HSPT: Logic: line up comparisons in one direction
Solve order questions by turning every comparison the same way, placing the items on one line, and choosing only what the line proves.
How do you keep track of order when a question gives several comparisons?
Short answer
Rewrite every comparison in the same direction and place the items on one line. The answer is the statement the line proves; anything the line leaves open can't be the answer.
Know first: Comparison words such as taller, heavier, before and north of, The difference between must and might
Step 1 of 5
Comparisons chain together
Some HSPT logical reasoning questions compare things: who is taller, which box is heavier, which town is farther north. If A is taller than B and B is taller than C, then A is taller than C. That chaining is the whole idea.
The hard part is that the comparisons often point in different directions. One sentence says heavier, the next says lighter. Turn them all the same way before you compare anything.
| Statement | Flipped | On a top-to-bottom line |
|---|---|---|
| Ivy is younger than Ben. | Ben is older than Ivy. | Ben above Ivy (older on top) |
| The cart is lighter than the wagon. | The wagon is heavier than the cart. | Wagon above cart (heavier on top) |
| Dover is south of Elton. | Elton is north of Dover. | Elton above Dover (north on top) |
| Pia arrived after Quinn. | Quinn arrived before Pia. | Quinn above Pia (earlier on top) |
Both versions say the same thing. Choose whichever direction matches the rest of the question.
Step 2 of 5
Build the line, then test the choices
Worked example: Four heights
Hal is taller than Jun. Kim is shorter than Jun. Lev is taller than Hal. Which statement must be true?
- AKim is taller than Hal.
- BJun is the shortest.
- CLev is taller than Kim.
- DHal is the tallest.
- 1
Turn every statement to taller
Hal over Jun. Jun over Kim (flipped from Kim is shorter than Jun). Lev over Hal.
- 2
Place them on the line
Tallest to shortest: Lev, Hal, Jun, Kim.
- 3
Test each choice
Lev sits above Kim, so Lev is taller than Kim is proved.
- 4
Why the others are there
The first choice flips Kim and Hal. Jun isn't the shortest, since Kim is below Jun. Hal isn't the tallest, since Lev is above Hal.
Answer
Lev is taller than Kim.
Find the wrong step
A student answers this question: The bakery is east of the bank. The school is west of the bank. Which statement must be true? (A) The bank is east of the bakery. (B) The school is east of the bakery. (C) The bakery is east of the school. (D) The school is farthest east.
- 1
Draws a line with west on the left and east on the right, and puts the bakery to the right of the bank.
- 2
Puts the school to the right of the bank too, because the school is named after the bank in the sentence.
What went wrong
West of the bank means to the left of the bank. Where a name appears in the sentence doesn't decide where it goes on the line.
- 3
Reads the line as bank, bakery, school and picks (D).
The fix
The correct line, west to east, is school, bank, bakery. The bakery is east of the school, so the answer is (C).
Step 3 of 5
Line them up yourself
Check yourself · Question 1
The red kite flew higher than the yellow kite. The green kite flew lower than the yellow kite. Which statement must be true?
Answer: B
Highest to lowest: red, yellow, green. Red is above green.
Check yourself · Question 2
Tess scored more points than Uma. Vic scored fewer points than Uma. Wes scored more points than Vic. Which statement must be true?
Answer: D
Most to fewest: Tess, Uma, Vic. Wes is somewhere above Vic, but nothing compares Wes with Tess or Uma. Tess is above Uma, and Uma is above Vic, so Tess scored more than Vic.
Trap answer: Wes scored more points than Uma.
Likely, but not proved
- Why it looks right
- Wes beat Vic, and Uma beat Vic too, so it feels as if Wes belongs near Uma or above her.
- Why it's wrong
- No statement compares Wes and Uma. Wes could be below Uma, between Uma and Tess, or above Tess.
- The right answer
- Tess scored more points than Vic, because Tess is above Uma and Uma is above Vic.
Check yourself · Question 3
Ridge Road is north of Lake Road. Mill Road is south of Lake Road. Gate Road is north of Ridge Road. Which statement must be true?
Answer: B
North to south: Gate, Ridge, Lake, Mill. Gate is at the top and Mill is at the bottom.
Common mistake
Placing items in the order the sentence happens to name them.
- Why it's tempting
- Reading left to right, the name you read earliest feels as if it should go first on the line.
- Do this instead
- Rewrite each comparison in your chosen direction before you place anything. The comparison word, not the word order, decides who goes where.
Step 4 of 5
What to remember
Remember
- Turn every comparison in the same direction before you place anything.
- Put the items on one line and read the answer off the line.
- If no statement links two items, any choice comparing them can't be proved.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
Sketch the line you built for the practice question. Which choice needed a fact the statements never gave?