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# A new sales clerk in a department store has been assigned to

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A new sales clerk in a department store has been assigned to [#permalink]

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18 Apr 2012, 23:52
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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?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%
[Reveal] Spoiler: OA

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Last edited by Bunuel on 19 Apr 2012, 01:44, edited 1 time in total.
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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19 Apr 2012, 01:42
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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?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%

# of items 100 (assume);
# of items that should be marked for sale is x;
# of items that should be at the regular price is 100-x;
# of items that are actually marked for sale 0.3*100=30.

Let's see how many items are marked for sale:
20% of 100-x (20% of the items that are supposed to be marked with their regular prices (100-x) are now marked for sale);
100-55=45% of x (since 55% of the items that are supposed to be marked for sale (x) are marked with regular prices, then the remaining 45% of x are marked for sale);

So, 0.2(100-x)+0.45x=30 --> x=40 (# of items that should be marked for sale).

So, # of the items that are supposed to be marked with their regular prices is 0.2*(100-40)=12, which is 12/30*100=40% of # of items that are actually marked for sale.

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Re: A new sales clerk in a department store has been assigned to [#permalink]

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19 Apr 2012, 01:55
Bunuel 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?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%

# of items 100 (assume);
# of items that should be marked for sale is x;
# of items that should be at the regular price is 100-x;
# of items that are actually marked for sale 0.3*100=30.

Let's see how many items are marked for sale:
20% of 100-x (20% of the items that are supposed to be marked with their regular prices (100-x) are now marked for sale);
100-55=45% of x (since 55% of the items that are supposed to be marked for sale (x) are marked with regular prices, then the remaining 45% of x are marked for sale);

So, 0.2(100-x)+0.45x=30 --> x=40 (# of items that should be marked for sale).

So, # of the items that are supposed to be marked with their regular prices is 0.2*(100-40)=12, which is 12/30*100=40% of # of items that are actually marked for sale.

Thanks bunnel
I had a hard time understanding this question.
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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19 Apr 2012, 07:30
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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?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%

Say there are 100 items in the store. Some of them are sale items (those that should be marked for sale) and the rest are regular items (should have regular prices)

20% of regular items are marked for sale. 45% of sale items are marked for sale (since 55% of sale items have regular prices). Total 30% of the items are marked for sale. So 30 items are marked for sale.
Does it remind you of something? Weighted Average!

regular items/sale items = w1/w2 = (45 - 30)/(30 - 20) = 3/2

Total 60% (=3/5) of the items are regular items. 20% of them are marked for sale so number of regular items marked for sale = 20% of 60 = 12
Out of the 30 items marked for sale, 12 are actually regular items which is 12/30 *100 = 40%
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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19 Apr 2012, 07:55
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Understand these questions carefully. You are guaranteed to get something similar in the exam.
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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19 Apr 2012, 22:30
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Thanks Bunnel. That was very helpful.

I arrived at C as well, however I used plugging in. (I happened to plug in 100 as total and 40 as number of items that should be on sale, hence arrived at C as well!)
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07 May 2012, 01:59
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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?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%

Hi Bunuel: I am sure you can provide a more better way to tackle this one
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Re: Kaplan free test PS - percentages [#permalink]

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27 May 2012, 04:03
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vibhav 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?

1.30%
2.35%
3.40%
4.45%
5.50%

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Re: A new sales clerk in a department store has been assigned to [#permalink]

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27 May 2012, 04:31
thanks guys! deciphering the language itself under time pressure seemed too much for me!
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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28 May 2012, 21:36
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Book marking for future reference : Vote for C

Total items : 100
Marked for Sale: 30%(100) = 30

Total Retail P items = x
Total Sales P items = (100-x)

20% of the items that are supposed to be marked with their regular prices are now marked for sale
20%(x) - marked for sale by mistake

55% of the items that are supposed to be marked for sale are marked with regular prices.
therefore, 45% of items marked correctly with sales price

So total we have

20%(x) + 45% (100-x) = 30

(20x + 4500 - 45x) / 100 = 30

4500 - 3000 = 25x

x = 60 (total items for retail price)

therefore total items for sales are = 40

20%(x) = 20%(60) = 12 items tagged wrongly for sale

therefore,

12 = z% (30)
z = 40%
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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27 Jul 2012, 01:49
VeritasPrepKarishma 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?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%

Say there are 100 items in the store. Some of them are sale items (those that should be marked for sale) and the rest are regular items (should have regular prices)

20% of regular items are marked for sale. 45% of sale items are marked for sale (since 55% of sale items have regular prices). Total 30% of the items are marked for sale. So 30 items are marked for sale.
Does it remind you of something? Weighted Average!

