NMIMS NPAT · Paper 1

20 MCQs · Quantitative Reasoning 7, Logical Reasoning 7, Verbal Reasoning 6

No negative marking and five options a question, as in the real test.

Tap an option to answer

Section 1 · Quantitative Reasoning

Q1Arithmetic › PercentagesEasy
A shop's sales rose by 20% in March over February and then fell by 15% in April over March. How did April's sales compare with February's?
Correct option A2% higher
Take February's sales as 100.
March: $100 \times 1.20 = 120$ .
April: $120 \times 0.85 = 102$ .
So April's sales are 2% higher than February's. Simply adding $20 - 15 = 5$ ignores that the fall is taken on a bigger base.
The Fast Way
Use the successive-change formula $a + b + \frac{ab}{100}$ .
$20 + (-15) + \frac{20 \times (-15)}{100} = 5 - 3 = 2$ .
So April is 2% higher.
Q2Arithmetic › Mixture & AlligationEasy
A milk and honey mixture is 20% honey. Another 120 ml of honey is added to it. After this addition, the resulting mixture has 150 ml of honey. What is the volume of milk in the final mixture?
Correct option C120 ml
Honey before the addition $= 150 - 120 = 30$ ml.
That 30 ml was 20% of the original mixture, so the original mixture was $30 \div 0.2 = 150$ ml.
Milk $= 150 - 30 = 120$ ml.
Adding honey does not change the milk, so the final mixture still has 120 ml of milk.
The Fast Way
Milk never changes, so find it in the original mixture.
Original honey $= 150 - 120 = 30$ ml is 20%, so milk (80%) is 4 times that.
$4 \times 30 = 120$ ml.
Q3Arithmetic › Ratio, Proportion & VariationEasy
A, B and C have some marbles. The ratio of the number of marbles with A to the number with B is 2 : 1. Also, the number of marbles with A to the number with C is 1 : 4. What is the approximate percentage of the total number of marbles that are with C?
Correct option C72.72%
A : B = 2 : 1 and A : C = 1 : 4 = 2 : 8.
So A : B : C = 2 : 1 : 8, a total of 11 parts.
C's share $= \frac{8}{11}$ of the total, which is about 72.72%.
The Fast Way
Make A the same in both ratios.
A : C = 1 : 4 = 2 : 8, so A : B : C = 2 : 1 : 8.
C has 8 of 11 parts, just under $\frac{3}{4}$ , so 72.72%.
Q4Arithmetic › Time, Speed & DistanceEasy
Meera cycles from her home to a library at 12 km/h and returns along the same road at 18 km/h. The round trip takes 5 hours in all. How far is the library from her home?
Correct option B36 km
Let the distance be $d$ km.
Time out + time back: $\frac{d}{12} + \frac{d}{18} = 5$ .
$\frac{3d + 2d}{36} = 5$ , so $5d = 180$ and $d = 36$ .
The library is 36 km away. Using the simple average speed 15 km/h gives 37.5 km, which is wrong.
The Fast Way
Same distance, so time is inversely proportional to speed: speeds 12 : 18 = 2 : 3 means times 3 : 2.
Split the 5 hours as 3 hours out and 2 hours back.
Distance $= 12 \times 3 = 36$ km.
Q5Algebra › Progression & SeriesMedium
Given: $f(x) = (1 + 1/x)$ and $f(k) \times f(k + 1) \times f(k + 2) \times \dots \times f(k + 99) = 11$ .
Quantity I: $k$
Quantity II: $11$
Pick the most exact relation that always holds.
Correct option BQuantity I $<$ Quantity II
$f(x) = \frac{x + 1}{x}$ , so the product is $\frac{k + 1}{k} \times \frac{k + 2}{k + 1} \times \dots \times \frac{k + 100}{k + 99}$ .
Every middle term cancels, leaving $\frac{k + 100}{k}$ .
$\frac{k + 100}{k} = 11$ gives $k + 100 = 11k$ , so $k = 10$ .
$10 < 11$ , so Quantity I $<$ Quantity II.
The Fast Way
Telescoping product: only the last numerator and the first denominator survive.
$\frac{k + 100}{k} = 11 \Rightarrow 10k = 100 \Rightarrow k = 10$ .
So Quantity I (10) is less than Quantity II (11).
Q6Algebra › Algebraic IdentitiesMedium
Decide whether the statement below is always true, sometimes true or never true.
If $x$ , $y$ and $z$ are positive integers and $p = \{[(x - 1)^2/x] + 2\} + \{[(y - 1)^2/y] + 2\} + \{[(z - 1)^2/z] + 2\}$ , then $p < 6$ .
Correct option CNever
Each bracket is $\frac{(x - 1)^2}{x} + 2 = \frac{x^2 - 2x + 1 + 2x}{x} = x + \frac{1}{x}$ .
For a positive integer $x$ , $(x - 1)^2 \geq 0$ , so each bracket is at least 2 (it equals 2 only at $x = 1$ ).
So $p \geq 2 + 2 + 2 = 6$ . Even the smallest case, $x = y = z = 1$ , gives $p = 6$ , which is not less than 6.
$p < 6$ is never true.
The Fast Way
Simplify one bracket: $\frac{(x - 1)^2}{x} + 2 = x + \frac{1}{x}$ .
For positive $x$ , $x + \frac{1}{x} \geq 2$ , so $p \geq 6$ .
$p < 6$ is never true.
Q7Data Interpretation › TablesMedium
The table shows the number of students (in hundreds) who joined four courses at a college in two years.
Course Year 1 Year 2
Arts 10 11
Commerce 30 39
Science 16 16
Management 4 6
Which course's share of the total intake rose by the most percentage points from Year 1 to Year 2?
Correct option BCommerce
Totals: Year 1 $= 10 + 30 + 16 + 4 = 60$ ; Year 2 $= 11 + 39 + 16 + 6 = 72$ .
Commerce: $\frac{30}{60}$ = 50% to $\frac{39}{72}$ = 54.2%, up about 4.2 points.
Management: $\frac{4}{60}$ = 6.7% to $\frac{6}{72}$ = 8.3%, up about 1.7 points.
Arts falls (16.7% to 15.3%) and Science falls (26.7% to 22.2%).
So Commerce gained the most share, even though Management grew fastest (50%).
The Fast Way
Total intake grew 20%; a share rises only if the course beats 20%, and the gain scales with its old share.
For a course growing $g$ %, gain in points $\approx$ old share $\times \frac{g - 20}{120}$ : Commerce $50 \times \frac{10}{120} \approx 4.2$ , Management $6.7 \times \frac{30}{120} \approx 1.7$ .
So Commerce, not the fastest grower.

