Placement Aptitude (Quant, Logical, Verbal) Module 15 – Critical reasoning
Strengthen, weaken, cause and course of action
Pick the option that most strengthens or weakens an argument, tell a cause from a common cause, and judge courses of action and selection tables.
What you will learn
- Choose the option that most strengthens or weakens an argument
- Decide whether two events are cause and effect, effects of a common cause, or independent
- Evaluate courses of action and selection decision tables
Before you start
What you’ll learn · Before you start
What you will learn
- Choose the option that most strengthens or weakens an argument
- Decide whether two events are cause and effect, effects of a common cause, or independent
- Evaluate courses of action and selection decision tables
Before you start
On this page
These items ask what would change an argument, what links two events and what to do about a problem. To strengthen an argument, pick the option that makes its conclusion more likely given its evidence, usually by ruling out a rival explanation; to weaken it, pick the option that makes the conclusion less likely, usually by offering another cause, exposing a flawed comparison or showing that a sample is unrepresentative. A cause comes before its effect and works through a plausible mechanism, and two events that go together may instead share a common cause. A course of action follows when it is practical, deals with the problem and creates no bigger one. TCS iON names decision-making among the reasoning areas of its NQT, and the SSC CGL syllabus lists judgment and decision making.
Strengthen and weaken
Find the gap between the evidence and the conclusion first, then ask what each option does to it. An option strengthens the argument when it closes the gap, and weakens it when it opens a rival explanation. To rank options, compare how likely each would be if the conclusion were true and if it were false: the Stanford entry on inductive logic shows that evidence moves a conclusion by the ratio of those two likelihoods. The argument here: “Since a bus lane opened on Station Road, the average bus trip from the station to the IT park has fallen from 41 to 33 minutes, so the lane has cut journey times.”
| Kind of option | Effect | On the bus-lane argument |
|---|---|---|
| Another cause | Weakens | The IT park moved its shift start past the rush that month |
| A flawed comparison | Weakens | “Before” trips were timed in the monsoon, “after” trips in a dry month |
| An unrepresentative sample | Weakens | The “after” trips were all timed on Sundays |
| A rival ruled out | Strengthens | Trips on a parallel road with no bus lane got no faster |
| A mechanism shown | Strengthens | Buses no longer wait behind turning cars at the two worst junctions |
| Off the point | Neither | The lane is painted red |
Cause and effect
Four ways two events can go together
Text description of the diagram
Four panels in a grid of two by two, each showing two events, A and B, as small boxes.
- A causes B: an arrow runs from A to B. A comes first and can produce B.
- B causes A: the arrow runs from B to A. The order runs the other way round.
- A common cause: a third box, C, sits above A and B, with an arrow from C to each of them and none between A and B. Hold C fixed, and the link between A and B goes.
- No link: A and B sit side by side with no arrow at all. They went together by chance.
Cause-and-effect items give two statements and ask how they are linked. Check the time order, since a cause comes before its effect; a mechanism, some plausible way for one to produce the other; and a rival, a third event that could produce both. The Stanford entry on fallacies lists the matching mistakes: taking mere sequence for cause, reversing cause and effect, and missing a common cause. Reichenbach’s common cause principle, in the same encyclopedia, says what a common cause does: it makes its effects go together, and holding it fixed makes the link vanish.
# A common cause, simulated. Rain makes the campus shop sell umbrellas and the canteen sell hot tea, and neither sale
# has any effect on the other. Over all days the two still go together; on rainy days alone, or dry days alone, the
# link disappears, because rain was producing both. The simulation is seeded, so it prints the same every time.
import random
from statistics import correlation, mean
rng = random.Random(2026)
def count(trials, chance):
"""How many of `trials` independent customers buy, each with probability `chance`."""
return sum(rng.random() < chance for _ in range(trials))
days = []
for _ in range(120):
rainy = rng.random() < 0.3
umbrellas = count(400, 0.10 if rainy else 0.01)
tea = count(1000, 0.30 if rainy else 0.20)
days.append((rainy, umbrellas, tea))
def report(label, rows):
u = [r[1] for r in rows]
t = [r[2] for r in rows]
print(f"{label:<11} {len(rows):>3} days umbrellas {mean(u):5.1f} a day tea {mean(t):5.1f} a day r = {correlation(u, t):+.2f}")
report("all days", days)
report("rainy days", [d for d in days if d[0]])
report("dry days", [d for d in days if not d[0]])Output
all days 120 days umbrellas 16.0 a day tea 235.2 a day r = +0.93 rainy days 40 days umbrellas 39.3 a day tea 298.9 a day r = +0.06 dry days 80 days umbrellas 4.3 a day tea 203.3 a day r = +0.01
Recorded with Python 3.14.8 on macOS 26 arm64. To run it yourself: mise exec python@3.14.8 -- python3 common_cause.py
Runs on this device, in your browser. The first run downloads Python (about 13.5 MB), which is kept for the next runs.
