Can someone solve this SHSAT logic question involving trolls? In a cartoon, four trolls stood in a line. Their names were Banto, Gretchen, Snowflake and Holly. One had green eyes, another had...

Can someone solve this SHSAT logic question involving trolls? 

In a cartoon, four trolls stood in a line. Their names were Banto, Gretchen, Snowflake and Holly. One had green eyes, another had purple ears, another had red teeth, and another had white hair.

1- The troll with the red teeth was directly in front of Snowflake, who had white hair.

2- Banto, who did not have green eyes, was behind Gretchen.

3- Gretchen had purple eyes

4- Snowflake was behind Holly. 

If the troll with green eyes stood behind Gretchen, then what was Gretchen's postition? 

F. first

G. second

H. third

J. fourth 

K. Cannot be determined based on information given 

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najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

The most important sentence of the problem statement is:

One had green eyes, another had purple ears, another had red teeth, and another had white hair.

There are four trolls and four attributes joined by word 'another' which make these attributes mutually exclusive.

Now we come to the problem.

According to (1), troll with 'red teeth' is directly in front of Snow Flake which I represent as:

Snow Flake (white hair) -> red teeth

Statement (2) & (3):

Banto (not green eyes) --> Gretchen (purple eyes hence not green eyes either)

So this leave us with Holly to have green eyes as Snow Flake has white hair and all these attributes are mutually exclusive.

Also either of Banto or Gretchen may have 'red teeth' or 'purple ears'

Staement (4) and earlier positional analysis give us following relationship:

Snow Flake (white hair) --> Holly (green eyes)

Banto --> Gretchen

Snow Flake -> red teeth

The above relationship lead to different possible positions depending on whether Banto or Gretchen has red teeth as under:

  • Snow Flake (white hair) -> Bento (red teeth) -> Gretchen (purple ears) -> Holly (green eyes)
  • Snow Flake (white hair) -> Bento (red teeth) -> Holly (green eyes) -> Gretchen (purple ears)
  • Banto (purple ears) -> Snow Flake (white hair) -> Gretchen (red teeth) -> Holly (green eyes)

From above three dispositions we cannot conclude a definite position of Gretchen hence answer is:

K. Cannot be determined based on information given 

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