If the book value of a certain piece of equipment was $5,000 exactly

Asked: If the book value of a certain piece of equipment was $5,000 exactly 5 years ago, what is its present book value?

(1) From the time the piece of equipment was purchased, its book value decreased by 10 percent of its purchase price each year of its life.
Present book value = $5000 * (.9)^5
SUFFICIENT

(2) The present book value of another piece of equipment is $2,000.
This is irrelevant information.
NOT SUFFICIENT

IMO A

Don't you think, depreciation is calculated upon purchase price and nothing is mentioned regarding purchase price in statement 1. It can be the depreciated price too

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Hi yashikaaggarwal Bunuel

The portion highlighted in red color makes the question confusing.
If it is not intended, then it may please be omitted.

Asked: If the book value of a certain piece of equipment was $5,000 exactly 5 years ago, what is its present book value?

(1) From the time the piece of equipment was purchased, its book value decreased by 10 percent of its purchase price each year of its life.
Since purchase price is not mentioned.
NOT SUFFICIENT

(2) The present book value of another piece of equipment is $2,000.
This is irrelevant information.
NOT SUFFICIENT

(1) + (2)
(1) From the time the piece of equipment was purchased, its book value decreased by 10 percent of its purchase price each year of its life.
Since purchase price is not mentioned.
(2) The present book value of another piece of equipment is $2,000.
This is irrelevant information.
NOT SUFFICIENT

IMO E

Substitute statement A with Book value. Would the answer be A then?

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(1) We're told the book value decreased by 10% of its purchase price. We know the price of the equipment was $5,000 exactly 5 years ago. However, we don't know the purchase price. Was it $10,000? $50,000? We don't know. Therefore we can't determine the present book value. INSUFFICIENT.

(2) Irrelevant. INSUFFICIENT.

(1&2) Combined, we can't conclude the present book value. INSUFFICIENT.

Answer is E.

­Statement 1 gives us the depreciation rate but not the purchase price. => insufficient

Statement 2 is irrelevant to the problem. => insufficient

Combined, both statements together are still insufficient to determine the present book value.

Answer is E­

OFFICIAL ANSWER
Algebra Applied problems
Determine the present book value of a piece of equipment, of which the book value exactly 5 years ago was $5,000.

(1) Given that the book value decreased 10% of the purchase price each year, it is not possible to determine the present book value because the purchase price is unknown as is the number of years ago the equipment was purchased. Consider the following chart, where P represents the purchase price.

Years after purchase Depreciation Book value
0 0 P
1 0.1P 0.9P
2 0.1P 0.8P
3 0.1P 0.7P
4 0.1P 0.6P
5 0.1P 0.5P
6 0.1P 0.4P
7 0.1P 0.3P
8 0.1P 0.2P
9 0.1P 0.1P
10 0.1P 0
11 0 0
12 0 0
13 0 0
For example, if “5 years ago” was 6 years after purchase and the book value was $5,000, then $5,000 = 0.4P and P = $12,500. In this case, the present book value (i.e., 5 years hence) is $0. On the other hand, if “5 years ago” was 2 years after purchase and the book value was $5,000, then $5,000 = 0.8P and P = $6,250. In this case, the present book value (i.e., 5 years hence) is 0.3($6,250) = $1,875; NOT sufficient.

(2) Given that the present book value of another piece of equipment is $2,000 gives no information about the certain piece of equipment under consideration; NOT sufficient.

Taking (1) and (2) together gives no more information than (1) alone since (2) gives information about another piece of equipment, not the piece under consideration.

The correct answer is E; both statements together are not sufficient.

Given: The book value of the equipment 5 years ago was $5,000.

To Find: The present book value of the equipment.

Statement 1: From the time of purchase, the book value decreased by 10% of its purchase price each year.

• Let the original purchase price be P.
• Each year, the value decreases by 10% of P (not the remaining value).
  
  • After T years, Value = P × \((0.9)^T\).
• We only know the book value 5 years ago ($5,000), but we do not know the original purchase price P nor do we know how many years after the original purchase was the 5-year-ago period.
• Without knowing P, we cannot determine the current value.

Statement 1 alone is insufficient.

Statement 2: The present book value of another piece of equipment is $2,000.

• This statement gives no information about the equipment in question.
• It is completely irrelevant.

Statement 2 alone is insufficient.

Statements 1 and 2 Combined:

• Statement 2 does not provide any useful information.
• Statement 1 remains insufficient since we do not know the original purchase price.

Even together, the statements are insufficient.

Correct Answer: E