Arithmetic, LOGICAL REASONING, VERBAL ABILITY Unit Test for CAT: 68 Questions with Solutions & Analysis

Attempt the Arithmetic, LOGICAL REASONING, VERBAL ABILITY Unit Test for CAT: 68 exam-level questions, detailed solutions and performance analysis. First questions free.

Paper breakdown

68 questions · 204 marks · 93.28 minutes. Quantitative Ability: 27 · Data Interpretation and Logical Reasoning: 22 · Verbal Ability and Reading Comprehension: 19

Free sample questions from Arithmetic, LOGICAL REASONING, VERBAL ABILITY Unit Test

Question 1 · Verbal Ability and Reading Comprehension NAT

Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
1. Boa Senior, who lived through the 2004 tsunami, the Japanese occupation and diseases brought by British settlers, was the last native of the island chain who was fluent in Bo.
2. The indigenous population has been steadily collapsing since the island chain was colonised by British settlers in 1858 and used for most of the following 100 years as a colonial penal colony.
3. Taking its name from a now-extinct tribe, Bo is one of the 10 Great Andamanese languages, which are thought to date back to pre-Neolithic human settlement of south-east Asia.
4. The last speaker of an ancient tribal language has died in the Andaman Islands, breaking a 65,000-year link to one of the world's oldest cultures.
5. Though the language has been closely studied by researchers of linguistic history, Boa Senior spent the last few years of her life unable to converse with anyone in her mother tongue.

Correct Answer:

Step-by-Step Solution

Key idea: This is a thematic scope question, recognisable because four sentences form a tight cluster around a specific linguistic artifact (the Bo language and its last speaker), while one sentence shifts to broad demographic history.

Step 1: Tag each sentence for its primary subject. Sentence 1 discusses Boa Senior and her fluency in Bo. Sentence 3 defines Bo as an ancient Great Andamanese language. Sentence 4 announces the death of the last speaker and the cultural loss. Sentence 5 describes Boa Senior's isolation from her mother tongue. All four share the specific theme of 'language extinction and personal connection'.

Step 2: Examine Sentence 2. It discusses the steady collapse of the indigenous population due to British colonisation and penal colonies. While historically related to the region, its focus is purely demographic and political, not linguistic or biographical.

Step 3: Test coherence without Sentence 2. Sentences 4, 3, 1, and 5 flow logically: News of death $\to$ Language background $\to$ Last speaker bio $\to$ Final tragic detail. Sentence 2 cannot be inserted without breaking this narrative arc about language.

Step 4: Confirm the odd one. Sentence 2 is the only one lacking direct reference to the Bo language or Boa Senior's relationship with it.

Answer: 2

Question 2 · Verbal Ability and Reading Comprehension NAT

Five jumbled up sentences, related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd one out and key in the number of the sentence as your answer:
1. The care with which philosophers examine arguments for and against forms of biotechnology makes this an excellent primer on formulating and assessing moral arguments.
2. Although most people find at least some forms of genetic engineering disquieting, it is not easy to articulate why: what is wrong with re-engineering our nature?
3. Breakthroughs in genetics present us with the promise that we will soon be able to prevent a host of debilitating diseases, and the predicament that our newfound genetic knowledge may enable us to enhance our genetic traits.
4. To grapple with the ethics of enhancement, we need to confront questions that verge on theology, which is why modern philosophers and political theorists tend to shrink from them.
5. One argument is that the drive for human perfection through genetics is objectionable as it represents a bid for mastery that fails to appreciate the gifts of human powers and achievements.

Correct Answer:

Step-by-Step Solution

Key idea: This is a register shift question, recognisable because four sentences engage in a philosophical exposition on the ethics of genetic enhancement, while one shifts to reviewing a specific text or primer.

Step 1: Identify the core theme. Sentence 3 introduces the dual nature of genetics: preventing diseases and enhancing traits.

Step 2: Trace the philosophical exploration. Sentence 2 notes the difficulty in articulating why genetic engineering is disquieting. Sentence 4 explains that grappling with this requires confronting theological questions. Sentence 5 provides a specific philosophical argument against enhancement (bid for mastery).

