M40-43

Question

If a certain tree reached a height of 78 inches by the end of 2023, did it grow by less than 15 inches that year?

(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.
 
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.

Bunuel · Answer

Official Solution:

If a certain tree reached a height of 78 inches by the end of 2023, did it grow by less than 15 inches that year?

Assume the height of the tree at the end of 2022 was \(h\) inches. The question then becomes whether \(h + 15 > 78\), or equivalently, whether \(h > 63\).

(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.

This implies \(1.3h > 78\), which simplifies to \(h > 60\). This information alone is not sufficient to determine whether \(h > 63\).

(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.

This implies \(1.2h < 78\), which simplifies to \(h < 65\). This information alone is also not sufficient to determine whether \(h > 63\).

(1)+(2) Combining the statements, we find \(60 < h < 65\). However, this range still does not conclusively answer whether \(h > 63\).

Answer: E

Yayatijadhav27 · Answer

Where are the options?

Bunuel · Answer

Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post  ALL YOU NEED FOR QUANT .

Hope this helps.

SMeadows · Answer

This is very helpful. I appreciate it! I'm substantially less confused now. ((Not sarcasm))

Yayatijadhav27 · Answer

Thank you so much for a proper and detailed walkthrough and explaination. It really helped!

bumpbot · Answer

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M40-43

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