National Aptitude Test for Intermediate Students ( 12 years of education)
Section 1
Quantitative section
Q.1 Arshad went shopping with D Rupees. He spent 20% of his money on a shirt and 25% on a shirt and 25% of what was left on a pair of shoes. What percentage of the original D Rupees did he spend?
(a)25% (b)40% (c) 45% (d) 47% (e) 50%
Q.2 Both the length and width of a certain rectangle are event numbers, and the length is three times the width. Each of the following could be the perimeter of such a rectangle EXCEPT
(a) 32 (b) 64 (c) 120 (d) 160 (e) 192
Q.3 A, B, and C each drove 100 mile lengths of a 300 mile course at speeds of 40, 50 and 60 miles per hour respectively. What fraction of the total time did A drive?
(a) 15/74 (b) 4/15 (c) 15/37 (d) 3/5 (e) 5/4
Q.4 In a student body the ratio of men of men to women was 1 to 4. After 140 additional men were admitted. the ratio of men to women became 2 to 3. How large was the student body after the additional men were admitted?
(a) 700 (b) 560 (c) 280 (d) 252 (e) 224
Q.5 A boy walking the road at 3 km per hour is overtaken by a truck traveling at 40 km per hour. If the truck breaks down 1 km beyond where it passes the boy, how many minutes after the breakdown does the boy reach the truck?
(a) 21.5 (b) 20 (c) 18(34/37) (d) 18(26/43) (e) 18.5
Q.6 A warehouse had a square floor with area 10,000 square meters. A rectangular addition was built along one entire side of the warehouse that increased the floor area by one half as much as the original floor area. How many meters did the addition extend beyond the original building?
(a) 5:56 (b) 5:58 (c) 6:00 (d) 6:23 (e) 6:26
Q.7 A digital wristwatch was set accurately at 8:30 a.m. and then lost 2 seconds every 5 minutes. What time was indicated on the watch at 6:30 p.m. of the same day if the watch operated continuously until that time?
(a) 7.5% (b) 9(3/8)% (c) 10.5% (d) 12% (e) 15%
Q.8 A 5 liter jug contains 4 liters of a slat water solution that is 50% salt. If 1.5 liters of solution spills out of the jug, and the jug is then filled to capacity with water, approximately what percent of the resulting solution in the jug is salt?
Q.9 The average of three different positive integers is 100 and the largest of these three integers is 120. What is the least possible value of the smallest of these integers?
(a) 1 (b) 10 (c) 61 (d) 71 (e) 80
Q.10 A hat maker bought a box of hats, 1/4 of which were brown. The hat maker sold 2/3 of the hats including 4/5 of the brown hats. What fraction of the unsold hats were brown?
(a) 1/60 (b) 2/15 (c) 3/20 (d) 3/5 (e) ¾
Q.11 At a special sale, 5 tickets can be purchased for the price of three tickets. If five tickets are purchased at this sale, the amount saved will be percent of the original price of the five tickets?
(a) 20% (b) 33.5% (c) 40% (d) 60% (e) 66 (2/3)%
Q.12 Working independently Tehmina can do a certain job in 12 hours. Working independently, Asma can do the same job in 9 hours. If Tehmina works independently at the job for 8 hours and then Asma works independently, how many hours will it take Asma to complete the remainder of the job?
(a) 2/3 (b) 3/4 (c) 1 (d) 2 (e) 3
Q.13 Three stacks containing equal numbers of chips are to be made from 9 red chips. 7 blue chips and 5 green chips. If all of these chips are used and each stack contains at least 1 chip of each color, what is the maximum number of red chips in any one stack?
(a) 7 (b) 6 (c) 5 (d) 4 (e) 3
Q.14 In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus and the remaining 8 km by car. What is the distance in km from the dormitory to the city?
(a) 30 (b) 45 (c) 60 (d) 90 (120)
Q.15 A family made a down payment of Rs.75 and borrowed the balance on a set of books that cost Rs.400. The balance with interest was paid in 23 monthly payments of Rs. 16 each and a final payment of Rs.9. The amount of interest paid was what percent of the amount borrowed?
(a) 6% (b) 12% (c) 14% (d) 16% (e) 20%
Q.16 A grocer purchased a quantity of bananas at 3 kg for Rs.0.50 and sold the entire quantity at 4 kg for Rs.1.00. How many kg did the grocer purchase if the profit from selling the bananas was Rs. 10?
