The price of an item is discounted 10 percent . . .

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sun Dec 10, 2017 10:53 am

The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

The OA is E.

How can I calculate this without knowing the starting price of the item? Experts, may you give me any help? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sun Dec 10, 2017 10:53 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Sun Dec 10, 2017 11:22 am

M7MBA wrote:The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

The OA is E.

How can I calculate this without knowing the starting price of the item? Experts, may you give me any help? Thanks in advanced.

You could pick an easy number to be the starting price: 100
Day 1: discounted 10%. 10% of 100 is 10, so sale price = 100 - 10 = 90
Day 2 discounted 10%. 10% of 90 is 9, so new price . = 90 - 9 = 81.
Day 3: discounted 20%. 20% of 81 is 16.20. 81 - 16.20 = 64.80.

We're asked what % the price of day 3 (64.80 ) is of the sale price on day 1: (90.) 64.80/90 = 648/900 = 9 *72/9 * 100 = 72. The answer is E. [spoiler]

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Sun Dec 10, 2017 11:25 am

DavidG@VeritasPrep wrote:
M7MBA wrote:The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

The OA is E.

How can I calculate this without knowing the starting price of the item? Experts, may you give me any help? Thanks in advanced.
You could pick an easy number to be the starting price: 100
Day 1: discounted 10%. 10% of 100 is 10, so sale price = 100 - 10 = 90
Day 2 discounted 10%. 10% of 90 is 9, so new price . = 90 - 9 = 81.
Day 3: discounted 20%. 20% of 81 is 16.20. 81 - 16.20 = 64.80.

We're asked what % the price of day 3 (64.80 ) is of the sale price on day 1: (90.) 64.80/90 = 648/900 = 9 *72/9 * 100 = 72. The answer is E. [spoiler]

Note that the algebra is virtually identical.
Say the starting price is P.
Day 1: discounted 10%. Sale Price = .9P
Day 2 discounted 10%. New Price . = .9*.9P = .81P
Day 3: discounted 20%. New Price = .8 * .81P = .648P

Price Day 3/Day 1 = .648P/.9P = .72P

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GMATWisdom: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Nov 29, 2017 4:38 pm; Thanked: 14 times

by GMATWisdom » Sun Dec 10, 2017 11:35 am

M7MBA wrote:The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

The OA is E.

How can I calculate this without knowing the starting price of the item? Experts, may you give me any help? Thanks in advanced.

let us assume sale price on day 1 after 10% discount is 100
then sale price on day 2 would be = 100- 10= 90 (10% of 100 is 10)
and the sale price on day3 would be = 90 - 18 = 72 (20% of 90 is 18)
hence the sale price of day3 as compared to sale price of day1 is = 72%
therefore D is the correct option.

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