Course	Year 1	Year 2
Arts	10	11
Commerce	30	39
Science	16	16
Management	4	6

Section 2 · Logical Reasoning

Q8Logical Reasoning › SeriesEasy
Find the next number in the series: 4, 6, 12, 14, 28, 30, ?
Correct option D60
The rule alternates: add 2, then double.
$4 + 2 = 6$ , $6 \times 2 = 12$ , $12 + 2 = 14$ , $14 \times 2 = 28$ , $28 + 2 = 30$ .
Next comes doubling: $30 \times 2 = 60$ .
The Fast Way
Look at the jumps: small, big, small, big.
Every small jump is +2 and every big jump doubles the term.
After +2 comes doubling: $30 \times 2 = 60$ .
Q9Logical Reasoning › Coding-DecodingEasy
In a certain code, PLANT is written as QNDRY. How is SHORE written in that code?
Correct option ETJRVJ
Compare letter by letter: P to Q is +1, L to N is +2, A to D is +3, N to R is +4, T to Y is +5.
Apply the same shifts to SHORE: S + 1 = T, H + 2 = J, O + 3 = R, R + 4 = V, E + 5 = J.
So SHORE is written as TJRVJ.
The Fast Way
Spot the growing shift: +1, +2, +3, +4, +5.
Check only the letters where the options differ: S + 1 = T, H + 2 = J, O + 3 = R, E + 5 = J.
Only TJRVJ fits.
Q10Logical Reasoning › Direction SenseEasy
Ravi walks 9 km north, turns right and walks 8 km, turns right again and walks 4 km, and then turns left and walks 4 km. How far is he now from his starting point, and in which direction?
Correct option A13 km, north-east
Take the start as (0, 0) with north as up.
9 km north: (0, 9). A right turn faces east; 8 km: (8, 9).
Another right turn faces south; 4 km: (8, 5). Facing south, a left turn faces east; 4 km: (12, 5).
Distance $= \sqrt{12^2 + 5^2} = 13$ km. He is east and north of the start, so north-east.
The Fast Way
Net displacement: total the east-west and north-south moves separately.
East $= 8 + 4 = 12$ ; north $= 9 - 4 = 5$ .
5-12-13 triplet: 13 km, north-east.
Q11Critical Reasoning › SyllogismsMedium
Select the conclusion that best follows from the statement given below.
Statement:
No one who likes to watch baseball likes to watch basketball, and all those who like to watch basketball also like to watch football.
Conclusions:
I. All those who like to watch football like to watch baseball.
II. No one who likes to watch baseball likes to watch football.
III. Some of those who like to watch football like to watch baseball.
Correct option ENone of the conclusions follow
Draw it: Basketball lies inside Football, and Baseball does not touch Basketball.
Baseball may or may not overlap the part of Football outside Basketball.
I fails: the basketball fans are football fans who cannot like baseball.
II fails: a baseball fan may still like football. III fails: it is possible that no football fan likes baseball.
So none of the conclusions must follow.
The Fast Way
For each conclusion, draw the one possible case that breaks it.
Baseball fully outside Football kills I and III; Baseball overlapping Football kills II.
So none of the conclusions follow.
Q12Logical Reasoning › Blood RelationsEasy
In a code, $X + Y$ means X is the mother of Y, $X - Y$ means X is the brother of Y, $X \times Y$ means X is the father of Y and $X \div Y$ means X is the sister of Y.