Step 3: Examine Sentence 1. It states that the care with which philosophers examine these arguments makes "this" an excellent primer. The word "this" implies a reference to a specific book or text, which is absent from the other sentences.

Step 4: Verify coherence without Sentence 1. Sentences 3, 2, 4, and 5 form a cohesive philosophical discussion on the ethics of biotechnology, without any meta-commentary about a primer.

Answer: 1

Question 3 · Verbal Ability and Reading Comprehension NAT

The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
1. The work is more than the text, for the text only takes on life, when it is realized and furthermore the realization is by no means independent of the individual disposition of the reader.
2. The convergence of text and reader brings the literary work into existence and this convergence is not to be identified either with the reality of the text or with the individual disposition of the reader.
3. From this polarity it follows that the literary work cannot be completely identical with the text, or with the realization of the text, but in fact must lie halfway between the two.
4. The literary work has two poles, which we might call the artistic and the aesthetic; the artistic refers to the text created by the author, and the aesthetic to the realization accomplished by the reader.

Correct Answer:

4321

Step-by-Step Solution

Key idea: This is a Culture, Literature and Textual Sequencing question dealing with literary theory (reader-response theory). It follows a strict definitional structure: introducing poles, deducing the midpoint, defining the convergence, and concluding with the nature of the work.

Why this method applies: Sentence 3 begins with "From this polarity it follows," which strictly mandates that it follows a sentence defining a "polarity." Sentence 4 defines the "two poles."

Step 1: Identify the opener. Sentence 4 introduces the "two poles" of the literary work: the artistic (text) and the aesthetic (realization). This is a self-contained definition that requires no prior context.

Step 2: Attach the deduction. Sentence 3 starts with "From this polarity it follows" and concludes that the work must lie "halfway between the two." The phrase "this polarity" directly references the "two poles" in Sentence 4. This locks 4-3.

Step 3: Define the midpoint. Sentence 2 explains that the "convergence of text and reader" brings the work into existence, and that it is neither just the text nor just the reader. This defines the "halfway" point mentioned in Sentence 3.

Step 4: Conclude the nature of the work. Sentence 1 states that the work is "more than the text" because the text only takes on life when realized. This elaborates on the convergence described in Sentence 2 and serves as the concluding insight.

Common trap: Placing Sentence 1 before Sentence 2 breaks the logical flow from defining the convergence to explaining why the work is more than just the text.

Answer: 4321

Question 4 · Verbal Ability and Reading Comprehension NAT

The four sentences (labelled 1, 2, 3 and 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
1. Look forward a few decades to an invention which can end the energy crisis, change the global economy and curb climate change at a stroke: commercial fusion power.
2. To gain meaningful insights, logic has to be accompanied by asking probing questions of nature through controlled tests, precise observations and clever analysis.
3. The greatest of all inventions is the über-invention that has provided the insights on which others depend: the modern scientific method.
4. This invention is inconceivable without the scientific method; it will rest on the application of a diverse range of scientific insights, such as the process transforming hydrogen into helium to release huge amounts of energy.

Correct Answer:

3214

Step-by-Step Solution

Key idea: This is a Science and Technology sequencing question moving from a general concept to a specific future application. It uses an "über-invention" to specific invention structure.

Why this method applies: Sentence 4 begins with "This invention", which must refer to a specific invention mentioned in the preceding sentence. Sentence 1 introduces "commercial fusion power", making 1 the mandatory predecessor to 4.

Step 1: Establish the foundational concept. Sentence 3 introduces the "über-invention": the modern scientific method. This is the broadest statement and sets the theme.

Step 2: Elaborate on the foundation. Sentence 2 explains what the scientific method entails: logic accompanied by probing questions and controlled tests. Thus, 3 is followed by 2.

Step 3: Introduce the specific application. Sentence 1 asks the reader to look forward to a specific invention: commercial fusion power.

Step 4: Link the specific to the general. Sentence 4 states that "This invention" (fusion power) is inconceivable without the scientific method and relies on insights like transforming hydrogen into helium.

