Ashoka Aptitude Assessment PYQ Paper 1

Q1Arithmetic › Time, Speed & DistanceMedium

An Ashoka student cycles $90$ km at $45$ km/h, then travels $120$ km by bus at $60$ km/h, and finally takes a cab for $90$ km at $90$ km/h. What is the average speed for the entire journey?

Correct option D $60$ km/h

Average speed is total distance over total time, not the average of the three speeds.

Distance: $90 + 120 + 90 = 300$ km.

Time: $\frac{90}{45} + \frac{120}{60} + \frac{90}{90} = 2 + 2 + 1 = 5$ hours.

Average speed $= \frac{300}{5} = 60$ km/h.

The Fast Way

Average speed is total distance over total time, and here every leg's time is a whole number.

Times: $\frac{90}{45} = 2$ , $\frac{120}{60} = 2$ , $\frac{90}{90} = 1$ , so $300$ km in $5$ hours.

So the average speed is $60$ km/h (65 is the plain mean of the speeds, the trap).

Q2Critical Reasoning › Argument StructureEasy

"In a recent news report on crime rates, it was mentioned that there's been an increase in crime in cities that have recently implemented stricter gun control laws. This clearly demonstrates that gun control doesn't work and, in fact, leads to higher crime rates. The data speaks for itself, showing that when citizens are disarmed, criminals are emboldened, and crime rises. Therefore, it's evident that the solution to reducing crime is to relax or eliminate gun control measures."

Which of the following is definitely a flaw in the argument presented in the paragraph?

Correct option BThe argument assumes a direct causal relationship based on a correlation.

The argument notes two things together, stricter gun laws and more crime in some cities, and concludes that the laws caused the crime.

That is a causal claim built on a correlation: crime may have been rising already (perhaps why the laws were passed), or something else may explain both.

'Fails to mention any data' is wrong, since it cites a news report, and the sample size and emotional tone are not definitely flaws from what is given.

So the definite flaw is that it assumes a direct causal relationship based on a correlation.

The Fast Way

Spot the 'together, therefore because' jump.

Crime rose where stricter laws arrived and the argument blames the laws: the classic correlation-causation flaw.

So: it assumes a direct causal link from a correlation.

Q3Geometry › MensurationEasy

For an art installation, a triangular metal frame has a right angle at one corner. The two arms forming the right angle are 20 cm and 21 cm long. What is the area of the triangular frame?

Correct option D210 sq. cm

In a right triangle, the two arms that meet at the right angle work as the base and the height.

Area $= \frac{1}{2} \times 20 \times 21 = 210$ sq. cm.

You do not need the hypotenuse at all here. The answer is D.

The Fast Way

The two arms at the right angle are base and height; ignore the hypotenuse.

Halve the even arm first: $10 \times 21$ .

So the area is $210$ sq. cm.

Q4Logical Reasoning › SeriesEasy

In a non-verbal figure series, each figure is a square containing an arrow and small black dots on its boundary. Figure 1 has an arrow pointing up and 1 dot at the top-left corner. Figure 2 has the arrow pointing right and 2 dots at the top-left and top-right corners. Figure 3 has the arrow pointing down and 3 dots at the top-left, top-right, and bottom-right corners. Figure 4 has the arrow pointing left and 4 dots, one at each corner. Which figure should come next?

Correct option DArrow pointing up with 5 dots, four corners plus one at the midpoint of the top side

Track two things separately: the arrow and the dots.

The arrow turns $90^\circ$ clockwise each time: up, right, down, left. So the next arrow points up again.

The dots go 1, 2, 3, 4, so the next figure needs 5 dots.

Only one option has an upward arrow with 5 dots: four corners plus one on the top side.

Option A has the correct (upward) arrow but only 4 dots, so it breaks the counting rule. The answer is D.

The Fast Way

Track the two features separately and let each one kill options.

Arrow turns $90^\circ$ clockwise (up, right, down, left), so next is up: the left and right arrows die. Dots go 1, 2, 3, 4, so next has 5: the 4-dot figure dies.

So the next figure has the arrow pointing up with 5 dots, four corners plus one on the top side.

Q5Geometry › MensurationEasy

A design club is making a circular badge with diameter 28 cm. A $90^\circ$ sector of the badge is coloured blue. Using $\pi = \frac{22}{7}$ , what is the area of the blue sector?