If $P \times Q - R + S$ , how is P related to S?
Correct option DMaternal grandfather
$P \times Q$ : P is the father of Q.
$Q - R$ : Q is the brother of R, so R is also P's child.
$R + S$ : R is the mother of S.
So P is the father of S's mother: P is S's maternal grandfather.
The Fast Way
Decode left to right and keep track of genders.
P is the father of Q, whose sister R is S's mother.
Mother's father: maternal grandfather.
Q13Logical Reasoning › PuzzlesMedium
Manjeet, Rahim, Ram and Divya are four friends who live in a village. It is known that:
I. Each friend lives in a differently coloured house - orange, yellow, green and blue.
II. Each friend owns a different pet - Bee, Dee, Cee and Tee.
III. The pets each feed on different things - leaves, fish, vegetables and insects.
IV. Manjeet does not live in the blue house.
V. Tee eats leaves but does not live with Rahim or Divya.
VI. Dee does not eat insects.
VII. Ram lives in an orange house but does not own Cee or Tee.
VIII. The pet that feeds on insects does not live in the green or blue house.
IX. Rahim does not feed vegetables or insects to his pet, which is neither Dee nor Cee.
Which pet eats fish?
Correct option ABee
Tee does not live with Rahim or Divya (V), and Ram does not own Tee (VII), so Manjeet owns Tee, which eats leaves.
Rahim's pet is not Dee or Cee (IX) and Tee is taken, so Rahim owns Bee. Ram cannot own Cee, so Ram owns Dee and Divya owns Cee.
Rahim does not feed vegetables or insects (IX) and leaves belong to Tee, so Bee eats fish.
For completeness: Dee does not eat insects (VI), so Dee eats vegetables and Cee eats insects; then Divya is in yellow (VIII), Manjeet in green (IV) and Rahim in blue.
So Bee eats fish; Manjeet's pet (Tee) eats leaves.
The Fast Way
Fix the owners first; the food follows from them.
Tee can only be Manjeet's, so Rahim (not Dee or Cee) owns Bee.
Rahim's pet eats neither vegetables nor insects, and leaves are Tee's, so Bee eats fish.
Q14Logical Reasoning › Seating ArrangementMedium
Six friends, Arun, Bela, Chirag, Divya, Esha and Farid, sit around a circular table, facing the centre.
Bela sits second to the right of Esha.
Farid sits opposite Bela.
Arun is an immediate neighbour of Farid.
Divya is not an immediate neighbour of Esha.
Who sits immediately to the right of Esha?
Correct option EChirag
Facing the centre, a person's right is the anticlockwise side.
Number the seats 1 to 6 clockwise with Esha at 1. Bela, second to her right, is at 5; Farid, opposite Bela, is at 2.
Arun is next to Farid, at 1 or 3; seat 1 is Esha's, so Arun is at 3.
Chirag and Divya take seats 4 and 6. Seat 6 is next to Esha, so Divya is at 4 and Chirag at 6.
Seat 6 is the seat anticlockwise of Esha, so Chirag sits immediately to her right (Farid is on her left).
The Fast Way
Anchor Esha, place every fixed clue, and use the 'not' clue last.
Bela two seats anticlockwise, Farid opposite Bela, Arun on Farid's free side.
Divya cannot sit beside Esha, so Chirag takes her anticlockwise seat: Chirag is on her right.