Answer: 3214

Question 5 · Verbal Ability and Reading Comprehension NAT

The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
1. A popular response is the exhortation to plant more trees.
2. It seems all but certain that global warming will go well above two degrees—quite how high no one knows yet.
3. Burning them releases it, which is why the scale of forest fires in the Amazon basin last year garnered headlines.
4. This is because trees sequester carbon by absorbing carbon dioxide.

Correct Answer:

2143

Step-by-Step Solution

Key idea: This is a Problem-Solution-Complication sequencing question, recognisable because it moves from a macro problem to a proposed solution, its rationale, and finally a complication.

Why this method applies: Sentence 1 mentions "A popular response," which requires a preceding problem. Sentence 3 contains unresolved pronouns ("them," "it") that must follow the introduction of "trees" and "carbon."

Step 1: Identify the opening context. Sentence 2 introduces the broad problem: global warming will go well above two degrees. This sets the stage without backward references.

Step 2: Connect the proposed solution. Sentence 1 introduces "a popular response" to this problem: the exhortation to plant more trees. The phrase "a popular response" implies a problem has already been stated. Thus, 2 is followed by 1.

Step 3: Explain the rationale. Sentence 4 explains why planting trees is a response: "This is because trees sequester carbon by absorbing carbon dioxide." The phrase "This is because" directly supports Sentence 1.

Step 4: Introduce the complication. Sentence 3 states "Burning them releases it," where "them" refers to the trees mentioned in Sentences 4 and 1, and "it" refers to the carbon mentioned in Sentence 4. This provides the counter-point about forest fires.

Common trap: Starting with 1 leaves "A popular response" without a preceding problem. Placing 3 before 4 leaves "them" and "it" without clear antecedents.

Answer: 2143

Question 6 · Data Interpretation and Logical Reasoning NAT

Common Description: At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu.
At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3.
The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher.
1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4.
2. Dolly and Falguni were the only employees who got the same rating across all the quarters.
3. The following is known about ratings given by Lalu:
• Bunty received a rating of 1 in Quarter 2.
• Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3. For how many employees can the scores at the end of Quarter 3 be determined with certainty?

Correct Answer:

Step-by-Step Solution

Key idea: This is a full-system simulation problem asking "for how many employees is the score determined with certainty?" We recognise it because the tight coupling of promotion/demotion rules across 6 employees over 3 quarters creates a nearly unique timeline.

Step 1: Establish Quarter 1 Baseline.

Elite: {A, B, C}. Novice: {D, E, F}.

Constants: D=2 always, F=3 always (derived from P4 analysis: F must be promoted Q1 to avoid distinctness clash in Q2).

Since F=3 in Q1, E must be 1 in Q1 (distinct {1,2,3}).

Elite Q1: B=1 (demoted). Remaining {2,3} for A, C.

Step 2: Simulate Transitions.

End Q1:

Novice Max (F=3) promoted.
Elite Min (B=1) demoted.

Q2 Start: Elite {A, C, F}, Novice {B, D, E}.

Q2 Ratings:

Novice {B, D, E}: B=1 (given), D=2 (const). E must be 3.

Elite {A, C, F}: F=3 (const). Remaining {1, 2} for A, C.

Who moves End Q2?

Novice Scores (Cumulative):

B: $1 + 1 = 2$ .

D: $2 + 2 = 4$ .

E: $1 + 3 = 4$ .

Tie D vs E. Latest rating: E(3) > D(2). E promoted.

Elite Scores (Cumulative):

F: $3 + 3 = 6$ .

A and C scores are roughly 3-5.

One of {A, C} is demoted.

Step 3: Analyze Certainty via Global Constraint.

Clue 1: A, B, C are ALL in Novice at start of Q4.

This means A and C must BOTH be demoted eventually.

Since one was demoted at Q2, the OTHER must be demoted at Q3.

This strict choreography fixes every quarterly rating for every person.

For instance, Asha rated 1 in Q3. Whether she is in Elite or Novice, this combined with the forced demotion path resolves the A/C symmetry.

Since the entire timeline is uniquely determined by the intersection of local rules and the global Q4 boundary condition, the scores for ALL 6 employees are certain.

