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A company bought some desks at a price of $150 each and some

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by swerve » Sat Jan 19, 2019 8:43 am

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Difficulty—

A company bought some desks at a price of $150 each and some chairs at a price of $50 each. Did the company buy more than 40 chairs?

1) The total price of the desk and chairs is 5,000.
2) The company bought fewer than 20 desks.

The OA is C

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Jan 20, 2019 12:20 am
swerve wrote:A company bought some desks at a price of $150 each and some chairs at a price of $50 each. Did the company buy more than 40 chairs?

1) The total price of the desk and chairs is 5,000.
2) The company bought fewer than 20 desks.

The OA is C

Source: GMAT Prep
Say the number of desks = x and the number of chairs = y

Thus, 150x + 50y = Total sales

We have to determine whether y ≥ 40.

Let's take each statement one by one.

1) The total price of the desk and chairs is 5,000.

150x + 50y = 5,000

=> 3x + y = 100

Case 1: Say y = 40, then x = 10. The answer is Yes.

Case 2: Say y = 10, then x = 30. The answer is No.

No unique answer. Insufficient.

2) The company bought fewer than 20 desks.

y < 20. There is no information about x. Insufficient.

(1) and (2) together

Case 1: Say y =16, then from 3x + y = 100, we have x = (100 - 16)/3 = 28 < 40. The answer is No.

Case 1: Say y =1, then from 3x + y = 100, we have x = (100 - 1)/3 = 33 < 40. The answer is No.

Unique answer.

The correct answer: C

Hope this helps!

-Jay
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by GMATGuruNY » Sun Jan 20, 2019 3:56 am
swerve wrote:A company bought some desks at a price of $150 each and some chairs at a price of $50 each. Did the company buy more than 40 chairs?

1) The total price of the desk and chairs is 5,000.
2) The company bought fewer than 20 desks.
Test the THRESHOLD.
In the question stem, the threshold is 40 CHAIRS.
The total cost of 40 chairs = 40*50 = 2000.

Statement 1: The total price of the desks and chairs is 5,000.
It is possible that 40 chairs are purchased (at a total cost of $2000) or that MORE CHAIRS are purchased.
INSUFFICIENT.

Statement 2: The company purchased fewer than 20 desks.
No way to determine the number of chairs purchased.
INSUFFICIENT.

Statements 1 and 2 combined:
The THRESHOLD in statement 2 is 20 desks.
The total cost of 20 desks = 20*150 = 3000.
If 20 desks are purchased at a cost of $3000, the remaining $2000 will be spent on exactly 40 chairs.
Since FEWER than 20 desks are purchased, the amount spent on the chairs must be GREATER than $2000, implying that MORE than 40 CHAIRS are purchased.
SUFFICIENT.

The correct answer is C.
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