regular items/sale items = w1/w2 = (45 - 30)/(30 - 20) = 3/2

Total 60% (=3/5) of the items are regular items. 20% of them are marked for sale so number of regular items marked for sale = 20% of 60 = 12
Out of the 30 items marked for sale, 12 are actually regular items which is 12/30 *100 = 40%

Hi,
Can you explain more about the weighted average ?Thanks
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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27 Jul 2012, 10:53
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Here is a pure algebraic approach:

If in the store there are $$R$$ items that should sell at regular price, and $$S$$ items that should sell at reduced price,
then the total number of items is $$R + S$$.
$$30%$$ of them, or $$0.3(R + S)$$ items are now marked for sale and this is comprised of $$0.2R$$ and $$0.45S$$,
as wrongly $$20%$$ of the regular items, and only $$45%$$ of the sale items were marked for sale ($$55%$$ of the sale items were marked regular).
So, $$0.3(R + S) = 0.2R + 0.45S$$, from which we can deduce that $$0.1R = 0.15S$$, or $$2R = 3S.$$

We have to evaluate the ratio $$\frac{0.2R}{0.3(R+S)}$$ - out of those marked for sale, what fraction/percentage should be marked regular.

$$\frac{0.2R}{0.3(R+S)}=\frac{2R}{3R+3S}=\frac{2R}{3R+2R}=\frac{2R}{5R}=\frac{2}{5}=40%$$.

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Re: A new sales clerk in a department store has been assigned to [#permalink]

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27 Jul 2012, 21:51
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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25 Aug 2012, 08:21
+1 C

Use the chart to solve sets. And be careful in distinguis between a percentage of the total and a percentage of a particular group.
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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24 Sep 2012, 23:46
Bunuel 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?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%

# of items 100 (assume);
# of items that should be marked for sale is x;
# of items that should be at the regular price is 100-x;
# of items that are actually marked for sale 0.3*100=30.

Let's see how many items are marked for sale:
20% of 100-x (20% of the items that are supposed to be marked with their regular prices (100-x) are now marked for sale);
100-55=45% of x (since 55% of the items that are supposed to be marked for sale (x) are marked with regular prices, then the remaining 45% of x are marked for sale);

So, 0.2(100-x)+0.45x=30 --> x=40 (# of items that should be marked for sale).

So, # of the items that are supposed to be marked with their regular prices is 0.2*(100-40)=12, which is 12/30*100=40% of # of items that are actually marked for sale.

Did not understand - 100-55=45% of x (since 55% of the items that are supposed to be marked for sale (x) are marked with regular prices, then the remaining 45% of x are marked for sale)
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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03 Nov 2012, 05:55
Bunuel 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?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%

# of items 100 (assume);
# of items that should be marked for sale is x;
# of items that should be at the regular price is 100-x;
# of items that are actually marked for sale 0.3*100=30.

Let's see how many items are marked for sale:
20% of 100-x (20% of the items that are supposed to be marked with their regular prices (100-x) are now marked for sale);
100-55=45% of x (since 55% of the items that are supposed to be marked for sale (x) are marked with regular prices, then the remaining 45% of x are marked for sale);

So, 0.2(100-x)+0.45x=30 --> x=40 (# of items that should be marked for sale).

So, # of the items that are supposed to be marked with their regular prices is 0.2*(100-40)=12, which is 12/30*100=40% of # of items that are actually marked for sale.

Bunuel - Can we do this problem via 2 set matrix / charts. Could you please show us how?. It will be really helpful. My sincere thanks.

Cheers
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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Re: A new sales clerk in a department store has been assigned to [#permalink]

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12 May 2014, 21:59
Can this problem be solved using the double-set matrix technique?
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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21 Jul 2014, 18:05
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Dienekes wrote:
Can this problem be solved using the double-set matrix technique?

I think this could be better understood if using this 2x2 Matrix attached.
Attachments

Screen Shot 2014-07-21 at 8.01.12 PM.png [ 13.68 KiB | Viewed 4474 times ]

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Re: A new sales clerk in a department store has been assigned to [#permalink]

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23 Jul 2014, 22:54
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Regular ................... Sale .................... Total

100-x ............................. x .................... 100 (Assume)

20% of regular is marked sale $$= \frac{20(100-x)}{100}$$

55% of sale is marked regular, which also means 45% of sale is "actually" for sale $$= \frac{45x}{100}$$

Total sale = 30

$$\frac{20(100-x)}{100} + \frac{45x}{100} = 30$$

x = 40

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Re: A new sales clerk in a department store has been assigned to   [#permalink] 23 Jul 2014, 22:54

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