In the Hartshorn Building, most but not all of the third floor offices

Question

In the Hartshorn Building, most but not all of the third floor offices are larger than any office on the second floor. The fourth-floor offices are all larger than any office on the second floor. However, all the second-floor offices are larger than any office on the first floor.

If the statements above are true, which one of the following must also be true?

(A) Some first-floor offices are as large as the smallest fourth-floor offices.

(B) Some first-floor offices are as large as the smallest third-floor offices.

(C) Some third-floor offices are not as large as the largest first-floor offices.

(D) Some third-floor offices are not as large as the smallest fourth-floor offices.

(E) Some fourth-floor offices are not as large as the largest third-floor offices.

rajdeep212003 · Answer

I think option D must be true.

Here’s how I visualized it:

4th floor > 2nd floor > 1st floor

For the 3rd floor, the passage says “most but not all” offices are larger than any office on the 2nd floor.

That means:

• most 3rd-floor offices > all 2nd-floor offices 
• but at least one 3rd-floor office is NOT larger than every 2nd-floor office

And since every 4th-floor office is larger than every 2nd-floor office, the smallest 4th-floor office is still bigger than all 2nd-floor offices.

So that weaker/smaller 3rd-floor office must be smaller than at least some 4th-floor offices.

That directly supports option D:

“Some third-floor offices are not as large as the smallest fourth-floor offices.”

---

Why the other choices are not guaranteed:

(A) Nothing connects 1st-floor offices to the size of the smallest 4th-floor office.

(B) Same issue. We cannot conclude anything comparing 1st-floor offices with the smallest 3rd-floor offices.

(C) This reverses the comparison too strongly. 
All 2nd-floor offices are larger than all 1st-floor offices, but the passage never says any 3rd-floor office is smaller than a 1st-floor office.

(E) We do not know whether some 4th-floor offices are smaller than the largest 3rd-floor offices. 
It is possible that all 4th-floor offices are larger than all 3rd-floor offices.

So D is the only statement that must be true based on the relationships given.

— Rajdeep

guddo · Answer

In the Hartshorn Building, most but not all of the third floor offices are larger than any office on the second floor. The fourth-floor offices are all larger than any office on the second floor. However, all the second-floor offices are larger than any office on the first floor.
 
 If the statements above are true, which one of the following must also be true?

The key phrase is “most but not all.” That means at least one third floor office is not larger than every second floor office. So at least one third floor office is no larger than some second floor office. Since every fourth floor office is larger than every second floor office, that third floor office must be smaller than the smallest fourth floor office.

(A) Some first-floor offices are as large as the smallest fourth-floor offices.

Wrong. Every fourth floor office is larger than every second floor office, and every second floor office is larger than every first floor office. So no first floor office can be as large as a fourth floor office.

(B) Some first-floor offices are as large as the smallest third-floor offices.

Wrong. We do not know this. The smallest third floor office could still be larger than every first floor office.

(C) Some third-floor offices are not as large as the largest first-floor offices.

Wrong. The third floor office that is not larger than every second floor office could still be larger than every first floor office.

(D) Some third-floor offices are not as large as the smallest fourth-floor offices.

Correct. At least one third floor office is no larger than some second floor office, and every fourth floor office is larger than every second floor office. So at least one third floor office is  not as large as the smallest fourth floor office .

(E) Some fourth-floor offices are not as large as the largest third-floor offices.

Wrong. The passage does not tell us that any third floor office is larger than any fourth floor office.

Answer: (D)

yc168 · Answer

OE for reference:

Overview:  
This passage gives you information about how the size of the offices on the first, third, and fourth floors of the Hartshorn Building compare with the size of the offices on the second floor. Note that the comparisons between the fourth and second, and the second and first, are quite stark: every fourth-floor office is larger than any second-floor office, and every second-floor office is larger than any first-floor office.
Your task is to select the answer choice that  must  be true if the information you have been given in the passage is true. It is probably best to approach this question by considering each of the answer choices in turn. If, given the information in the passage, an answer choice could be false, then you can rule that choice out.

The Correct Answer:

D  The passage tells you that every fourth-floor office is bigger than even the largest second-floor office, and it tells you that some of the offices on the third floor are not bigger than the largest second-floor offices. So you know that every fourth-floor office is bigger than some of the third-floor offices. That is, some third-floor offices are smaller than every fourth-floor office. So if the statements in the passage are true, (D) must be true.

The Incorrect Answer Choices:

A  The passage tells you that the fourth-floor offices are all larger than any second-floor office. And it tells you that every second-floor office is larger than even the largest first-floor office. We can conclude from this that the smallest fourth-floor office is bigger than even the largest first-floor office. This contradicts what (A) says. Therefore, not only can (A) be false if the statements in the passage are true, (A) must be false.

B, C  (B) says that the largest first-floor offices are as big as the smallest third-floor offices. And (C) says that the largest first-floor offices are bigger than the smallest third-floor offices. So both (B) and (C) could be false if it is possible that the smallest third-floor office is bigger than the largest first-floor office.
The first statement in the passage tells you that the smallest third-floor office is no bigger than the largest second-floor office. But as far as this statement is concerned, the smallest third-floor office might be a lot bigger than some of the smaller second- floor offices. The passage also tells you that  every  second-floor office is bigger than even the largest first-floor office. That means that, as far as the information in the passage is concerned, the smallest third-floor office might be much bigger than the largest first-floor office. So both (B) and (C) can be false.

E  According to (E), the largest third-floor offices are bigger than the smallest fourth-floor offices. This could be false if it is possible that every fourth-floor office is bigger than every third-floor office (including the largest).
The second statement in the passage tells you that every office on the fourth floor is bigger than any second-floor office, but it doesn't say how much bigger they are. So as far as this statement is concerned, every fourth-floor office might be many times as large as the largest second-floor office. The first statement in the passage tells you that most of the third-floor offices are bigger than every second-floor office. But as far as this statement is concerned, even the largest third-floor office might be only slightly larger than the largest second-floor office. Thus, as far as the information in the passage is concerned, every office on the fourth floor could be much bigger than even the largest third-floor office. So (E) does not have to be true.

In the Hartshorn Building, most but not all of the third floor offices

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Critical Reasoning (CR) Questions

In the Hartshorn Building, most but not all of the third floor offices

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards