Government Operational Research Service (GORS) Assessment Quantitative Reasoning and Aptitude Tests Syllabus

What is an assumption in the context of evaluating an argument?

An unstated premise that the argument needs to be true for its conclusion to follow. If the assumption is false, the argument's logic collapses.

What is the 'negation test' for identifying a necessary assumption?

Negate the candidate assumption: if its negation makes the argument fall apart (conclusion no longer supported), it is a necessary assumption; if the argument survives, it is not.

How do you strengthen versus weaken an argument?

Strengthen by adding evidence that supports the conclusion or confirms an assumption; weaken by introducing evidence that attacks an assumption, offers an alternative explanation, or contradicts the conclusion.

In a True / False / Cannot Say verbal test, when do you answer 'True'?

Only when the statement logically and necessarily follows from the information given in the passage alone — it must be fully supported by the text.

In a True / False / Cannot Say verbal test, when do you answer 'False'?

When the statement directly contradicts the passage, or cannot be true given the information provided.

In a True / False / Cannot Say verbal test, when do you answer 'Cannot Say'?

When the passage neither confirms nor contradicts the statement — there is insufficient information to decide, even if the statement seems plausible from outside knowledge.

What is the single most common error to avoid in True/False/Cannot Say items?

Using outside knowledge or assumptions. Judge each statement ONLY against the passage; what is true in the real world is irrelevant if the text does not state it.

What is an effective reading-comprehension-under-time-pressure strategy for verbal reasoning passages?

Read the statement/question first, then scan the passage for the relevant keywords or section, rather than reading the whole passage in depth before seeing what is asked.

Why is paraphrasing in answer options a trap in verbal reasoning, and how do you handle it?

Test writers reword passage ideas; a correct option may use synonyms while a wrong option copies passage wording but changes meaning. Match on meaning, not on matching words.

What distinguishes deductive reasoning from inductive reasoning?

Deductive reasoning moves from general premises to a logically certain conclusion (if premises are true, conclusion must be true). Inductive reasoning generalises from specific observations to a probable conclusion (conclusion is likely, not guaranteed).

In a number sequence, what should you check first to find the rule?

The difference between consecutive terms (arithmetic), then the ratio (geometric), then second differences, alternating patterns, or position-based rules like squares/primes.

What is the general term of an arithmetic sequence with first term $a$ and common difference $d$?

$a_n = a + (n-1)d$, and the sum of the first $n$ terms is $S_n = \frac{n}{2}\big(2a + (n-1)d\big)$.

What is the general term of a geometric sequence with first term $a$ and common ratio $r$?

$a_n = a\,r^{\,n-1}$, and the sum of the first $n$ terms (for $r\neq 1$) is $S_n = a\frac{r^{n}-1}{r-1}$.

Identify the rule and next term: $2, 6, 12, 20, 30, \dots$

Differences increase by 2 each time ($4,6,8,10\dots$); equivalently $a_n = n(n+1)$. The next term is $42$.

In diagrammatic/inductive reasoning items, what are the common transformation rules between shapes?

Rotation, reflection, translation, change in size, change in number of elements/sides, change in shading/colour, and alternation. Identify which attribute changes consistently across the sequence.

In a 'find the odd one out' diagrammatic item, what is the systematic approach?

List the attributes (shape, count, shading, orientation, symmetry) and find the single attribute on which one figure differs while all others share a common rule.

What general approach do situational judgement tests reward when ranking responses?

Prioritise actions that are professional, follow procedure/policy, address the core problem directly, consider stakeholders, and escalate appropriately — over self-serving, avoidant, or rule-breaking actions.

In a prioritisation task, how do you order competing tasks?

Rank by urgency and importance (impact if not done, deadlines, dependencies, and stakeholders affected), typically handling high-impact/high-urgency items first while not neglecting important non-urgent work.

What is Fermi estimation?

A method of getting an approximate answer to a quantitative problem by breaking it into estimable factors, using order-of-magnitude assumptions, and multiplying them — accepting that errors partially cancel.

What does 'order of magnitude' mean and how do you compare two quantities by it?

An order of magnitude is a factor of 10 (a power of 10). Two quantities differ by $n$ orders of magnitude if their ratio is about $10^{n}$; compare via $\log_{10}$ of each value.

Estimate to one significant figure: $\frac{612 \times 0.49}{31}$. What is the quick approach?

Round first: $\frac{600 \times 0.5}{30} = \frac{300}{30} = 10$. Rounding to convenient numbers gives a fast order-of-magnitude check (exact $\approx 9.7$).

To make $x$ the subject of $v = u + at$, how do you solve for $t$?

Subtract $u$, then divide by $a$: $t = \frac{v - u}{a}$.

How do you rearrange $A = \frac{1}{2}(a+b)h$ to make $b$ the subject?

$b = \frac{2A}{h} - a$. (Multiply both sides by 2, divide by $h$, then subtract $a$.)

What is the order of operations used when evaluating or manipulating a formula?

BIDMAS/BODMAS: Brackets, Indices (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

Solve the linear equation $3x - 7 = 11$ and state the method.

Add 7 to both sides ($3x = 18$), then divide by 3: $x = 6$. Keep the equation balanced by doing the same operation to both sides.

State the quadratic formula for solving $ax^{2} + bx + c = 0$.

$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$, where the discriminant $b^{2} - 4ac$ determines the number of real roots.

In function notation, what does $f(x) = 2x + 3$ mean and what is $f(4)$?

$f$ is a rule mapping an input $x$ to an output; $f(4)$ substitutes $x=4$: $f(4) = 2(4)+3 = 11$.

What is the laws-of-indices rule for multiplying and dividing powers with the same base?

$a^{m} \times a^{n} = a^{m+n}$ and $\frac{a^{m}}{a^{n}} = a^{m-n}$; also $(a^{m})^{n} = a^{mn}$ and $a^{0} = 1$.

In a spreadsheet, what does an absolute reference like $A\$1$ do versus a relative reference $A1$ when copied down?

A relative reference ($A1$) shifts with the copy (becomes $A2$, $A3$); an absolute reference (with $\$$, e.g. $A\$1$ or $\$A\$1$) keeps the locked row/column fixed when the formula is copied.

In spreadsheet-style reasoning, how does SUM(B2:B5) differ from B2+B5, and what does a function like AVERAGE compute?

SUM(B2:B5) adds every cell in the contiguous range B2,B3,B4,B5, whereas B2+B5 adds only those two cells. AVERAGE(range) returns the mean: sum of the cells divided by the count of cells.