(a) 40 (b) 60 (c) 90 (d) 120 (e) 240
Q.17 There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
(a) 101 (b) 103 (c) 106 (d) 107 (e) 109
Q.18 Out of a total of 1000 employees at a certain corporation 52% are female and 40% of these females work in research. If 40% of the total number of employees work in research how many male employees do NOT work in research?
(a) 520 (b) 480 (c) 392 (d) 208 (e) 88
Q.19 An instructor scored a student’s test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answer. If the student answered all the questions and received a score of 38 how many questions did that student answer correctly?
(a) 19 (b) 38 (c) 41 (d) 44 (e) 46
Q.20 In each production lot of a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size B. If 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?
(a) 15 (b) 25 (c) 30 (d) 35 (e) 40
Section 2
Analytical Section
We must conclude from Robert’s statement that
Robert does not know many liars
Bush is a liar
Bush likes to be in a position of power
Robert is a good friend of Bush conclude from Robert’s statement that
Robert heard Bush telling a lie
Q.2 “Only rich people buy cars”
We conclude from this statement that:
No rich person buys a truck
Anyone who buys a car must be rich
At least one rich person will buy a car
All poor people are without cars
Some poor people buy cars
Q.3 “The doctor has never lost a patient”
This statement would seem very foolish if the patient knew that the doctor
Is a very capable and qualified person
Has just started practicing medicine
Has seen more patients than any other doctor
Can handle patients with many different diseases
Has spent more than six years in medical college and post-graduation.
All the Steel Rods in a concrete roof are either parallel or perpendicular to one another. The Rods are all straight.
Rods R1, R2, R3, R4 and R5 are parallel to one another
Rods R6, R7, R8, R9, R10, R11 and R12 are parallel to one another.
Rod R1 is one foot East of Rod R2.
Rod R2 is half a foot West of Rod R3
Rod R4 is one foot West of Rod R5
Rod R6 is half a foot South of Rod R7
Rod R8 is one foot North of Rod R9.
Rod R10 is half a foot North of Rod R11.
Rod R10 is one foot South of Rod R12
Rod R8 is one foot North of Rod R11.
Rod R4 is two feet West of Rod R2
Rod R5 and Rod R2 intersect.
Rod R12 is one and a half feet north of Rod R11
Rod R4 is at least two feet West of Rod R1
Q.5 If Rod R5 is somewhere between Rods R2 and R3, then which of the following is false
Rod R4 is less than one foot from Rod R2
Rod R3 is less than one and a half feet from Rod R4
Rod R5 is less than one foot from Rod R1
The distance from Rod R5 to Rod R2 added to the distance from Rod R5 Rod R3 is half a feet
Rod R4 is two feet West of Rod R1
Q.6 Which of the following possibilities would make two Rods coincide?
If Rod R11 is half a foot North of Rod R8
If Rod R4 is half a foot East of Rod R1
If Rod R8 is half a foot North of Rod R 10
If Rod R3 is one foot West of Rod R4
If Rods R5 and R2 are half a foot apart or Rods R7 and R9 are half a foot apart.
Q.7 If Rod X is parallel to Rod R8 and Rod X is half a foot South of Rod R9 and one foot North of Rod R6, which two Rods would be half a foot apart?
R8 and X
X and R7
R9 and R6
R9 and R7
R8 and R6
Q.8 A paragraph from a book on wildlife states: “The eagle is a bird that lives only in inland mountains.
When removed from this habitat, he dies. The eagle cannot survive in captivity: several zoo keepers will attest to this fact. These birds make excellent pets, and I have photographed many of them in my contact with tribes living on the plains near the coast”
The author is probably:
(a) A liar (b) An explorer (c) A novelist
(d) A zoologist (e) An amateur photographer
1. Everybody likes somebody
2. Somebody likes somebody
3. Nobody likes anybody
(a) 1 only (b) 2 only (c) 3 only (d) 1 and 2 only (e) 2 and 3 only
Questions 10-13 relate to the following statements:
The top six students in the intermediate examination are to be given medals according to their positions inadvertently they have been made to stand in a queue in the wrong order by one of the organizers of the ceremony. As a result of the error, the following situation exists:
1. Any two students who ordinarily would be adjacent are no longer so
2. Exactly one of the students is currently occupying his/her correct position in the queue.
3. Student 1 is standing after student 6, and exactly one other student separates them.
4. Student 4 is not last.
5. Student 5 occurs before student 2.
Q.10 Which of the following must be false?
