Given signs signify something and on that basis, assume the given statement to…
2023
Given signs signify something and on that basis, assume the given statement to be true. Answer the question basis the information provided “*” denotes larger than “%” denotes equal to “/“denotes not equal to “-” denotes smaller than “+” denotes not smaller than “X” denotes not larger than If A - B and B - C, then Select one
- A.
A%C
- B.
A+C
- C.
A*C
- D.
A/C
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept
In symbol-substitution reasoning questions, each non-standard symbol first has to be decoded into the standard mathematical relation it stands for; only then can the given statements be combined. Once decoded, the transitive property of strict inequality applies: if one quantity is smaller than a second, and that second quantity is smaller than a third, the first quantity is smaller than the third as well.
Symbol | Meaning |
|---|---|
* | larger than |
% | equal to |
/ | not equal to |
- | smaller than |
+ | not smaller than |
X | not larger than |
Application
Decode the two given statements using the legend above: "A - B" means A is smaller than B, and "B - C" means B is smaller than C.
Apply the transitive property of strict inequality: since A is smaller than B, and B is smaller than C, A must be smaller than C.
Decode each option and test it against "A is smaller than C": A%C means A equal to C, which a strict inequality rules out; A+C means A not smaller than C (i.e. A at least as large as C), which also contradicts A being smaller than C; A*C means A larger than C, again contradicted; A/C means A not equal to C, and two quantities linked by a strict smaller-larger relation can never be equal, so this option always holds.
Cross-check
Substitute any concrete numbers consistent with the premises, say A = 1, B = 2, C = 3 (so A is smaller than B, and B is smaller than C, as required). Testing the options: A%C is 1 equal to 3 — false; A+C is 1 not smaller than 3 — false; A*C is 1 larger than 3 — false; A/C is 1 not equal to 3 — true. Only the "not equal to" option holds for every such substitution, confirming it as the necessary conclusion.