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An office supply store carries an inventory of 1,345 differe

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sandy
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An office supply store carries an inventory of 1,345 differe [#permalink] New post   05 Aug 2018, 14:54
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An office supply store carries an inventory of 1,345 different products, all of which it categorizes as “business use,” “personal use,” or both. There are 740 products categorized as
“business use” only and 520 products categorized as both “business use” and “personal use.”

Quantity A
Quantity B
The number of products characterized as “personal use”
600


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: An office supply store carries an inventory of 1,345 differe [#permalink] New post   06 Aug 2018, 06:33
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Explanation

Use the overlapping sets formula for two groups: Total = Group 1 + Group 2 – Both + Neither. But first, add 740 (“business use” only) + 520 (“business use” and “personal use”) to get
1,260, the total number of products categorized as “business use.”

Also note that the problem indicates that all of the products fall into one or both of the two categories, so “neither” in this formula is equal to zero:

Total = Business + Personal – Both + Neither

1,345 = 1,260 + P – 520 + 0

1,345 = 740 + P

605 = P

Quantity A is greater. Note that the question asked for the number of products characterized as “personal use” (which includes products in the “both” group). If the problem had asked for the number of products characterized as “personal use” only, you would have had to subtract the “both” group to get 605 – 520 = 85. In this problem, however, Quantity A equals 605.
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Re: An office supply store carries an inventory of 1,345 differe [#permalink] New post   06 Aug 2018, 04:09
The solution can be solved this way,

We know that from the question , the total products under business use will be 1260 ( 520+740).
The remaining 85 products will be under the products of “not business use” .
If there are no products under “not business use” & personal use ( only personal use), The minimum value for total products under personal use will be 520 .
Similarly the maximum value of the products under personal use will happen , when all the 85 products do comes under “personal use” & “ not business use” ( only personal use), i.e. 520 +85 =605.
Hence the products under personal use will be between 540 & 605
The answer is “D”
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Re: An office supply store carries an inventory of 1,345 differe [#permalink] New post   23 Aug 2018, 07:44
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Explanation

Use the overlapping sets formula for two groups: Total = Group 1 + Group 2 – Both + Neither.

But first, add 740 (“business use” only) + 520 (“business use” and “personal use”) to get 1,260, the total number of products categorized as “business use.”

Also note that the problem indicates that all of the products fall into one or both of the two categories, so “neither” in this formula is equal to zero:

Total = Business + Personal – Both + Neither

1,345 = 1,260 + P – 520 + 0

1,345 = 740 + P

605 = P

Quantity A is greater. Note that the question asked for the number of products characterized as “personal use” (which includes products in the “both” group). If the problem had asked for the number of products characterized as “personal use” only, you would have had to subtract the “both” group to get 605 – 520 = 85. In this problem, however, Quantity A equals 605.
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Re: An office supply store carries an inventory of 1,345 differe [#permalink] New post   Updated on: 11 Jan 2019, 14:25
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Ok! lets try this way.
first off, since the option for neither business nor personal use doesn't exist, we cant make a table
Secondly, its stated that 740 items are used for BUSINESS ONLY, which means these items are not included in both business and personal
520 items are considered both business and personal, and there is no limitation on Personal items being both business and personal.
B for business=740
X+520 = personal since we can include Personal and Both in this bin

B+X+520=1345

740+X+520=1345
X=85
then Personal = 85+520= 605

605 is greater than 600

Originally posted by HappyMathtutor on 07 Jan 2019, 00:25.
Last edited by HappyMathtutor on 11 Jan 2019, 14:25, edited 1 time in total.
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Re: An office supply store carries an inventory of 1,345 differe [#permalink] New post   11 Jan 2019, 14:11
Answer: B
740 just business
520 both
p just personal
Total = just business + both + just personal
1345 =740 + p + 520
p = 1345 - 740 - 520 = 85
A: The number of products characterized as “personal use” = 85
B: 600
B is bigger than A.
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Re: An office supply store carries an inventory of 1,345 differe [#permalink] New post   29 Nov 2019, 06:55
Fatemeh wrote:
Answer: B
740 just business
520 both
p just personal
Total = just business + both + just personal
1345 =740 + p + 520
p = 1345 - 740 - 520 = 85
A: The number of products characterized as “personal use” = 85
B: 600
B is bigger than A.


:shock: :shock:

:arrow: OA is A. Please correct urself.
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Re: An office supply store carries an inventory of 1,345 differe [#permalink] New post   29 Nov 2019, 06:57
vishnupriyathiru wrote:
The solution can be solved this way,

We know that from the question , the total products under business use will be 1260 ( 520+740).
The remaining 85 products will be under the products of “not business use” .
If there are no products under “not business use” & personal use ( only personal use), The minimum value for total products under personal use will be 520 .
Similarly the maximum value of the products under personal use will happen , when all the 85 products do comes under “personal use” & “ not business use” ( only personal use), i.e. 520 +85 =605.
Hence the products under personal use will be between 540 & 605
The answer is “D”


OA is A.
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Re: An office supply store carries an inventory of 1,345 differe [#permalink] New post   08 Oct 2022, 04:08
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Re: An office supply store carries an inventory of 1,345 differe [#permalink]
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