Your run, in this browser
Across all 120 days the umbrella and tea sales correlate at +0.93, yet within rainy days the figure is +0.06 and within dry days +0.01. Rain produces both, and neither sale affects the other.
Courses of action and decision tables
A course of action follows if it is practical, deals with the problem or its cause, and does not create a bigger problem; shutting something down or banning it everywhere usually fails the last check. A selection decision table, which AMCAT’s syllabus lists under deductive reasoning, gives criteria and the exceptions that send a candidate elsewhere. Apply the criteria in order: an exception applies only when every other criterion is met, and “data inadequate” fits only when a missing fact could change the outcome.
An internship selects a final-year student with a CGPA of at least 7.0, a data analysis course and all 8 weeks available. A CGPA from 6.5 to 7.0 with a published project goes to the head of the programme, and 6 or 7 weeks to the waiting list, provided every other condition is met. Nisha (final year, CGPA 7.4, course done, 8 weeks) is selected; Omar (the same, but CGPA 6.8 and a published project) goes to the head.
Five solved items
- Strengthen. “Students who use the college’s study app score higher, so the app raises scores.” Best support: users improved after they began, while similar students without it stayed level.
- Weaken. The same argument: students who already score well are the likeliest to install the app.
- Cause. A: the main road was dug up for a water pipe. B: shops on the road reported lower sales that month. A causes B: it came first, and customers could not reach the shops.
- Common cause. A: the canteen sold more cold drinks. B: more students fainted at the morning assembly. Both are effects of a common cause, a heat wave.
- Course of action. Problem: many students miss the 8:30 lecture because the college bus often arrives late. I: run the bus 15 minutes earlier. II: cancel all morning lectures. Only I follows; II creates a bigger problem.
Your turn
The exercise turns the internship table into code, and the ten items after it are untimed.
Exercise · Easy · Python
Apply a selection decision table to one candidate
An internship programme selects a candidate who meets all four conditions:
- is a final-year student;
- has a CGPA of at least 7.0;
- has completed a course in data analysis;
- can work for all 8 weeks.
Two exceptions apply only to a candidate who meets every other condition:
- a CGPA from 6.5 up to 7.0 with a published project is referred to the head of the programme;
- 6 or 7 weeks of availability puts the candidate on the waiting list.
Every other candidate is rejected. Write decide(final_year, cgpa, data_course, weeks, published) that returns "select", "refer", "wait" or "reject". All five facts are given: two booleans, a number, a boolean, a whole number of weeks and a boolean.
Starter code · selection.py
def decide(final_year, cgpa, data_course, weeks, published):
"""The table's decision for one candidate: "select", "refer", "wait" or "reject"."""
# Replace this line with your code.
return NoneThe sample tests · test_selection.py
from selection import decide
def test_meets_all_four():
"""Every condition met"""
assert decide(True, 7.4, True, 8, False) == "select"
def test_cgpa_exception():
"""CGPA 6.8 with a published project, everything else met"""
assert decide(True, 6.8, True, 8, True) == "refer"
def test_cgpa_without_project():
"""CGPA 6.8 and no project: the exception does not apply"""
assert decide(True, 6.8, True, 8, False) == "reject"
def test_weeks_exception():
"""Six weeks, everything else met"""
assert decide(True, 7.9, True, 6, False) == "wait"
def test_two_conditions_missed():
"""An exception applies only when every other condition is met"""
assert decide(True, 6.8, True, 6, True) == "reject"
def test_not_final_year():
"""No exception covers the first condition"""
assert decide(False, 8.6, True, 8, True) == "reject"
def test_boundaries():
"""At least 7.0, from 6.5, and fewer than 6 weeks"""
assert decide(True, 7.0, True, 8, False) == "select"
assert decide(True, 6.5, True, 8, True) == "refer"
assert decide(True, 7.2, True, 5, False) == "reject"A hint
Settle the two conditions that have no exception first: a candidate who is not in the final year, or has no data analysis course, is rejected whatever else is true. Then work out cgpa >= 7.0 and weeks >= 8 once each, and try the outcomes in the order the table gives them.
Results of the sample tests
| Test | Result | Details |
|---|
What your code printed
The sample tests run on this device, in your browser (Pyodide): nothing is sent to mysmartcopilot.com. The first run downloads Python (about 13.5 MB), which is kept for the next runs. A check in your browser is feedback for you, not proof that the code is right for every input.
Ten items, untimed
10 questions about this lesson. Every answer and why it is right is on the page, behind “Show the answer”. Your score stays in this browser.
Options ranked by how far they move the odds, and cause pairs worked Pro: opens with a Pro, Premium or Ultimate pass
“Most strengthens” and “most weakens” are questions of degree, and degree can be put into numbers. This part ranks six options on the bus-lane argument by how far each moves the odds, works eight cause-and-effect pairs, and reproduces the front-row trap with the fair test that removes it.
In this part:
- Six options ranked by how far they move the odds, with numbers
- Eight cause-and-effect pairs worked
- The front-row trap, reproduced with a fair test
2 runnable examples (Python) · about 3 minutes
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Eight candidates through a decision table, courses of action, and a timed set Pro: opens with a Pro, Premium or Ultimate pass
Decision tables reward order: the same facts give different answers when the criteria are applied out of order or an exception is stretched. This part runs eight candidates through the internship table by program, works six courses of action with the three checks, and ends with ten mixed items to answer in twelve minutes.
In this part:
- Eight candidates through the table, checked by a rule engine
- Six courses of action worked with the three checks
- Ten items in twelve minutes
- Answers with working
1 runnable example (Python) · about 4 minutes
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This part opens with any MySmartCoPilot pass.
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- 30 days₹179$5.99
- 1 year₹1,699$45
One payment; a pass never renews. The price shown is the total you pay: no fees or charges are added at checkout.
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Interview questions
-
Fresher · Warm-up
What makes an option strengthen an argument, rather than simply agree with its conclusion?
An option strengthens an argument when it makes the conclusion more likely given the argument's own evidence, usually by closing the gap between the two. In "Since the bus lane opened, trips fell from 41 to 33 minutes, so the lane cut journey times", the gap is whether the lane, rather than something else, caused the fall. "Trips on a parallel road without a lane got no faster" strengthens it, because it rules out a change across the whole city. "Bus lanes are a good idea" only agrees with the conclusion and adds no evidence that this lane did anything. A useful test: the more surprising the option would be if the conclusion were false, the more it strengthens.
-
Fresher
A coaching centre's leaflet says: "Students who joined our aptitude course scored 20 marks more on average in the placement test than students who did not, so our course raises scores by 20 marks." Name the two strongest weakeners, and the one fact that would most strengthen the claim.
-
Fresher
A councillor notes that the city's months with the most power cuts also have the most road accidents, and concludes that power cuts cause accidents. How would you judge the claim, and what data would settle it?
-
Fresher
Problem: in the college's online tests, many students copied answers shared in group chats. Which actions follow? I: hold the tests in exam halls. II: give each student questions drawn from a larger bank, in a different order. III: expel every student who belongs to such a group chat.
Key takeaways
- Strengthen by closing the gap between evidence and conclusion; weaken by opening a rival explanation.
- A cause comes first and has a mechanism; two effects of one cause go together without causing each other.
- A course of action must be practical, aimed at the problem and no worse than the problem.
- In a decision table, an exception applies only when every other criterion is met.
References
- Inductive Logic, sections 1.3 and 1.4: likelihood ratios and the ratio form of Bayes theorem (Stanford Encyclopedia of Philosophy)
- Reichenbach's Common Cause Principle (Stanford Encyclopedia of Philosophy)
- Fallacies, section 1: the core fallacies (Stanford Encyclopedia of Philosophy)
- AMCAT syllabus: Logical Ability (selection decision tables) (AMCAT)
- TCS iON National Qualifier Test (NQT): Cognitive reasoning areas (TCS iON)
- Combined Graduate Level Examination notice, section 13.10.1 (Tier-I syllabus) (Staff Selection Commission)
- statistics.correlation (Python Software Foundation)
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