Student 3 comes before student 2
Student 3 comes before student 4
Student 5 comes after student 1
Student 6 is second in order
Student 3 occurs last
Q.11 Which student cannot occur among the last three in the queue?
(a) 1 (b) 3 (c) 4 (d) 5 (e) 6
Q.12 Which students might be in their correct positions?
(a) 3 and 4 (b) 2 and 5 (c) 2 and 4 (d) 4 and 5 (e) 3 and 5
Q.13 Which of the following could possibly be true?
1. Student 6 comes after student 2
2. Student 4 comes after student 5
3. Student 6 comes after student 4
(a) 1 only (b) 2 only (c) 3 only (d) 2 and 3 only
Q.14 If Reema was mad, then Saima was mad and vice versa.
If neither Reema nor Saima were mad. Then you cannot believe Sheikh Sahib
You can believe Sheikh Sahib
Considering the above statements which of the following could not be true:
Both Reema and Saima were mad
Reema was mad but Saima was not
Saima was mad but Reema was not
(a) 1 only (b) 2 only (c) 3 only (d) 1 and 2 only
(e) 2 and 3
Q.15 (i) All king size cigarettes cause cancer
(ii) “Silver Bark” is the name of a new brand of king-size cigarettes
(iii) We can conclude from the above statements that
“Silver Bark” smokers may have cancer
“Silver Bark” causes cancer
Anyone with cancer smokes “Silver Bark”
Nobody who smokes regular cigarettes gets cancer
People with cancer prefer king-size cigarettes over regular cigarettes
Question 16-18 relate to the following statements:
1. An insurance company must insure four cars.
2. The cars that can be chosen are Toyota, Nissan, Honda, BMW or a Mercedes.
3. The company must insure either a BMW or a Mercedes, but no both.
4. The company cannot insure a Honda and a Charade together.
Q.16 If the insurance company insures BMW, which other car(s) must insure?
must it insure?
1. Charade
2. Nissan
3. Honda
(a) 1 only (b) 2 only (c) 3 only (d) 1 and 2 only
(e) 2 and 3 only
Q.17 How many different combinations of cars are available for the insurance company to choose from?
(a) 2 (b) 3 (c) 4 (d) 5 (e) more than 5
Q.18 Which car(s) must the insurance company insure?
1. Toyota
2. Nissan
3. Honda
(a) 1 only (b) 2 only (c) 3 only (d) 1 and 2 only
(e) 1.2 and 3
Q.19 All people that have guns are dangerous
All people either dangerous or have guns
Given the above assumptions, which of the following sentence(s) must be false?
Sentence(s) must be false?
1. All people that are dangerous have guns
2. Some people are not dangerous
3. There are people with guns that are not dangerous
(a) 1 only (b) 2 only (c) 3 only (d) 2 and 3 only (e) 1,2 and 3
Q.20 It is not true that both Mars and Venus will be explored by Space Research Ltd.
Which of the following is most nearly equivalent to the above claim?
Either Mars or Venus will be explored by Space Research Ltd.
Neither Mars or Venus will be explored by Space Research Ltd.
Mars and Venus will be explored by Space Research Ltd.
Mars will be explored by Space Research Ltd. Only if Venus is.
Either Mars or Venus will not be explored by Space Research Ltd.
SOLUTION OF Test NAT-I
Quantitative
Q.1 Original Rs. = D
Spent for shire = 20/100 * D = D/5
Left with Rs = D – D/5 = 4D / 5
Spent for shoes = 25/100 * 4D/5 = D/5
Total Amount Spent (i) & (ii) = D/5 = D/5
%age = (2D/5) * 100 = 40 Ans.
D
Q.2 Total time taken by A.B.C to drive 300 miles:
Perimeter = (x + 3x) * 2 = 8x
Answer should be odd and divisible by 8. 120 is divisible by 8 but its answer is not even so C is the answer.
Q.3 Total time taken by A.B.C to drive 300 miles:
= 100/40 + 100/50 + 100/60
= (150+120+100) / 60
= 370/60 = 37/6 Hours
Fraction of time taken by A = (100/40)
37/6
Q.4 Let the number of men in the student = x
No of women = 4 * x
After admission of 140 men, no. become = x + 140
Now the ratio is = (x + 140/4x = 2/3
3(x + 140) = 3 * 4x = 8x or 3x + 42 = 8x
5x = 420 x = 420 / 5 = 84
Size of the body after admission of 140 students.
