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# If a school district paid a total of \$35 per desk for x desks and a to

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Math Expert
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If a school district paid a total of \$35 per desk for x desks and a to  [#permalink]

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26 Apr 2019, 01:02
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If a school district paid a total of \$35 per desk for x desks and a total of \$30 per table for y tables, what was the total amount that the district paid for these desks and tables?

(1) The total amount the district paid for the y tables was \$900.
(2) x = 90, and the total amount the district paid for the x desks was 3.5 times the total amount the district paid for the y tables.

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Re: If a school district paid a total of \$35 per desk for x desks and a to  [#permalink]

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26 Apr 2019, 09:09
35X+30Y = ?

From S1:

30Y = 900
Y = 30.
No info about X.
Insufficient.

From S2:

X = 90
35*90 = 3150
Also, 3150 = 3.5*30Y
Y = 30.
Sufficient.

B is the asnwer.
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Re: If a school district paid a total of \$35 per desk for x desks and a to  [#permalink]

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27 Apr 2019, 06:31
The Logical approach to this question would focus on looking for the exact values of both x and y, required in order to find the total amounts.
Statement (1) refers just to y, and is thus not sufficient.
Statement (2) tells us the value of x, which allows us to find the total amount of the 35 dollar desks. It also gives us the ratio to the total price of the 30 dollar tables. Since the total amount is what we were looking for in the first place, that's enough.
The correct answer is B.

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Re: If a school district paid a total of \$35 per desk for x desks and a to  [#permalink]

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29 Apr 2019, 10:10
Top Contributor
Bunuel wrote:
If a school district paid a total of \$35 per desk for x desks and a total of \$30 per table for y tables, what was the total amount that the district paid for these desks and tables?

(1) The total amount the district paid for the y tables was \$900.
(2) x = 90, and the total amount the district paid for the x desks was 3.5 times the total amount the district paid for the y tables.

Given: School district paid a total of \$35 per desk for x desks and a total of \$30 per table for y tables
So, the TOTAL amount paid = 35x + 30y.

Target question: What was the total amount that the district paid for these desks and tables??

Statement 1: The total amount the district paid for the y tables was \$900.
This statement provides no information about x, the number of desks purchased.
Statement 1 is NOT SUFFICIENT

Statement 2: x = 90, and the total amount the district paid for the x desks was 3.5 times the total amount the district paid for the y tables.
So, the TOTAL amount the district paid for DESKS = (35)(90) = \$3150
We're told that \$3150 is 3.5 times the total amount the district paid for the y tables
So, the TOTAL amount the district paid for TABLES = \$3150/3.5 = \$900

So, the TOTAL amount paid for desks AND tables = \$3150 + \$900 = \$4050
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Brent
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Re: If a school district paid a total of \$35 per desk for x desks and a to  [#permalink]

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29 Apr 2019, 15:17
Hi All,

We're told that a school district paid a total of \$35 per desk for X desks and a total of \$30 per table for Y tables. We're asked for the total amount that the district paid for these desks and tables. This DS question revolves around basic Arithmetic, but you don't actually have to do any math to answer it...

(1) The total amount the district paid for the y tables was \$900.

The information in Fact 1 will help us to determine the value of Y (it's 900/30 = 30), but not the value of X. Thus, the answer to the question will change depending on what X is.
Fact 1 is INSUFFICIENT

(2) X = 90, and the total amount the district paid for the X desks was 3.5 times the total amount the district paid for the Y tables.

The information in Fact 2 will help to determine the total spent on the desks (\$35 x 90, although you don't have to calculate that to know that it WILL be a specific number). We can then divide that number by 3.5 to find the amount spent on the tables (again, we don't have to calculate it; we know that we COULD - and that it will be a specific number). With the money spent on the desks + the money spent on the tables, we can definitively answer the question.
Fact 2 is SUFFICIENT

Final Answer:

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If a school district paid a total of \$35 per desk for x desks and a to  [#permalink]

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14 May 2019, 04:49

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given
• A school district paid a total of \$35 per desk for x desks, and a total of \$30 per table for y tables.

We need to determine
• The total amount paid by the district for the desks and tables.

The total amount spent on desks = 35x
The total amount spent on tables = 30y
• Hence, the total amount spent = 35x + 30y
• Therefore, we need to know the values of x and y.

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, the total amount the district paid for the y tables was \$900.
• 30y = 900
However, we still don’t know the value of x or 35x.
Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, x is 90, and the total amount the district paid for x desks was 3.5 times the amount the district paid for the y tables.
• The total amount paid for desks = 90 × 35
• Therefore, the total amount paid for tables = (90*35)/3.5

As we can determine the total amount spent on desks and tables individually, we can determine the total amount spent on both together.
Hence, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 2 individually, this step is not required.
Hence, the correct answer choice is option B.

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If a school district paid a total of \$35 per desk for x desks and a to   [#permalink] 14 May 2019, 04:49
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