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

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

I'd like to add that the OG solution to this question is quite eloquent in that it doesn't assume that the printers are all equal in price until it tests evidence (2).

OG lays out the solution like this:

(1) \(P1 + P2 + P3 + S = $1,300\)
(2) \(P1 = P2 = P3 = 4S\)

Combined:
\(4S + 4S + 4S + S = $1,300\)

This may seem extremely obvious to some people and may not be helpful for everyone, but especially for GMATers that are prone to rushing and making silly mistakes (like me), I think this approach emphasises that we MUST NOT take things for granted and that we MUST pay special attention to nuances of these easy questions, which are worth A LOT of points.

Given, Company bought 3 printer & 1 scanner.
Price of 1 scanner =?

a) total price of 3 printer+1 scanner =$1300 (multiple values possible for scanner)

Not sufficient (Cancel DA)

b)price of printer = 4*price of scanner (Multiple values possible)
Not sufficient (Cancel B)

together a*b, two equation two variable. Sufficient to calculate price of 1 scanner.
Answer C

Posted from my mobile device

Answer: Option C

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Solution:


Question Stem Analysis:

We need to determine the price of the scanner, given that the company bought 3 printers and 1 scanner. We can let the price of the scanner be s and the price of a printer be p. We need to determine the value of s.

Statement One Alone:

With the information in statement one, we can create the equation:

3p + s = 1,300

With one equation and two variables, we can’t determine the value of s (or p). Statement one alone is not sufficient.

Statement Two Alone:

With the information in statement two, we can create the equation:

p = 4s

Again, with one equation and two variables, we can’t determine the value of s (or p). Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we see that:

3p + s = 1,300

and

p = 4s

Substituting 4s for p in the first equation, we have:

3(4s) + s = 1,300

13s = 1,300

s = 100

We see that the price of the scanner is $100.

Answer: C

Video solution from Quant Reasoning:
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