By How Many Dollars was The Price of a Certain Portable Tape Recorder GMAT Data Sufficiency

Question: By how many dollars was the price of a certain portable tape recorder reduced during a sale?
(1) During the sale, the price of the tape recorder was reduced by 25 percent.
(2) The price of the tape recorder after the reduction was $36.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: C
Solution and Explanation:

Approach Solution 1:
The question asks to find how many dollars the price of a certain portable tape recorder was reduced during a sale.
Statement 1: During the sale, the price of the tape recorder was reduced by 25 percent.
There is no such information given about the price of the tape recorder. Therefore, the statement alone is insufficient to find how many dollars the price of a tape recorder was reduced during a sale.
Statement 2: The price of the tape recorder after the reduction was $36.

There is no information given about the price of the tape recorder before the reduction. There exists no data regarding the percentage decrease. Hence the statement alone is insufficient to find how many dollars the price of a tape recorder was reduced during a sale.

Combining both statements, we get:
Let’s assume the cost of the tape recorder is X.
From statement (1) we get: the price of the tape recorder was reduced by 25%.
From statement (2) we get: the price after the reduction was $36.
Therefore; 75% of X = 36
=> 75/100 * X = 36
=> X = 48
Hence, the reduction in price = 48 − 36 = $12
Thus, both statements together are sufficient.

Approach Solution 2:
The question asks to find the reduction in the price of a tape recorder during the sale.

Statement 1 alone: During the sale, the price of the tape recorder was reduced by 25 percent.
25% reduction is stated in this statement. However, a 25% reduction over what quantity is not mentioned in the statement. Therefore, the statement alone is insufficient to get the reduction.
Statement 2 alone: The price of the tape recorder after the reduction was $36.
The new price given is $36. There is no such information regarding the old price. Hence, we cannot get the reduction. Hence, the statement alone is Insufficient.

Combining both statements, we get:
A 25% reduction implies that the new value is 75% (or 3/4) of the original value.
Hence, 3/4 * original = 36.
Therefore, original = 36 * 4/3 = 48.
The reduction in price = 48 − 36 = $12
Hence, both statements together are sufficient.

Approach Solution 3:
The question asks to find the reduction in the price of a tape recorder during the sale.

1. Statement (1) gives the reduction in percentage. However the real price is not mentioned. Hence the statement is insufficient.
2. Statement (2) gives the sales price. However there is no information about the real amount or percent reduction. Hence, insufficient.

Statement (1) and (2) together give both the sale price and percent reduction. Therefore, the real price could be derived. Hence, the reduction in price could be figured out. Thus, both the statement together are sufficient.

“By how many dollars was the price of a certain portable tape recorder”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2021”. The GMAT Quant section consists of 31 questions to be solved within 62 minutes. GMAT Data Sufficiency questions are featured with a problem statement that is followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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