Section 3 · Verbal Reasoning

Q15Grammar › PrepositionsEasy
Select the option that best completes the sentence below.
Please pay the electricity bill ______ time to avoid having your electricity supply cut off.
Correct option Con
'On time' means by the fixed or expected time, which is what a bill's due date needs.
'Inside time', 'to time' and 'at time' are not English phrases, and 'about time' means 'long overdue', which does not fit.
So the answer is 'on'.
The Fast Way
Recall the fixed phrase: 'on time' means punctually, by the due date.
No other choice makes a phrase with 'time' that fits paying a bill.
So 'on'.
Q16Grammar › Subject-Verb AgreementEasy
Select the word or phrase that is incorrect in the sentence below. Select 'No error' if the sentence has no errors.
A discount of 25% were given to customers purchasing clay lamps during the festival of lights.
Correct option Bwere
The subject is 'A discount', which is singular; 'of 25%' only describes it.
A singular subject takes 'was', so 'were' is the error.
Correct sentence: 'A discount of 25% was given to customers purchasing clay lamps during the festival of lights.'
The Fast Way
Find the real subject by stripping the 'of' phrase.
'A discount ... were given' puts a plural verb on a singular subject.
So 'were' is wrong.
Q17Vocabulary › SynonymsMedium
Despite two failed product launches, the founder remained sanguine about the company's future.
As used in the sentence, 'sanguine' most nearly means:
Correct option Aoptimistic
'Sanguine' means cheerfully hopeful, especially when things look difficult.
'Despite two failed launches' sets up a contrast: failures would make most people worried, but the founder stayed hopeful.
So 'optimistic' fits. 'Anxious' is what the failures would suggest, the opposite of what the contrast needs.
The Fast Way
Let the signal word decide: 'Despite' means the blank goes against the bad news.
Failures suggest worry, so the founder must feel the opposite.
So 'optimistic'.
Q18Vocabulary › Fill in the BlanksMedium
From the given words, fill in the blank with the most appropriate word.
In light of the recent happenings, the nation is again ______ in a debate on capital punishment.
Correct option Eembroiled
'Embroiled in' means deeply caught up in a conflict or argument, which suits a heated national debate.
'Riveted' takes 'by' or 'to' and means gripped; 'ridden' means full of something bad, as in 'debt-ridden'; 'tuned' and 'bounded' do not pair with 'in a debate'.
So 'embroiled'.
The Fast Way
Let the collocation decide: one is 'embroiled in' a debate or dispute.
None of the other words goes naturally with 'in a debate'.
So 'embroiled'.
Q19Verbal Ability › Para JumblesEasy
Rearrange the given sentences in a proper sequence to form a meaningful paragraph.
P. It all began during high school when Aisha moved to a hostel.
Q. She was grateful that she had the support of her family to help her through this difficult time.
R. Neither Aisha nor her parents expected that her life would take such an unfortunate turn.
S. Not long after this, Aisha was diagnosed with blood cancer so she had to leave school and focus on her treatment.
Correct option CRPSQ
R opens the story: an unexpected, unfortunate turn.
P says where 'it all began' (the hostel), and S follows with 'Not long after this', the diagnosis.
Q closes with how she got through 'this difficult time'.
So the order is RPSQ.
The Fast Way
Find the mandatory pair: 'Not long after this' in S must come right after the event in P.
Only one choice has P immediately before S, and it also ends with Q's 'this difficult time'.
So RPSQ.
Q20Reading Comprehension › Inference-BasedMedium
Read the passage and answer the question.
Cities that plant trees mainly for their looks often choose fast-growing species, because a new avenue then looks finished within a few years. Yet the cooling a tree provides depends far more on the width and density of its canopy than on its height, and fast growers tend to have thin, open crowns. A city that wants cooler streets in twenty years may therefore have to accept avenues that look bare for the first five.
Which of the following can be inferred from the passage?
Correct option DAn avenue's early appearance can be a poor guide to how well it will cool the street later.
The passage links three facts: looks-driven planting picks fast growers, which look finished early; fast growers tend to have thin crowns; cooling depends mainly on a wide, dense canopy.
So an avenue that looks complete early may cool poorly later, and one that looks bare at first may cool better. That is the inference.
'Never be planted' is too extreme. 'Most cities' goes beyond the passage, which speaks only of cities that plant for looks.
'Cooling matters more' is a value judgement the author does not make; the passage only states the trade-off ('may have to accept').
Height of thin versus dense crowns is never compared.
The Fast Way
Strike the extreme and out-of-scope options: 'never', 'most cities', 'grow taller'.
Of the two left, 'cooling matters more' is the author taking sides, which the passage never does.
The safe inference: early looks can be a poor guide to later cooling.