= x + 140 + 4x = 5 * 84 + 140
= 420 + 140 = 560 Ans.
Q.5 Speed of the boy = 3 Km / hrs
Speed of the truck = 40 km / hrs
Time taken by truck to cover one Km = 60/40
= 3/2 min
Time taken by the boy to cover 1 km = 60/3
= 20 min.
Time difference = 20 – 3/2 = 18.5 ,min
Q.6 Area of the original warehouse = 10000 mts.
One side of the “ “ “ = Sq. root of 10000 = 100 mts.
Increased area of the warehouse = 10000 mts.
Since one side of the warehouse remains unchanged i.e.
100 mts. The extension therefore = 5000 Sq. Mt.
Since one side of the warehouse remains unchanged i.e.
100 mts. The extension therefore = 5000/100 = 50 Mt.
Q.7 Setting Time = 8:30 a.m
Check time = 6: 30p.m.
Interval therefore = 8.30 – 6:30 = 10 hrs
Loss = 2 * 60/5 = 24 sec
Loss for the total interval i.e. 10 hrs. = 24 * 10
= 240 sec
= 240/60 = 4 min.
Q.8 Salt in 4 liter solution = 4 * 50/100 = 2L
Then 1.5 liter solution contains salt = 1.5 * 50/100
Remaining water after spillage = 4 – 1.5 = 2.5 L
Remaining salt after spillage = 2 – 75 = 1.25 L
Salt Percentage after filling the jug = (1.25 / 5) * 100
= 25 %
Q.9 Suppose the total number of hats in the box = x
No of Brown hats = ¼ * x
Their sum = 3*100 = 300
Sum of the remaining integers = 300 – 120
= 180
The second largest integer can therefore be:
= 120 – 1 = 119
Hence the least possible value of the smallest:
= 180 – 119 = 61
Q.10 Suppose the total number of hats in the box = x
No of Brown hats = ¼ * x
No of hats sold by the hat maker – 2x/3
Unsold = x/3
4/5 of the brown hats = x/4 * 4/5 = x/20
Unsold brown hats = x/4 – x/5 = x/20
Fraction of the unsold Brown hats = (x/20)
x/3
= 3/20
Q.11 Let the original price of 5 tickets = x Rs.
Price of three tickets = x Rs.
At special sale prince of 5 tickets = 3x/5 (given)
Amount saved for purchase of 5 tickets = x – 3x/5
= 2x/5
%age of saving = 2x/5
(x*100)
= (2/5) * 100 = 40
Q.12 Tehmina can finish the job independently in 12 hrs
Asma “ “ “ “ “ “ “ “ “ “ “ 9 hrs
Left over work by Tehmina = 12 – 8 = 4 hrs job But Asma’s work / hr as compared to Tehmina.
Asma will finish the remaining work in = 4*
Q.13 No of red chips = 9
“ green “ = 5
Total no of chips –9+7+5 – 21
No. of chips in each stock = 21/3 = 7
Therefore maximum 5 red chips can be in any one stack because 1 other color chips should be also there.
C is the Answer
Q.14 Distance covered by foot = 1/5
Distance covered by bus = 2/3
Let the total distance = x
Remaining distance i.e. covered by car:
= x – x/5 – 2x/3 = 8 (given)
(15x – 3x – 10x) / 15 = 8 km
solving equation
x = 60 km
Q.15 Down payment = Rs. 75
Cost of set of books = 400 Rs.
Borrowed amount = 400 – 75 = 325 Rs.
The payment paid (including interest) = 23 * 16 +9
= 377
Interest paid = 377 – 325 = 52 Rs.
(Amount of interest paid) * 100 = 52 /325*100
(Amount borrowed)
= 16 %
Q.16 Suppose the quantity = x
Purchase price = x/3 * 0.50 = x/6
Sale price = x/4 * 1 = x/4
Profit = x/4 – x/6 = 10 (given)
Solving equ.
x = 120
Q.17 No of divisible by 3 but between 100 – 110 are 120, 105 & 108 is not possible because it does not fulfill the condition
Let it be 102 & 2 = 104 but this divisible 4 * no left over is there therefore only 15 + 2 = 107 is the number of cards that fulfills all the conditional.
Q.18 Total no. of employees = 1000
No. of women = 52/100 *100
= 520
No. of women working in research 520 * 41/100
= 208
No. of men employees = 1000 – 520 = 480
No. of employee (men & women) working in research.