Answer: 6

Question 7 · Data Interpretation and Logical Reasoning NAT

Common Description: Instructions [42 - 46]
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.
The following additional information is known.
1. Xena trained more players than Yuki.
2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
4. The average of the ratings of all the players was 4.
5. Player-2 got the highest rating.
6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
7. Player-4's rating was double of Player-8's and less than Player-5's. What was the rating of Player-7?

Correct Answer:

Step-by-Step Solution

Key idea: This is an evaluation-matrix question mixing group counts, averages, and rating constraints. It is recognisable because the number of players coached by each coach and the average ratings must satisfy integer constraints.

Step 1: Define counts and averages.

Let $n_{X}, n_{Y}, n_{Z}$ be the numbers of players trained by Xena, Yuki, and Zara.

Let $a_{X}, a_{Y}, a_{Z}$ be their average ratings.

We are given $n_{X} + n_{Y} + n_{Z} = 8$ , each coach has at least 2 players, and $n_{X} > n_{Y}$ .

Also $a_{Y} = 2 a_{X}$ and $a_{Y} = a_{Z} + 2$ , so $a_{Z} = 2 a_{X} - 2$ .

Step 2: Use the count condition.

If $n_{Y} = 3$ , then $n_{X} \geq 4$ and $n_{Z} \geq 2$ , making the total at least 9, impossible.

Therefore $n_{Y} = 2$ .

Then $n_{X}$ can be 3 or 4, and $n_{Z}$ can be 3 or 2 respectively.

Step 3: Use the average equation.

Total rating sum is $8 \times 4 = 32$ .

If $n_{X} = 3$ and $n_{Z} = 3$ , then $3 a_{X} + 2 (2 a_{X}) + 3 (2 a_{X} - 2) = 32 ⟹ 13 a_{X} - 6 = 32 ⟹ a_{X} = 38/13$ .

Since ratings are integers, each group's total must be an integer. Hence this case is impossible.

Step 4: Take the remaining count case.

Therefore $n_{X} = 4$ and $n_{Z} = 2$ .

Check the averages: $4 a_{X} + 2 (2 a_{X}) + 2 (2 a_{X} - 2) = 32 ⟹ 12 a_{X} - 4 = 32 ⟹ a_{X} = 3$ .

Then $a_{Y} = 6$ and $a_{Z} = 4$ .

Group totals are Xena 12, Yuki 12, Zara 8.

Step 5: Assign coaches and ratings.

Player-1 and Player-4 must have the same coach. Since Player-1 is odd and Player-4 is even, only Xena can coach both.

Yuki trains only evens. Since P4 is Xena, Yuki must train two from {P2, P6, P8}. Sum = 12. Max rating is 7, so the ratings must be 5 and 7.

Zara trains only odds. Zara has 2 players. Sum = 8.

Player-5 and Player-7 are trained by the same coach and got the same rating. Since they are odd, they must be trained by Zara. Thus P5 and P7 are Zara's players, and their ratings are 4 and 4 (sum = 8).

The rating of Player-7 is 4.

Answer: 4

Question 8 · Quantitative Ability MCQ

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

A.
11.5
B.
10
C.
12.5
D.
12

Correct Answer:

Step-by-Step Solution

Key idea: this is a work-rate question with different working durations. Work completed equals rate multiplied by time, and the same total work can be expressed in two different scenarios.

Step 1: Define rates.

Let Rahul’s rate be $r$ work per hour.

Let Gautam’s rate be $g$ work per hour.

Step 2: Calculate actual working hours.

Rahul starts at 9 AM and works till 5 PM, so Rahul works 8 hours.

Gautam joins at 11 AM and works till 5 PM, so Gautam works 6 hours.

Therefore, actual work done is:

$W = 8 r + 6 g .$

Step 3: Use the hypothetical scenario.

If both had started at 9 AM and worked together, they would have finished 30 minutes earlier than 5 PM, i.e. at 4:30 PM.

From 9 AM to 4:30 PM is 7.5 hours.

So in the hypothetical case:

$W = 7.5 (r + g) .$

Step 4: Equate the two expressions for the same work.

