%.

(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%

When you modify the original condition and the question, the question becomes if the discounted price is bigger than the maximum $30*10%+$18*10%+$10*10%=$5.8. However, in 1), the discounted price is minimum $20*20%+$12*25%+$5*0%=$7, which is always yes and sufficient.
Therefore, the answer is A.

-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

bumpbot · Answer

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Every item in an apparel shop has a tag that is either blue, green or

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