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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 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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shadabkhaniet 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.

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

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New post 19 Apr 2012, 01:55
Bunuel wrote:
shadabkhaniet 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.

Answer: C.


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

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

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New post 27 May 2012, 04:31
thanks guys! deciphering the language itself under time pressure seemed too much for me!

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New post 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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New post 27 Jul 2012, 01:49
VeritasPrepKarishma wrote:
shadabkhaniet 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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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.

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

Hence, answer C.
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Re: A new sales clerk in a department store has been assigned to [#permalink]

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New post 24 Sep 2012, 23:46
Bunuel wrote:
shadabkhaniet 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.

Answer: C.


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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Can this problem be solved using the double-set matrix technique?

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

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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

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

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New post 09 Jul 2016, 01:08
Bunuel wrote:
shadabkhaniet 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.

Answer: C.


I got the answer..but first got it wrong..the numbers did not seem to add up..because I assumed one thing..its written "she has marked 30% of the items for sale"..so I assumed she was told to do this only(mark 30% of the items for sale). But that's not true..the language is not hard to decipher..but..and here's my question..
Shouldn't it be clearly stated that the percentage of goods that she has marked(30%) is not the same as the percentage of goods that she was actually asked to mark?..please clarify..because I think that with this addition..there's no scope left for misunderstanding..

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

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shadabkhaniet 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%



Answer: Option C

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

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New post 12 Nov 2016, 06:39
shadabkhaniet 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%


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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