$8 r + 6 g = 7.5 (r + g) .$

Expand the right side:

$8 r + 6 g = 7.5 r + 7.5 g .$

Bring terms together:

$8 r - 7.5 r = 7.5 g - 6 g .$

$0.5 r = 1.5 g .$

Multiply by 2:

$r = 3 g .$

Step 5: Find the total work in terms of $g$ .

Substitute $r = 3 g$ into $W = 8 r + 6 g$ :

$W = 8 (3 g) + 6 g = 24 g + 6 g = 30 g .$

Step 6: Find Rahul’s alone time.

Rahul’s rate is $r = 3 g$ .

Time taken by Rahul alone:

$\frac{W}{r} = \frac{30 g}{3 g} = 10 hours .$

Answer: Option B, 10.

Common trap: using the wrong number of hours. Gautam did not work 8 hours in the actual case; he worked only 6 hours because he joined at 11 AM.

Question 9 · Quantitative Ability MCQ

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

A.
6
B.
15
C.
10
D.
12

Correct Answer:

Step-by-Step Solution

Key idea: this is a two-train meeting question, recognisable because trains start from opposite stations, meet, and then continue to the opposite stations.

Step 1: Let train A's speed be $a$ and train B's speed be $b$ . Let them meet after $t$ minutes.

Step 2: The question says train A reaches station Y in 10 minutes. This means A's total time from X to Y is 10 minutes. So the full distance XY is:

$X Y = 10 a .$

Step 3: Before meeting, A travels for $t$ minutes, so A covers:

$XM = a t .$

B also travels for $t$ minutes, so B covers:

$YM = b t .$

Step 4: After meeting, train B must cover the remaining distance from M to X. That distance is exactly the distance A had covered before meeting:

$MX = a t .$

Step 5: Train B takes 9 minutes after meeting to reach X. Therefore:

$9 b = a t .$

So:

$t = \frac{9 b}{a} .$

Step 6: The whole distance XY is also the sum of distances covered before meeting:

$a t + b t = 10 a .$

Factor:

$t (a + b) = 10 a .$

Step 7: Substitute $t = \frac{9 b}{a}$ :

$\frac{9 b}{a} (a + b) = 10 a .$

Step 8: Let $r = \frac{b}{a}$ . Then:

$9 r (1 + r) = 10.$

Expand:

$9 r + 9 r^{2} = 10.$

$9 r^{2} + 9 r - 10 = 0.$

Step 9: Solve the quadratic:

$r = \frac{- 9 + 81 + 360}{18} = \frac{- 9 + 441}{18} = \frac{- 9 + 21}{18} = \frac{12}{18} = \frac{2}{3} .$

The negative root is impossible for speed.

Step 10: So:

$b = \frac{2}{3} a .$

Step 11: Train B's total time from Y to X is:

$\frac{X Y}{b} = \frac{10 a}{\frac{2}{3} a} = 10 \times \frac{3}{2} = 15 minutes .$

Answer: option B.

Question 10 · Quantitative Ability MCQ

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is

A.
90
B.
120
C.
75
D.
60

Correct Answer:

Step-by-Step Solution

Key idea: This is a fill pipes, drain pipe, and switch-off question, recognisable because multiple pipes with different roles operate under different timing scenarios, giving equations to find individual rates.

Why this method: Each scenario gives one equation in the pipe rates. We solve the system, then use the constraint on Pipe A's time to select the valid solution.

Step-by-step working:

Define rates:

Pipe A fills in $a$ hours: rate = $\frac{1}{a}$
Pipe B empties in $b = a - 1$ hours: rate = $- \frac{1}{a - 1}$
Pipe C fills in $c$ hours: rate = $\frac{1}{c}$

Equation from scenario 1 (A, B, C together fill in 2 hours):

$\frac{1}{a} - \frac{1}{a - 1} + \frac{1}{c} = \frac{1}{2}$ ... (1)

Equation from scenario 2 (B and C for 1 hour, then C alone for 1.25 hours):

$1 \times (- \frac{1}{a - 1} + \frac{1}{c}) + 1.25 \times \frac{1}{c} = 1$
$- \frac{1}{a - 1} + \frac{1}{c} + \frac{5}{4 c} = 1$
$- \frac{1}{a - 1} + \frac{9}{4 c} = 1$ ... (2)