Correct option A154 cm²

The radius is half the diameter: $r = 14$ cm.

Full circle: $\pi r^2 = \frac{22}{7} \times 14 \times 14 = 616$ cm².

A $90^\circ$ sector is $\frac{90}{360} = \frac{1}{4}$ of the circle.

Blue area $= \frac{616}{4} = 154$ cm², so the answer is A.

Careful: 616 is the whole badge, not the sector.

The Fast Way

A $90^\circ$ sector is a quarter circle: cancel before you multiply.

$\frac{1}{4} \times \frac{22}{7} \times 14 \times 14 = 22 \times \frac{14 \times 14}{28} = 22 \times 7$ .

So the blue sector is $154$ cm² (616 is the whole badge).

Q6Logical Reasoning › Direction SenseEasy

A student walks 9 km east from the library to a café, then turns left and walks 12 km to a bookstore. From there, she turns left again and walks 4 km to a bus stop. What is her shortest distance from the library, and in which direction is she now from the library?

Correct option B13 km, North-East

Put the library at $(0, 0)$ , with east as $+x$ and north as $+y$ .

9 km east takes her to $(9, 0)$ . A left turn while facing east means facing north, so 12 km takes her to $(9, 12)$ .

Another left turn means facing west, so 4 km takes her to $(5, 12)$ .

Distance $= \sqrt{5^2 + 12^2} = \sqrt{169} = 13$ km.

She is still east and north of the library, so she is North-East of it. The answer is B.

The Fast Way

Net displacement: add the east-west moves and the north-south moves, then look for a triplet.

East $9 - 4 = 5$ (the second left faces west), north $12$ : that is the 5-12-13 triplet.

Both are positive, so she is $13$ km, North-East.

Q7Arithmetic › Mixture & AlligationEasy

A café wants to make a 32 kg blend of coffee worth ₹530 per kg by mixing premium coffee worth ₹680 per kg with house coffee worth ₹440 per kg. How many kg of premium coffee should be used?

Correct option A12 kg

Let $p$ kg be premium coffee, so $32 - p$ kg is house coffee.

The total value must match: $680p + 440(32 - p) = 530 \times 32$ .

So $240p + 14080 = 16960$ , which gives $240p = 2880$ and $p = 12$ .

The Fast Way

Alligation cross: put the target price in the middle.

Premium : house $= (530 - 440) : (680 - 530) = 90 : 150 = 3 : 5$ .

Premium is $\frac{3}{8}$ of $32$ , so $12$ kg.

Q8Logical Reasoning › Direction SenseMedium

From the library entrance, Mira walks 4 km east, then turns left and walks 9 km, then turns right and walks 8 km, and finally turns right and walks 4 km. What is her straight-line distance from the library entrance, and in which direction is she now?

Correct option D13 km, north-east

Start at $(0, 0)$ , with east as $+x$ and north as $+y$ .

4 km east: $(4, 0)$ . Turning left means facing north, 9 km: $(4, 9)$ .

Turning right means facing east, 8 km: $(12, 9)$ . Turning right again means facing south, 4 km: $(12, 5)$ .

Distance $= \sqrt{12^2 + 5^2} = \sqrt{169} = 13$ km.

She is both east and north of the entrance, so the answer is D: 13 km, north-east.

The Fast Way

Net displacement: total the east moves and the north moves.

East $4 + 8 = 12$ , north $9 - 4 = 5$ : the 5-12-13 triplet.

Both positive, so she is $13$ km, north-east.

Q9Arithmetic › Mean, Median & ModeMedium

The numbers of start-up ideas submitted by seven student groups in a week were: $6, 8, 5, x, 7, 8$ , and $9$ . If the mean number of submissions was $7$ , what was the median number of submissions?

Correct option B $7$

A mean of $7$ over $7$ groups means the total is $7 \times 7 = 49$ .

The known values add to $6 + 8 + 5 + 7 + 8 + 9 = 43$ , so $x = 49 - 43 = 6$ .

In order: $5, 6, 6, 7, 8, 8, 9$ .

With $7$ values the median is the $4$ th one, which is $7$ .

Insight: a mean hands you a total; use it to unlock the missing value, then sort before reading the median.

The Fast Way

Deviation method: the deviations from the mean $7$ must add to zero.

