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A furniture company has warehouses in two cities: Madison an
[#permalink]
31 Jul 2020, 10:15

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Question Stats:

A furniture company has warehouses in two cities: Madison and York. The Madison warehouse stocks desks, tables, and chairs in a ratio of 5: 9: 15. If all the desks and tables are transferred from the Madison warehouse to the York warehouse, increasing that warehouse’s inventory of items by 20 percent, which of the following could be the number of items in the York warehouse after the transfer?

Indicate all such numbers.

A. 168

B. 280

C. 290

D. 336

E. 504

F. 600

Indicate all such numbers.

A. 168

B. 280

C. 290

D. 336

E. 504

F. 600

Re: A furniture company has warehouses in two cities: Madison an
[#permalink]
07 Aug 2020, 13:30

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Carcass wrote:

A furniture company has warehouses in two cities: Madison and York. The Madison warehouse stocks desks, tables, and chairs in a ratio of 5: 9: 15. If all the desks and tables are transferred from the Madison warehouse to the York warehouse, increasing that warehouse’s inventory of items by 20 percent, which of the following could be the number of items in the York warehouse after the transfer?

Indicate all such numbers.

A. 168

B. 280

C. 290

D. 336

E. 504

F. 600

Indicate all such numbers.

A. 168

B. 280

C. 290

D. 336

E. 504

F. 600

Essentially, we only care about the ratio of desks to tables from the Madison warehouse. The ratio of the chairs to the tables or the desks is irrelevant.

Therefore, the ratio we want to look at is Desks:Tables = 5:9.

So, at the Madison wearhouse, we can have:

5 desks and 9 tables

10 desks and 18 tables

15 desks and 27 tables

and so on.

Notice the total number of furniture are multiples of 14:

5 desks and 9 tables = 14 total

10 desks and 18 tables = 28 total

15 desks and 27 tables = 42 total

and so on.

So if we send any multiple of 14 total pieces of furniture to the York Warehouse, this should increase their inventory by 20%.

This can be written as:

[Inventory Before Transfer](1.2) = [Inventory After Transfer]

Example:

10(1.2) = 12 (20% increase from 10 to 12)

100(1.2) = 120 (20% increase from 100 to 120)

*note we are not using the multiple of 14 restriction here*

And it'll be helpful to have this equation, just to conceptually understand what's going on:

[Inventory After Transfer] - [Inventory Before Transfer] = [Some multiple of 14 (pieces of furniture sent from Madison Warehouse)]

Example:

14 - 0 = 14 (14 is a multiple of 14)

140 - 14 = 126 (126 is a multiple of 14)

*note we are not using the restriction of 20% increase here*

I used backsolving and both equations above to get the answers:

(I'll denote [Inventory Before Transfer] as I_B, and plug in the answer choices to [Inventory After transfer])

A. 168 ...->... (I_B)(1.2) = 168 ...->... I_B = 140 ...->... 168 - 140 = 28 ...->... 28 is a multiple of 14, so A works (10 desks and 18 tables)

B. 280 ...->... (I_B)(1.2) = 280 ...->... I_B = 233.3333 ...->... The Inventory from before cannot be a decimal, so B does not work.

C. 290 ...->... (I_B)(1.2) = 290 ...->... I_B = 241.6667 ...->... The Inventory from before cannot be a decimal, so C does not work.

D. 336 ...->... (I_B)(1.2) = 336 ...->... I_B = 280 ...->... 336 - 280 = 56 ...->... 56 is a multiple of 14, so D works (20 desks and 36 tables)

E. 504 ...->... (I_B)(1.2) = 504 ...->... I_B = 420 ...->... 504 - 420 = 84 ...->... 84 is a multiple of 14, so E works (30 desks and 54 tables)

F. 600 ...->... (I_B)(1.2) = 600 ...->... I_B = 500 ...->... 600 - 500 = 100 ...->... 100 is not a multiple of 14, so F does not work

So the answers are A,D, and E

Re: A furniture company has warehouses in two cities: Madison an
[#permalink]
31 Jul 2020, 19:31

1

Bookmarks

5/9/15 is incorrect, it should be 5/8/15 or 4/9/15 or 5/9/14 only then asnwers will be correct.

Re: A furniture company has warehouses in two cities: Madison an
[#permalink]
01 Aug 2020, 00:39

1

esaktasynov wrote:

5/9/15 is incorrect, it should be 5/8/15 or 4/9/15 or 5/9/14 only then asnwers will be correct.

Only desks and tables were transferred (5+9), so the given answers are correct.

Option B should be added.

Re: A furniture company has warehouses in two cities: Madison an
[#permalink]
01 Aug 2020, 12:09

1

Say Total inventory at York was T before transfer.

So, after tranfer, it becomes 1.2T.

So, basically we need to find 1.2T where T is the Total inventory at York before transfer.

Therefore, T has to be an integer.

If we try each option and compare it with 1.2T only A, D, E, F give integer value for T.

Now, T+14x = 1.2T (5x+9x increase in total of York)

Solving this equation, we get T=70x.

So, T has to be a multiple of 7.