Simplify equation (1):

$\frac{1}{c} = \frac{1}{2} - \frac{1}{a} + \frac{1}{a - 1} = \frac{1}{2} + \frac{1}{a ( a - 1 )}$ ... (1')

From equation (2):

$\frac{9}{4 c} = 1 + \frac{1}{a - 1} = \frac{a}{a - 1}$
$\frac{1}{c} = \frac{4 a}{9 ( a - 1 )}$ ... (2')

Set (1') = (2') and solve:

$\frac{1}{2} + \frac{1}{a ( a - 1 )} = \frac{4 a}{9 ( a - 1 )}$
Multiply by $18 a (a - 1)$ :
$9 a (a - 1) + 18 = 8 a^{2}$
$9 a^{2} - 9 a + 18 = 8 a^{2}$
$a^{2} - 9 a + 18 = 0$
$(a - 3) (a - 6) = 0$
$a = 3$ or $a = 6$

Apply constraint $a < 5$ :

$a = 3$

Find $c$ :

From (2'): $\frac{1}{c} = \frac{4 \times 3}{9 \times 2} = \frac{12}{18} = \frac{2}{3}$
$c = \frac{3}{2}$ hours = 90 minutes

Answer: Pipe C takes 90 minutes to fill the empty tank.

Question 11 · Quantitative Ability MCQ

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

A.
20
B.
17
C.
16
D.
21

Correct Answer:

Step-by-Step Solution

Key idea: This is a bounds from more-than and less-than question, recognisable because inequality constraints on combined times give a range for an individual worker's time, and we identify which option falls outside that range.

Why this method: The work equation gives an exact relationship. The inequality constraints bound the rates, which bound Rakshita's solo time.

Step-by-step working:

Define rates:

Let Rahul's rate = $r$ , Rakshita's rate = $k$ , Gurmeet's rate = $g$ (work per day)

Write the work equation:

All three work 6 days, then Rakshita alone 3 days:
$6 (r + k + g) + 3 k = 1$
$6 (r + g) + 9 k = 1$ ... (*)

Let $p = r + g$ (combined rate of Rahul and Gurmeet):

From (*): $6 p + 9 k = 1$ , so $k = \frac{1 - 6 p}{9}$

Apply constraint 1: All three take more than 7 days:

$\frac{1}{p + k} > 7$ , so $p + k < \frac{1}{7}$
$p + \frac{1 - 6 p}{9} < \frac{1}{7}$
$\frac{9 p + 1 - 6 p}{9} < \frac{1}{7}$
$\frac{3 p + 1}{9} < \frac{1}{7}$
$7 (3 p + 1) < 9$
$21 p < 2$
$p < \frac{2}{21}$

Apply constraint 2: Rahul and Gurmeet take less than 15 days:

$\frac{1}{p} < 15$ , so $p > \frac{1}{15}$

Find the range of Rakshita's time:

Rakshita's time = $\frac{1}{k} = \frac{9}{1 - 6 p}$
When $p = \frac{1}{15}$ : $\frac{1}{k} = \frac{9}{1 - 6/15} = \frac{9}{3/5} = 15$
When $p = \frac{2}{21}$ : $\frac{1}{k} = \frac{9}{1 - 12/21} = \frac{9}{3/7} = 21$
Since $\frac{1}{15} < p < \frac{2}{21}$ , we get $15 < \frac{1}{k} < 21$

Check the options:

20: in $(15, 21)$ ✓ possible
17: in $(15, 21)$ ✓ possible
16: in $(15, 21)$ ✓ possible
21: NOT in $(15, 21)$ since the upper bound is strict

Answer: Rakshita's time cannot be 21 days.

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Arithmetic, LOGICAL REASONING, VERBAL ABILITY Unit Test for CAT: 68 Questions with Solutions & Analysis

Attempt the Arithmetic, LOGICAL REASONING, VERBAL ABILITY Unit Test for CAT: 68 exam-level questions, detailed solutions and performance analysis. First quest

68 Qs

Total Questions

204 Marks

Total Marks

93.28 Mins

Duration

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Marking Scheme

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Quantitative Ability

27 Qs

40% of total marks

Data Interpretation and Logical Reasoning

22 Qs

32% of total marks

Verbal Ability and Reading Comprehension

19 Qs

28% of total marks

Free Solved Questions with Step-by-Step Solutions

Authentic examination problems with detailed derivations and answer keys.