Known deviations $-1, +1, -2, 0, +1, +2$ sum to $+1$ , so $x$ is $1$ below $7$ : $x = 6$ .

Sorted $5, 6, 6, 7, 8, 8, 9$ : the middle (4th) value is $7$ .

Q10Critical Reasoning › Assessing EvidenceEasy

Niyati wants to understand how safe women in her country feel. She finds some resources online.

P - A book about women Prime Ministers that the country has had.

Q - A documentary about women's experiences using public transportation.

R - A detailed report about the participation of women in the police force.

S - An article discussing the laws that protect women's rights in the workforce.

Which of the following (combinations of) resources will she DEFINITELY need in order to get the most accurate information?

Correct option BOnly Q

Niyati's question is how safe women feel, which is about women's own experience.

The documentary on women's experiences of using public transportation records exactly that, so it is the resource she must have.

The book on women Prime Ministers, the report on women in the police and the article on workplace laws describe leaders, jobs and rules, not how safe women feel day to day.

So she will definitely need only Q.

The Fast Way

Match the evidence to the exact question: 'feel' calls for women's own experiences.

Only the documentary records feelings; the rest are about laws, careers and leaders.

So the answer is Only Q.

Q11Number System › Number PropertiesHard

An event team is numbering the entry passes from 1 to 350. How many times does the digit ‘3’ appear in all the pass numbers written?

Correct option B126

Count the 3s place by place.

Units place: $3, 13, 23, \ldots, 343$ gives 35 threes.

Tens place: 30 to 39, 130 to 139, 230 to 239 and 330 to 339 give $4 \times 10 = 40$ threes.

Hundreds place: 300 to 350 gives 51 threes.

Total $= 35 + 40 + 51 = 126$ , so the answer is B.

A number like 333 is handled correctly, because each of its 3s is counted in its own place.

The Fast Way

Each full block of 100 has $20$ threes: 10 in the units place, 10 in the tens place.

$1$ to $299$ : $3 \times 20 = 60$ . $300$ to $350$ : $51$ in the hundreds place, $5$ in the units (303 to 343), $10$ in the tens (330 to 339).

$60 + 51 + 5 + 10 = 126$ .

Q12Logical Reasoning › PuzzlesMedium

Six founders, Asha, Dev, Farah, Kabir, Meera, and Rohan, live on different floors of a 6-floor startup residence, with floor 1 being the lowest and floor 6 being the highest. Kabir lives on floor 2. Farah lives immediately below Rohan. Rohan does not live on the top floor. Meera lives somewhere above Dev, and Asha lives somewhere above Meera. Dev lives on an odd-numbered floor. Who lives on the top floor?

Correct option AAsha

Kabir is on 2, Dev is on an odd floor, and the order Dev < Meera < Asha must hold.

Dev cannot be on 5: Meera would be on 6 with no room above for Asha.

If Dev is on 3, the free floors are 1, 4, 5, 6. Farah and Rohan need consecutive floors with Rohan not on 6, so they take 4 and 5. Then Meera must be on 6 (above Dev), leaving no room for Asha. Impossible.

So Dev is on 1. Farah and Rohan take 3 and 4, or 4 and 5, and Meera and Asha fill the other two floors with Asha higher.

Either way, Asha is on floor 6. The answer is A.

The Fast Way

Ask who can be on top: the top-floor person has nobody above.

Dev has Meera above, Meera has Asha above, Farah has Rohan above, Rohan is not on top, Kabir is on 2.

Only Asha is left, so Asha lives on the top floor.

Q13Algebra › Quadratic EquationsMedium

A student team wants to set up a rectangular food stall against a long wall, so fencing is needed only for the front and the two sides. They have 72 metres of fencing. What is the maximum possible area of the stall?

Correct option C648 sq. m

Let each side be $y$ m and the front be $x$ m. Fencing: $x + 2y = 72$ , so $x = 72 - 2y$ .

Area $A = y(72 - 2y) = 72y - 2y^2$ .

This downward parabola peaks at $y = \frac{72}{2 \times 2} = 18$ , which gives $x = 36$ .

Maximum area $= 36 \times 18 = 648$ sq. m, so the answer is C.

The Fast Way

Wall on one side: the best front is half the fencing and each side a quarter.

Front $= 36$ , each side $= 18$ .

Area $= 36 \times 18 = 648$ sq. m (36 and 18 are lengths, not the area).