Among A, D, E, F => F is NOT a multiple of 7.

Hence, correct answers are A, D, E.

So, after tranfer, it becomes 1.2T.

So, basically we need to find 1.2T where T is the Total inventory at York before transfer.

Therefore, T has to be an integer.

If we try each option and compare it with 1.2T only A, D, E, F give integer value for T.

Now, T+14x = 1.2T (5x+9x increase in total of York)

Solving this equation, we get T=70x.

So, T has to be a multiple of 7.

Among A, D, E, F => F is NOT a multiple of 7.

Hence, correct answers are A, D, E.

Re: A furniture company has warehouses in two cities: Madison an
[#permalink]
05 Sep 2021, 07:26

sj24 wrote:

Say Total inventory at York was T before transfer.

So, after tranfer, it becomes 1.2T.

So, basically we need to find 1.2T where T is the Total inventory at York before transfer.

Therefore, T has to be an integer.

If we try each option and compare it with 1.2T only A, D, E, F give integer value for T.

Now, T+14x = 1.2T (5x+9x increase in total of York)

Solving this equation, we get T=70x.

So, T has to be a multiple of 7.

Among A, D, E, F => F is NOT a multiple of 7.

Hence, correct answers are A, D, E.

So, after tranfer, it becomes 1.2T.

So, basically we need to find 1.2T where T is the Total inventory at York before transfer.

Therefore, T has to be an integer.

If we try each option and compare it with 1.2T only A, D, E, F give integer value for T.

Now, T+14x = 1.2T (5x+9x increase in total of York)

Solving this equation, we get T=70x.

So, T has to be a multiple of 7.

Among A, D, E, F => F is NOT a multiple of 7.

Hence, correct answers are A, D, E.

I applied the same logic but I couldn't eliminate option F. Can you please explain why it has to be a multiple of 7. I am still confused.

Re: A furniture company has warehouses in two cities: Madison an
[#permalink]
26 Sep 2021, 23:41

2

koala wrote:

sj24 wrote:

Say Total inventory at York was T before transfer.

So, after tranfer, it becomes 1.2T.

So, basically we need to find 1.2T where T is the Total inventory at York before transfer.

Therefore, T has to be an integer.

If we try each option and compare it with 1.2T only A, D, E, F give integer value for T.

Now, T+14x = 1.2T (5x+9x increase in total of York)

Solving this equation, we get T=70x.

So, T has to be a multiple of 7.

Among A, D, E, F => F is NOT a multiple of 7.

Hence, correct answers are A, D, E.

So, after tranfer, it becomes 1.2T.

So, basically we need to find 1.2T where T is the Total inventory at York before transfer.

Therefore, T has to be an integer.

If we try each option and compare it with 1.2T only A, D, E, F give integer value for T.

Now, T+14x = 1.2T (5x+9x increase in total of York)

Solving this equation, we get T=70x.

So, T has to be a multiple of 7.

Among A, D, E, F => F is NOT a multiple of 7.

Hence, correct answers are A, D, E.

I applied the same logic but I couldn't eliminate option F. Can you please explain why it has to be a multiple of 7. I am still confused.

I guess the bit till T + 14x = 1.2T is correct. This will reduce the answer choices to A,D,E,F as mentioned by koala.

Further you need to see that the answer choice conform to the expression on the L.H.S of the equation i.e., T + 14x.

Check Option A: 168

If 1.2 T = 168 ,

then T = 168/1.2 = 140

and 14x = 28 (168 - 140 = 28) (x should be an integer)

x = 28/14 = 2 (option A is correct)

Check Option D: 336

If 1.2 T = 336,

then T = 336/1.2 = 280

and 14x = 56 (336 - 280 = 56) (x should be an integer)

x = 56/14 = 4 (option D is also correct)

Similarly check option E and F. E works and F doesn't.

Re: A furniture company has warehouses in two cities: Madison an
[#permalink]
08 Aug 2022, 14:24

2

Hey, I think there is a more mathematical way to solve it, please correct me if I am wrong.

New York Amount: Y

Madison Amount: 5M+9M+15M=29M

Function (can look like this or different, but with similar logic):

Current New York Amount + New York Tables and Chairs = 1.2 (Current New York Amount)

Y + 14M = 1.2Y

Solve it:

0.2Y = 14M

Y = 70M

Here is the trap!

In the question, they are about the Madison Amount after getting the tables and chairs.

Y + 14M

It is same as 70M + 14M = 84M

Now you can just check which answers are divisible by 84.

168 / 84 = 2

336 / 84 = 4

504 / 84 = 6

New York Amount: Y

Madison Amount: 5M+9M+15M=29M

Function (can look like this or different, but with similar logic):

Current New York Amount + New York Tables and Chairs = 1.2 (Current New York Amount)

Y + 14M = 1.2Y

Solve it:

0.2Y = 14M

Y = 70M

Here is the trap!

In the question, they are about the Madison Amount after getting the tables and chairs.

Y + 14M

It is same as 70M + 14M = 84M

Now you can just check which answers are divisible by 84.

168 / 84 = 2

336 / 84 = 4

504 / 84 = 6

gmatclubot

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