6.2 Data Sufficiency: Hidden Anchors, Redundant Clues, and Other Traps
Key Takeaways
A pair of clues that restates the same relationship, such as 2 desks plus 3 chairs costing $3,100 and 4 desks plus 6 chairs costing $6,200, adds no information and is insufficient.
Two linear equations in two unknowns give one solution only when one is not a multiple of the other.
Inequality clues such as 'more than 30' give a range, which identifies a single answer only when a stem condition like 'different whole numbers' closes the range.
Stem conditions such as 'only the winner', 'one per year' or 'shortest service' often act as the anchor that turns two relative clues into a definite answer.
The most common trap is a pair that orders most candidates but leaves one person, value or position unconstrained.
6.2 Data Sufficiency: Hidden Anchors, Redundant Clues, and Other Traps
Quick Answer: Wrong options in CRE Data Sufficiency questions are rarely random. Each is usually a pair that looks connected but leaves the answer open. The five traps to check are: the partial ranking, the decoy link, the redundant restatement, the range that never closes, and the double answer from squares or absolute values. The stem often supplies the missing anchor, so read it as carefully as the clues.
Trap 1: the partial ranking
A pair can put three of four candidates in perfect order and still fail. In the CSB's race sample, clues (3) and (4) prove Jordan beat Jack and John, but say nothing about Joseph. Before marking a "who" or "which" answer, run a roll call: name every candidate and say how the pair fixes or rules out each one.
| Candidate | Status under the pair | Verdict |
|---|---|---|
| Fixed by the pair | Exact value or position known | OK |
| Ruled out by the pair | Proven unable to be the answer | OK |
| Not mentioned | Could still be the answer | Pair fails |
Trap 2: the decoy link
A decoy link relates two items correctly but never reaches the anchor or the target. In the race sample, clue (2) (Joseph versus Jack) paired with clue (1) (John's time) produces two isolated facts. Ask: do the two clues share an item? If they share none, and the stem does not connect them, they cannot combine into one answer.
Trap 3: the redundant restatement
Some clues say the same thing in different words or numbers:
- "Ada is 3 years older than Ben" and "Ben is 3 years younger than Ada".
- "2 desks and 3 chairs cost $3,100" and "4 desks and 6 chairs cost $6,200".
The second pair looks like two equations, but the second is simply the first multiplied by 2. Two equations give one solution only when they are independent. A quick test for two equations in the same two unknowns: if the coefficients of one are a constant multiple of the other's, the pair is redundant.
| Pair of equations | Independent? | Result |
|---|---|---|
| 2d + 3c = 3,100 and 4d + 6c = 6,200 | No (second is double the first) | Infinitely many solutions: insufficient |
| 2d + 3c = 3,100 and d = c + 500 | Yes | One solution: c = 420, d = 920 |
| d + c = 450 and 3d - 2c = 300 | Yes | One solution: c = 210, d = 240 |
Solving fully is optional. Once you see two independent linear equations in two unknowns, you know there is one answer. On the Aptitude Test you may use a permitted calculator, but the sufficiency decision usually comes before any arithmetic.
Trap 4: the range that never closes
Clues with "more than", "at least" or "fewer than" give a range, not a value:
- "The office has more than 30 full-time staff" plus "there are three times as many full-time as part-time staff" gives part-time staff greater than 10, which is still many possible values.
- A range becomes a single value only if the stem or another clue closes it. For example, "more than 30" and "fewer than 33", with "a multiple of 4", gives 32.
Watch for stem conditions that close ranges silently: "different whole numbers", "one officer per year", or "the shortest" and "the longest".
Trap 5: double answers from squares and distances
Quantity clues sometimes hide two possibilities:
- "The square of the difference between their ages is 16" means the difference is 4 in either direction.
- "The two offices are 3 floors apart" means above or below.
Such a clue settles the answer only when another clue or a stem fact fixes the direction ("A is older", "B is on a higher floor").
Hidden anchors in the stem
The most valuable fact is often not in the numbered list:
| Stem fact | How it works as an anchor |
|---|---|
| "Only the winner finished in 10 minutes" | Any runner shown to take exactly 10 minutes is the winner |
| "Lui has the shortest service" | Removes one candidate when you look for the longest |
| "One officer joined in each year from 2018 to 2022" | Turns a relative chain into exact years at the boundary |
| "Only the tallest building is over 200 metres" | Any building shown to exceed 200 metres is the tallest |
Underline the stem fact before reading the clues. Then look for the pair that connects a candidate to it.
A worked practice example
Four colleagues, Fong, Ip, Kam and Lui, have different whole numbers of years of service. Lui has the shortest service. Which TWO pieces of information can tell you who has the longest service?
(1) Fong has 12 years of service. (2) Ip has more years of service than Kam. (3) Lui has 3 fewer years than Fong. (4) Kam has more years of service than Fong. (5) Ip has 2 more years than Lui.
- (2) and (4): Ip is above Kam, and Kam is above Fong. Lui is the shortest by the stem, so Ip is the longest. This pair is sufficient because the stem removes Lui.
- (1) and (3): Fong 12 and Lui 9, but Ip and Kam are unknown: insufficient.
- (3) and (5): Ip is 1 year below Fong, but Kam is unknown: insufficient.
- (1) and (4): Kam is above Fong, but Ip could be higher still: insufficient.
- (2) and (5): Ip is above Kam and Lui, but Fong is unknown: insufficient.
A five-second elimination scan
Before working through any pair in detail, scan the options for quick eliminations:
- No shared item and no stem link: eliminate.
- Value question but no anchor anywhere in the pair or stem: eliminate.
- Pair mentions only items that cannot be the answer: eliminate.
- Pair restates one relationship twice: eliminate.
The options left are usually two or fewer. Test those carefully with the roll call from Trap 1.
A department bought desks and chairs. All desks cost the same and all chairs cost the same. Which TWO pieces of information can tell you the price of one chair?
(1) Two desks and three chairs cost $3,100 in total. (2) Four desks and six chairs cost $6,200 in total. (3) A desk costs $500 more than a chair. (4) The department bought 20 chairs. (5) The department's total bill was $15,500.
(1) and (4)
(2) and (3)
(1) and (2)
(3) and (5)
(4) and (5)
Four colleagues, Fong, Ip, Kam and Lui, have different whole numbers of years of service. Lui has the shortest service. Which TWO pieces of information can tell you who has the longest service?
(1) Fong has 12 years of service. (2) Ip has more years of service than Kam. (3) Lui has 3 fewer years than Fong. (4) Kam has more years of service than Fong. (5) Ip has 2 more years than Lui.
(1) and (3)
(2) and (5)
(1) and (4)
(2) and (4)
(3) and (5)
A district office employs full-time and part-time staff. Which TWO pieces of information can tell you how many part-time staff it has?
(1) The office has 40 staff in total. (2) There are three times as many full-time staff as part-time staff. (3) Full-time staff outnumber part-time staff by 18. (4) The office has more than 30 full-time staff. (5) Part-time staff make up less than half of all staff.
(1) and (2)
(1) and (5)
(3) and (5)
(4) and (5)
(2) and (4)
Sections you finish are checked off in the contents.