= 40/100 * 1000 = 400
No. of men working in research = 400 – 208 = 192
No. of men not “ “ “ “ “ “ = 480 – 192 = 288
Q.19 No. of total question = 50
Suppose the correct Ans. x number
Incorrect answer = 50 – x
x – ( 50 – x) 2 = 38 or x – 100 + 2x = 38
or 3x = 138 x = 46
Q.20 10 red shoes are of size A
So red shoes of size B = 25 – 10 = 15
50 shoes must be of size B
So blue shoes of size B are = 50 – 15 = 35
Analytical
Q.1 B Since “Every Liar” According to Robert statement is politician. Therefore; Bush who is a liar must also be a politician
Question of Robert’s Knowledge of many liars does not arise. (c) and (d) are also irrelevant because the relation is only between a liar and a politician.
(e) too is also insufficient for the conclusion.
Q.2 B There is no restriction on a rich people to buy trucks. (c) is discarded as it restricts to one rich person. (d) is also discarded as some rich may not buy cars. (e) only rich people buy cars and not some poor people buy cars.
Q.3 B Even capable and qualified doctors loose patients. Question of comparisons does not arise. Patients with many diseases may also be lost. (e) cannot mean in any way that no patient is lost.
Therefore the only possibility of lost of a patient is that he has just started practice. i.e. option (b)
4-7 Prepare a chart from the given information.
R4 R5 R2 R3 R1
R 12
1 feet 1 feet one feet
R10 ½ feet ½
R8
1 feet
R9 1 feet
½ feet
R7
R6
N
W E
S
Q.4 D
Discarded R8 is on south moreover distance between R8 and R11 is unknown
Discarded since distance between R5 and R2 (consequently R2 and R4) in unknown.
R5 and R2 are parallel which don’t intersect.
True answer.
This is not necessarily true because R5 and R2 might be combined.
Q.5 E
Is true since distance between R4 and R5 is one foot
Is true because R5 lies between R2 and R3 which can’t be equal to
R4 => R5+R2 =>R3=1+1/2 feet
Is true because the distance between R2 and R1 is one feet.
Is also true because the sum of two parts of the same is the same R2 =>R5+R5+R3=1/2 foot.
Is false because R2=> 1 foot and R4 & R5 is also one foot.
Q.6 E
Is discarded because other conditions are contradicted
Is discarded because other conditions are contradicted
Is discarded because other conditions are contradicted
Is discarded because other conditions are contradicted
It’s the answer since its first part makes the two rods R5 and R3 coincided without contradicting other conditions.
Q.7 B Since this is the only one which satisfies all the conditions (see from the chart)
Q.8 A Rest are discarded because the eagle lives only in inland mountains. Outside the habitat he dies. Then the author cannot photograph them in tribes living in plains near the coast.
Q.9 O As nobody likes nobody means that none is like by anyone whereas a & b have liking for others.
Q.10 B D and E necessarily false
May or may not
Not at all
May or may not
Not at all
Not at all
Q.11 C is the true answer
Q.12 D is the true answer.
Q.13 E is the true answer.
Q.14 A Since Sheikh Sahib is to be believed either Reema or Saima was made & if one of them was made the other must also be mad. Therefore both were mad. Rest of the statements do not satisfy the conditions.
Q.15 B Silver Bark, although a new brand of king size cigarettes causes cancer as all the king size cause it. It is the size which cause cancer and no other is the cause
Q.16-18.
|
BMW |
Honda |
Toyota |
Nissan |
|
Mercedes |
Charade |
|
|
Q.16 B The company has the option to ensure charade or Honda but it must ensure Nissan Therefore B (2) is the answer.
Q.17 C Because we cam make one combination with BMW including Honda and the second including Charade with Nissan and Toyota Similarly two combinations are possible with Mercedes. Hence in all four combinations are possible.
Q.18 D The company has to insure four cars. It can either insure a Mercedes or a BMW. Also it can either insure Charade or Honda. So it must insure Toyota and Nissan both.
Q.19 A
(1) is false because people are either dangerous or have guns so dangerous people do not necessarily possess guns.
(2) This is not false because due to 2nd assumption all the people are not dangerous they have only guns.
(3) This , too , is not false as stated above
Q.20 A Jamil’s disagreement is not due to any restriction by Rashid on liking of haleem by Lahorie’s only on their love for haleem,(c) is irrelevant. (d) and (e) are also discarded on similar grounds.
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