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A new sales clerk in a department store has been assigned

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saxenashobhit Senior | Next Rank: 100 Posts
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A new sales clerk in a department store has been assigned

Post Thu Jul 07, 2011 5:26 am
A new sales clerk in a department store has been assigned to mark sale items with red tags, and she has marked 30% of the store items for sale. However, 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. What percent of the items that are marked for sale are supposed to be marked with regular prices?

30%

35%

40%

45%

50%

Kaplan question 26 - http://www.scribd.com/doc/58999877/GMAT-Practice-Set-6-Quant

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Post Thu Dec 07, 2017 9:29 am
saxenashobhit wrote:
A new sales clerk in a department store has been assigned to mark sale items with red tags, and she has marked 30% of the store items for sale. However, 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. What percent of the items that are marked for sale are supposed to be marked with regular prices?

30%

35%

40%

45%

50%
Since this a percent problem, we can assign a “good” number as the total number of items in the store. So, let’s say the total number of items in the store is 100. Since the sales clerk has marked 30% of the store items for sale, she has marked 30 items as sale items, and therefore 70 items are regular-price items.

We assume the total number of items is 100, and let’s assume that x items were supposed to be marked as sales items. Thus, 100 - x items were supposed to be marked as regular-price items.

Looking back at the given information, we know that 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. Thus:

0.2(100 - x) = number of items that are marked as sale items but should be marked as regular-priced items, and thus:

0.8(100 - x) = number of items that are marked (correctly) as regular-price items.

0.55x = number of items that are marked as regular-price items but should be marked as sale items, and thus:

0.45x = number of items that are marked (correctly) as sale items.

Recall that 30 items are marked as sale items and 70 items as regular-price items. Therefore, we have:

0.45x + 0.2(100 - x) = 30

and

0.55x + 0.8(100 - x) = 70

Let’s solve the first equation:

0.45x + 0.2(100 - x) = 30

45x + 20(100 - x) = 3000

45x + 2000 - 20x = 3000

25x = 1000

x = 40

[Note: If we solve the second equation instead of the first, we will also get x = 40.]

The problem asks: “What percent of the items that are marked for sale are supposed to be marked with regular prices?”

Since we have that 0.2(100 - x) is the number of items marked as sale items when they should be marked as regular-price items, and we have that x = 40, there are:

0.2(100 - 40) = .2(60) = 12 such items.

We also have that a total of 30 items are marked for sale, so the percentage of the marked sale items that are supposed to be marked with regular prices is 12/30 = 4/10 = 0.4 = 40%.

Answer: C

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Post Thu Jul 07, 2011 1:12 pm
saxenashobhit wrote:
A new sales clerk in a department store has been assigned to mark sale items with red tags, and she has marked 30% of the store items for sale. However, 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. What percent of the items that are marked for sale are supposed to be marked with regular prices?

30%

35%

40%

45%

50%

Kaplan question 26 - http://www.scribd.com/doc/58999877/GMAT-Practice-Set-6-Quant
Another approach would be to treat this as a mixture problem and use alligation.

Let total = 100.

Let S = number meant to be on sale.
Let R = number meant to be at the regular price.

Percentage of S marked for sale = 45.
Percentage of R marked for sale = 20.
Percentage of total mixture marked for sale = 30.

According to alligation:

The proportion of each element in the mixture is equal to the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the final mixture.

Proportion of S = 30-20 = 10.
Proportion of R = 45-30 = 15.
Ratio of S:R = 10:15 = 2:3.

Since 2+3=5, R = 3/5 of the total number of items.
Thus, R = (3/5)*100 = 60.
Of these 60 items, .2*60 = 12 have been incorrectly marked for sale.
Thus, of the 30 items marked for sale, the percentage marked incorrectly = (12/30)*100 = 40%.

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Post Thu Jul 07, 2011 10:38 am
saxenashobhit wrote:
A new sales clerk in a department store has been assigned to mark sale items with red tags, and she has marked 30% of the store items for sale. However, 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. What percent of the items that are marked for sale are supposed to be marked with regular prices?

30%

35%

40%

45%

50%

Kaplan question 26 - http://www.scribd.com/doc/58999877/GMAT-Practice-Set-6-Quant
I solved this quickly by guessing and checking.

20% of the items that should be at the regular price are incorrectly marked.
55% of the items that should be on sale are incorrectly marked.
Since a higher percentage of the items that should be on sale are incorrectly marked, the percentage that should be on sale is likely greater than 30% (the percentage that are actually marked for sale).

Let total = 100.
Let items that should be on sale = 40.
55% of these are incorrectly marked, implying that 45% are correctly marked:
Number marked for sale = .45*40 = 18.

Items that should be at the regular price = 100-40 = 60.
Number that are incorrectly marked for sale = .2*60 = 12.

Total marked for sale = 18+12 = 30. Success!

Since 12 of the items that should be at the regular price have been incorrectly marked for sale, 12 of the 30 items marked for sale are incorrect:
12/30 * 100 = 40%.

The correct answer is C.

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If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

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StoneBlack Senior | Next Rank: 100 Posts Default Avatar
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Post Thu Jul 07, 2011 8:23 am
yes answer is 40%. Same approach as above but took a long time to figure out the meanings of the sentences!

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Post Thu Jul 07, 2011 6:59 am
Hi,
Let the total number of items be 100
Let x be the ones supposed to be marked for sale
the remaining (100-x) are supposed to be marked with regular prices.
Actually she marked 20% of (100-x) for sale i.e. (100-x)/5
She also marked 55% of supposed to be marked sale as regular prices. So, the remaining 45% of supposed to be marked sale are marked for sale. i.e. (9/20)x
given that total 30% are marked for sale
So, (100-x)/5 + (9/20)x = 30
So, x = 40
Number of items that are marked for sale which are supposed to be marked with regular prices = (100-x)/5 = 12
So, percentage is 12/30 = 40%

Hence, C

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