Question 1

Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer. 1. Boa Senior, who lived through the 2004 tsunami, the Japanese occupation and diseases brought by British settlers, was the last native of the island chain who was fluent in Bo. 2. The indigenous population has been steadily collapsing since the island chain was colonised by British settlers in 1858 and used for most of the following 100 years as a colonial penal colony. 3. Taking its name from a now-extinct tribe, Bo is one of the 10 Great Andamanese languages, which are thought to date back to pre-Neolithic human settlement of south-east Asia. 4. The last speaker of an ancient tribal language has died in the Andaman Islands, breaking a 65,000-year link to one of the world's oldest cultures. 5. Though the language has been closely studied by researchers of linguistic history, Boa Senior spent the last few years of her life unable to converse with anyone in her mother tongue.

Question 2

Five jumbled up sentences, related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd one out and key in the number of the sentence as your answer: 1. The care with which philosophers examine arguments for and against forms of biotechnology makes this an excellent primer on formulating and assessing moral arguments. 2. Although most people find at least some forms of genetic engineering disquieting, it is not easy to articulate why: what is wrong with re-engineering our nature? 3. Breakthroughs in genetics present us with the promise that we will soon be able to prevent a host of debilitating diseases, and the predicament that our newfound genetic knowledge may enable us to enhance our genetic traits. 4. To grapple with the ethics of enhancement, we need to confront questions that verge on theology, which is why modern philosophers and political theorists tend to shrink from them. 5. One argument is that the drive for human perfection through genetics is objectionable as it represents a bid for mastery that fails to appreciate the gifts of human powers and achievements.

Question 3

The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer: 1. The work is more than the text, for the text only takes on life, when it is realized and furthermore the realization is by no means independent of the individual disposition of the reader. 2. The convergence of text and reader brings the literary work into existence and this convergence is not to be identified either with the reality of the text or with the individual disposition of the reader. 3. From this polarity it follows that the literary work cannot be completely identical with the text, or with the realization of the text, but in fact must lie halfway between the two. 4. The literary work has two poles, which we might call the artistic and the aesthetic; the artistic refers to the text created by the author, and the aesthetic to the realization accomplished by the reader.

Question 4

The four sentences (labelled 1, 2, 3 and 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer: 1. Look forward a few decades to an invention which can end the energy crisis, change the global economy and curb climate change at a stroke: commercial fusion power. 2. To gain meaningful insights, logic has to be accompanied by asking probing questions of nature through controlled tests, precise observations and clever analysis. 3. The greatest of all inventions is the über-invention that has provided the insights on which others depend: the modern scientific method. 4. This invention is inconceivable without the scientific method; it will rest on the application of a diverse range of scientific insights, such as the process transforming hydrogen into helium to release huge amounts of energy.

Question 5

The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer: 1. A popular response is the exhortation to plant more trees. 2. It seems all but certain that global warming will go well above two degrees—quite how high no one knows yet. 3. Burning them releases it, which is why the scale of forest fires in the Amazon basin last year garnered headlines. 4. This is because trees sequester carbon by absorbing carbon dioxide.

Question 6

Common Description: At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher. 1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4. 2. Dolly and Falguni were the only employees who got the same rating across all the quarters. 3. The following is known about ratings given by Lalu: • Bunty received a rating of 1 in Quarter 2. • Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3. For how many employees can the scores at the end of Quarter 3 be determined with certainty?

Question 7

Common Description: Instructions [42 - 46] Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest. The following additional information is known. 1. Xena trained more players than Yuki. 2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different. 3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating. 4. The average of the ratings of all the players was 4. 5. Player-2 got the highest rating. 6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara. 7. Player-4's rating was double of Player-8's and less than Player-5's. What was the rating of Player-7?

Question 8

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

Question 9

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

Question 10

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is

Question 11

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

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