Q14Critical Reasoning › Statements & InferencesEasy

Classify the following statements as Fact (F), Judgment (J), or Inference (I). Statements: 1. The new student-run café at Nivaan University sold 1,200 cups of cold coffee in its first week. 2. The café is clearly the most exciting campus initiative this year. 3. Since cold coffee outsold tea by three to one, students at Nivaan seem to prefer cold beverages during afternoon breaks. 4. The café remains open from 9 a.m. to 7 p.m. on weekdays.

Correct option AFJIF

A fact can be checked, a judgement is an opinion, and an inference is a conclusion drawn from evidence.

1. The number of cups sold can be counted and checked: Fact.

2. 'Clearly the most exciting' is a personal opinion: Judgement.

3. It uses data (cold coffee outsold tea 3 to 1) to reach a conclusion about preferences, signalled by 'since' and 'seem to': Inference.

4. Opening hours can be verified: Fact.

That gives FJIF, option A.

The Fast Way

Fix the easy facts first, then let them kill options.

1 (cups sold) and 4 (opening hours) can be checked, so F _ _ F; the option starting with J dies.

2 says 'clearly the most exciting', an opinion, so J; 3 reasons from data with 'since' and 'seem to', so I.

So the code is FJIF.

Q15Critical Reasoning › Statements & InferencesMedium

Adriana Petryna, in a book about the Chernobyl nuclear disaster, coined the term "Biological Citizenship". This refers to the ways in which Ukrainian citizens in Chernobyl-affected regions negotiate with state institutions based on their perceived levels of radiation exposure, to avail the benefits that are, on paper, offered to all citizens. For instance, some may undergo complex medical examinations and tests to prove their radiation exposure and establish their eligibility for state-provided compensation as "Chernobyl-sufferers".

One's citizenship status, generally, comes with certain rights and guaranteed access to state amenities. Based on the above passage, what does citizenship DEFINITELY mean for "Chernobyl-sufferers" in Ukraine?

Correct option CThe benefits of citizenship are dependent on their ability to prove suffering.

In the passage, citizens in Chernobyl-affected regions must prove their radiation exposure, through medical tests, to get benefits that are on paper offered to all citizens.

So for these citizens, getting the benefits of citizenship depends on proving their suffering. That is what the passage definitely shows.

The strongest traps say they become political citizens only after proving suffering, or have only biological citizenship. The passage never says they lack political citizenship; they are already citizens negotiating for benefits.

That benefits are easily available only to non-sufferers is never stated.

So for 'Chernobyl-sufferers', the benefits of citizenship are dependent on their ability to prove suffering.

The Fast Way

'Definitely' means restate the passage and add nothing.

Its example is people proving radiation exposure to qualify for compensation, which is benefits conditional on proof; the other options invent claims about political citizenship.

So: the benefits depend on their ability to prove suffering.

Q16Critical Reasoning › Argument StructureEasy

If a person claims that something is true, it is their responsibility to provide evidence in support of their assertion. It is incorrect to claim that something is true simply because nobody else has proved it wrong. For example, someone might claim that ghosts exist, but does not prove it. Instead, they shift the burden of proof to others, by stating that anyone who disagrees should prove ghosts don't exist. This is called the Burden of Proof fallacy, and it makes the proponent's argument invalid.

Glossary-

assertion: a statement that one believes to be true, used as part of an argument

Which of the following statements is an example of the Burden of Proof fallacy?

Correct option DMy brother claims that all of our family's land should pass on to him, and has challenged me to provide one reason why it should not.

The fallacy has two parts: someone makes a claim, and instead of proving it, demands that others disprove it.

The brother claims all the family land should pass to him, gives no reason, and challenges the speaker to give one reason why it should not. The burden has been shifted.

The test option is the strongest distractor, but the teacher's assumption rests on evidence (nobody answered correctly), so no burden is shifted.

The marketing option draws a conclusion from inconclusive data, and the construction-site option backs its claim with evidence (everyone who crossed at night was hurt); neither asks anyone to disprove a claim.

So the Burden of Proof example is the brother's claim to the family land.

The Fast Way

Look for the tell-tale move: 'prove me wrong'.

Only the brother makes a claim and then challenges the other person to argue against it.

So the example is the brother demanding a reason why the land should not pass to him.

