I05-21

Question

Three types of gemstones—emeralds, garnets, and amethysts—discovered during a recent archaeological expedition will be selected for display at a local museum based on the following criteria:
 
• Six stones will be chosen for the display, including both polished and unpolished stones.
 
• No more than three stones of any one type will be included, and at least one stone of each type must be selected.
 
• At least one unpolished garnet must be included.
 
• If more than one emerald is selected, the same number of amethysts, with the same finish (polished / unpolished), must also be selected.
 
If two polished emeralds are selected for the display, and assuming that all the criteria are met, select for  Must be true  the statement that must be true, and select for  Must be false  the statement that must be false. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Since more than one emerald is selected (specifically two polished emeralds), the criteria require that both the number and type of emeralds and amethysts must match. Thus, two polished amethysts must also be included. Selecting three emeralds and three amethysts would leave no room for a garnet, which violates the rule that at least one of each type must be included. Therefore, the display includes exactly two emeralds and exactly two amethysts, all polished.
 
This leaves two remaining stones, which must both be garnets, with  at least one  of them unpolished to satisfy the criteria. Thus:
 
• Must be true: An unpolished garnet is included in the display.
 
• Must be false: Exactly two polished garnets are included in the display.

Correct answer:

Must be true  "An unpolished garnet is included in the display. "

Must be false  "Exactly two polished garnets are included in the display."

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

RITESH1984 · Answer

Very good quality question simple but easy to miss under exam condition because of time pressure.

harshitasinghal · Answer

I wanted to clarify if this arrangement is possible too?

2 Polished Emeralds, 2 Polished Amethysts + P/UP Amethyst + P/UP Garnet

As the ques mentions the same number and finish of amethysts must be selected too (same as emeralds) :- minimum that no. of A are selected as E, but there's no rule that it has to be maximum too.

Bunuel · Answer

That arrangement is  not possible . The rule says:

This means the count must  match exactly , not “at least.” So with 2 polished emeralds, you must have  exactly 2 polished amethysts , no more and no fewer. Adding any extra amethyst (polished or unpolished) would break the 1-to-1 correspondence required by the rule.

Karym · Answer

I like the solution - it’s helpful.

I05-21

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

Must be true	Must be false
		An unpolished garnet is included in the display.
		A polished garnet is included in the display.
		Exactly two unpolished garnets are included in the display.
		Exactly two polished garnets are included in the display.
		Both a polished garnet and an unpolished garnet are included in the display.