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A company bought 3 printers and 1 scanner. What was the price of the

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A company bought 3 printers and 1 scanner. What was the price of the  [#permalink]

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A company bought 3 printers and 1 scanner. What was the price of the scanner ?


(1) The total price of the printers and the scanner was $1,300.

(2) The price of each printer was 4 times the price of the scanner.



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(DS12265)

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Re: A company bought 3 printers and 1 scanner. What was the price of the  [#permalink]

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New post 21 Jun 2018, 09:44
Bunuel wrote:
A company bought 3 printers and 1 scanner. What was the price of the scanner ?


(1) The total price of the printers and the scanner was $1,300.

(2) The price of each printer was 4 times the price of the scanner.



NEW question from GMAT® Official Guide 2019


(DS12265)


Let the price of each printer be x.
and price of each scanner be y.

FOR 3 printer & 1 scanner , Total Price = 3x + y

Statement 1 :- The total price of the printers and the scanner was $1,300.

So \(3x + y = 1300\)

We have only one equation. We can't get unique value of y.

Hence insufficient.

Statement 2 :- The price of each printer was 4 times the price of the scanner.

This is : \(x = 4y\)

This is also insufficient to find the price of the scanner.

Statement 1 and Statement 2 :-

Gives us two equation. \(3x + y = 1300\) and \(x = 4y\)

Solving this would give us the price of the scanner.

Ans - C
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Re: A company bought 3 printers and 1 scanner. What was the price of the  [#permalink]

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New post 21 Jun 2018, 10:27

Solution



Given:
    • A company bought 3 printers and 1 scanner

To find:
    • The price of the scanner

Analysing Statement 1
    • As per the information given in statement 1, the total price of the printers and the scanner was $1300
      o From this statement, we can’t find out the individual price of a scanner

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, the price of each printer was 4 times the price of scanner
    • If we assume the price of the scanner to be p, then price of each printer will be 4p
      o Hence, total cost of 3 printers and 1 scanner = 3 * 4p + p = 13p
    • But we don’t know the value of 13p

Hence, statement 2 is not sufficient to answer

Combining Both Statements
If we combine the data from both the statements, we can say:
    • 13p = 1300

From this we can find out the value of p

Hence, the correct answer is option C.

Answer: C
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A company bought 3 printers and 1 scanner. What was the price of the  [#permalink]

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New post 23 Jun 2018, 17:54
Top Contributor
Bunuel wrote:
A company bought 3 printers and 1 scanner. What was the price of the scanner ?

(1) The total price of the printers and the scanner was $1,300.
(2) The price of each printer was 4 times the price of the scanner.


Let P = price of ONE printer
Let S = price of ONE scanner

Target question: What is the value of S?

Statement 1: The total price of the (3) printers and the (1) scanner was $1,300.
So, we can write: 3P + S = 1300
Does this provide enough information to determine the value of S?
No.
There are several cases that satisfy statement 1. Here are two:
Case a: P = 400 and S = 100. Notice that these values meet the condition that 3P + S = 1300. In this case, the answer to the target question is S = 100
Case b: P = 300 and S = 400. Notice that these values meet the condition that 3P + S = 1300. In this case, the answer to the target question is S = 400
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The price of each printer was 4 times the price of the scanner.
So, we can write: P = 4S
There are several cases that satisfy statement 2. Here are two:
Case a: P = 400 and S = 100. Notice that these values meet the condition that P = 4S. In this case, the answer to the target question is S = 100
Case b: P = 800 and S = 200. Notice that these values meet the condition that P = 4S. In this case, the answer to the target question is S = 200
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 3P + S = 1300
Statement 2 tells us that P = 4S
Since we COULD solve this system of equations for P and S, we COULD answer the target question (although we would NEVER waste our valuable time actually solving the system on test day.)
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

ASIDE: If we solve the system, we get P = $400 and S = $100

Cheers,
Brent
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Re: A company bought 3 printers and 1 scanner. What was the price of the  [#permalink]

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New post 17 Jul 2018, 22:23
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