Q17Arithmetic › Mixture & AlligationMedium

An 80-litre cooler contains a mango drink that is 75% mango pulp and 25% water. A vendor removes 20 litres of the mixture and replaces it with 20 litres of water. He repeats the same process one more time. What is the final ratio of mango pulp to water?

Correct option A27:37

Start: 80 L, with 60 L pulp and 20 L water.

Each round removes $\frac{20}{80} = \frac{1}{4}$ of the mixture, and only water goes back in, so the pulp keeps $\frac{3}{4}$ of itself each time.

After two rounds: pulp $= 60 \times \left(\frac{3}{4}\right)^2 = 60 \times \frac{9}{16} = 33.75$ L.

The volume is still 80 L, so water $= 80 - 33.75 = 46.25$ L.

Ratio $= 33.75 : 46.25 = 135 : 185 = 27 : 37$ , so the answer is A.

The Fast Way

Notice the starting 75% is itself $\frac{3}{4}$ , the same factor each swap keeps, so the pulp carries three such factors.

Pulp fraction $= \left(\frac{3}{4}\right)^3 = \frac{27}{64}$ , and the rest, $\frac{37}{64}$ , is water.

Pulp to water is 27 : 37.

Q18Logical Reasoning › Blood RelationsEasy

Priya is the only daughter of Harish. Harish is married to Leela. Dev is Priya’s brother. Asha is Dev’s spouse. Sam is Priya’s child, and Rohan is the child of Dev and Asha. What is Sam’s relationship to Rohan?

Correct option CCousin

Priya is Harish's only daughter and Dev is her brother, so Priya and Dev are siblings.

Sam is Priya's child, and Rohan is the child of Dev and his spouse Asha.

So Sam and Rohan are children of a sister and a brother, which makes them cousins. The answer is C.

'Brother' and 'sister' fail because they have different parents, and 'uncle' fails because both are grandchildren of Harish, the same generation.

The Fast Way

Generation check first: Sam and Rohan are both grandchildren of Harish, so 'Uncle' dies.

Sam is Priya's child and Rohan is Dev's child (through Asha), and Priya and Dev are siblings.

Children of siblings are cousins, so Sam is Rohan's Cousin.

Q19Algebra › Quadratic EquationsMedium

For a student startup’s pop-up stall, $60$ metres of branding tape is available to fence three sides of a rectangular space, with the fourth side along a wall. What is the maximum possible area of the stall?

Correct option C $450$ sq m

Let each side meeting the wall be $x$ m and the side parallel to the wall be $y$ m.

The tape covers three sides: $2x + y = 60$ , so $y = 60 - 2x$ .

Area $= x(60 - 2x) = 450 - 2(x - 15)^2$ .

This is largest when $x = 15$ , so $y = 30$ and the area is $15 \times 30 = 450$ sq m.

The Fast Way

Wall on one side: the side along the wall gets half the tape.

Parallel side $= 30$ , each side meeting the wall $= 15$ .

Area $= 30 \times 15 = 450$ sq m.

Q20Critical Reasoning › Statement & AssumptionMedium

The student council argues: “The university should extend the library’s closing time from 10 p.m. to midnight during internship season. Last year, when the library remained open till midnight for two weeks, more students submitted internship applications before the deadline. Therefore, longer library hours will help students complete applications on time this year too.” Which assumption does the argument depend on?

Correct option CThe increase in timely submissions last year was at least partly due to the extended library hours.

An assumption is something the argument needs: if it were false, the conclusion would collapse.

The argument jumps from 'longer hours and more on-time applications happened together last year' to 'longer hours cause on-time applications'.

That only works if the longer hours actually helped last year, which is option C. Negate it: if the rise had nothing to do with the library hours, last year's evidence gives no reason to extend them.

B is tempting, but it is too strong. The library does not have to be the only late-night workspace; longer hours could still help even if other spaces exist.

A and D miss the point: the argument is about submitting on time, not about getting better internships or what the university ought to do in general.

The Fast Way

Negate the assumption and see if the argument dies.

The argument goes from 'longer hours and more timely submissions happened together' to 'longer hours will help'. Negate 'the rise was at least partly due to the longer hours' and last year proves nothing.

So it depends on the increase in timely submissions being at least partly due to the extended library hours ('only place' is more than it needs).

Ashoka Aptitude Assessment · Paper 1

Logical, Quantitative & Critical Reasoning