mathewhe/aqua_rat huggingface dataset:
Question: The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1200, then what is the income of P1?
(A) s.800
(B) s.2400
(C) s.3000
(D) s.3200
(E) s.4200
Rationale: Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 1200 …(i) and 4x – 2y = 1200 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1200 -> x = 600
P1’s income = Rs 5*600 = Rs.3000
ANSWER:C
Answer: (C) s.3000
Question: If x : y = 4 : 7, find the value of (6x + 2y) : (5x – y)
(A) 7:13
(B) 38:7
(C) 3:13
(D) 2:3
(E) 38:13
Rationale: Explanation:
Given: X/Y = 4/7
(6x + 2y) : (5x – y)
= (6*4 + 2*7) : (5*4 – 7)
38:13
ANSWER: E
Answer: (E) 38:13
Question: If w/x = 1/3 and w/y = 2/3, then (x + y)/y =
(A) 2
(B) 4
(C) 5
(D) 3
(E) 7
Rationale: Ratio 1:
3w = x
Ratio 2:
3w = 2y
x = 2y
(x+y)/y = (2y+y)/y = y(2+1)/y = 3
Answer is D
Answer: (D) 3
Question: Mike, Jim and Bob are all professional fisherman. Mike can catch 15 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?
(A) 64
(B) 70
(C) 85
(D) 98.
(E) 112.
Rationale: All of them catch fishes in relation to number 15....
2/3*15+2*15+2*1.5*15*2/3=70
Answer is B
Answer: (B) 70
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 120 m
(B) 180 m
(C) 324 m
(D) Cannot be determined
(E) None of these
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
ANSWER:E
Answer: (E) None of these
Question: Two tailors P and Q are paid a total of Rs. 550 per week by their employer. If P is paid 120 percent of the sum paid to Q, how much is Q paid per week?
(A) 200
(B) 300
(C) 150
(D) 100
(E) 250
Rationale: Consider x
x+120 Of x =550
11/5x=550
x=550*5/11 = 250
ANSWER E
Answer: (E) 250
Question: Choose the missing terms out of the given alternatives.
QPO, SRQ, UTS, WVU, ?
(A) XVZ
(B) ESD
(C) ZYA
(D) VWX
(E) YXW
Rationale: E
YXW
Each term consists of three consecutive letters in reverse order. The first letter and the last letter of the next term are the same.
Answer: (E) YXW
Question: If a*b*c=130, b*c*d = 65, c*d*e=1000 and d*e*f=150 the (a*f)/(c*d) = ?
(A) 1/2
(B) 1/4
(C) 3/4
(D) 1/3
(E) None of these
Rationale: Explanation :
aâˆ—bâˆ—c/bâˆ—câˆ—d= 130/65 => a/d = 2
dâˆ—eâˆ—f/câˆ—dâˆ—e= 150/1000 => f/c = 1/4
a/d* f/c = 2 * 15/10 = 1/3
Answer : D
Answer: (D) 1/3
Question: Two unbiased coin are tossed .what is the probability of getting atmost one head?
(A) 1/3
(B) 3/4
(C) 5/7
(D) 8/9
(E) 2/3
Rationale: Here S={HH,HT,TH,TT}
Let Ee=event of getting one head
E={TT,HT,TH}
P(E)=n(E)/n(S)=3/4
Ans: B
Answer: (B) 3/4
Question: Anne bought doughnuts for a class breakfast party. She bought 9 chocolate doughnuts, 7 coconut doughnuts, and 9 jam-filled doughnuts. How many doughnuts did Anne buy in all?
(A) 25
(B) 36
(C) 39
(D) 21
(E) 11
Rationale: Add the numbers of doughnuts.
9 + 7 + 9 =25.
Answer is A.
Answer: (A) 25
Question: Four people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 16
Rationale: Consider E and J one. But, in this arrangement they can sit in two different combinations.
E first and J second or J first and E second.
Total we have (E and J) and the two other persons= 4 arrangements to do.
Total arrangements= 4*2= 8
C is the answer
Answer: (C) 8
Question: If the sides of a rectangle are increased by 25%, what is the percentage increase in the area?
(A) 54.25%
(B) 56.25$
(C) 53.25%
(D) 55.25%
(E) 58.25%
Rationale: If sides are a and b, after increase sides would be 1.25a and 1.25 b.
Percentage increase in area = (1.25a*1.25b - ab) *100/ab = 56.25%
Answer : B
Answer: (B) 56.25$
Question: The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 3 as its largest number?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16
(E) 1/32
Rationale: The set S has 2^5 = 32 subsets.
The number 5 is in half of these subsets.
Of the remaining 16 subsets, 4 is an element in 8 of them.
Of the remaining 8 subsets, 3 is an element in 4 of them.
Thus 3 is the largest number in 4 subsets of S.
The probability that 3 is the largest number is 4/32 = 1/8.
The answer is C.
Answer: (C) 1/8
Question: The age of father 10 years ago was thirce the age of his son.Ten years hence,father’s age will be twice that of his son.The ration of their present ages is :
(A) 5:2
(B) 7:3
(C) 9:2
(D) 13:4
(E) None of these
Rationale: Solution
Let the ages of father and son 10 year ago be 3x and x years respectively.
Then,(3x + 10)+10 = 2[(x +10)+10 ⇔ 3x + 20 = 2x + 40 ⇔ x =20.
∴ Required ratio =(3x +10) : (x + 10) = 70 : 30 : 7 : 3. Answer B
Answer: (B) 7:3
Question: Mary’s annual income is $15,000 and John’s annual income is $16,000. By how much must Mary’s annual income increase so that it constitutes 50% of Mary and John’s combined income?
(A)  $1,000
(B)  $4,000
(C)  $7,000
(D)  $11,000
(E)  $25,000
Rationale: Let Mary's income increase by x, then the equation will be
15,000 + x= (50/100)* (15,000 + x + 16000 )
15,000 + x = (1/2) * (31,000 + x)
30,000 + 2x = x + 31,000
x =1,000
So, Answer will be A
Answer: (A)  $1,000
Question: The area of the largest circle that can be drawn inside a square of side 28 Cm in length is:
(A) 600
(B) 646
(C) 616
(D) 636
(E) 606
Rationale: Radius of required circle = 14 Cm
its area = 22/7 × 14 × 14
44 × 14 = 616 Cm(power)2
Answer is C.
Answer: (C) 616
Question: Find the curved surface area, if the radius of a cone is 7 m and slant height is 14 m?
(A) 308
(B) 369
(C) 434
(D) 476
(E) 513
Rationale: Cone curved surface area = Ï€rl
22/7 Ã— 7 Ã— 14 = 22 Ã— 14 = 308 m(power2)
Answer is A.
Answer: (A) 308
Question: Two brothers took the GMAT exam, the higher score is U and the lower one is V. If the difference between the two scores is equal to their average, what is the value of V/U ?
(A) 3
(B) 2
(C) 1/2
(D) 1/3
(E) There isn't enough data to answer the question.
Rationale: Answer is D : 1/3
U - V = (U + V)/2
Solving for V/U = 1/3
D
Answer: (D) 1/3
Question: The sale price bags listed for Rs.2000 after successive discount is 25% and 15% is?
(A) 415
(B) 425
(C) 435
(D) 445
(E) 455
Rationale: 2000*(75/100)*(85/100)
= 425
Answer: B
Answer: (B) 425
Question: The perimeters of two squares are 36 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
(A) 16.4 cm
(B) 24 cm
(C) 88 cm
(D) 55 cm
(E) 34 cm
Rationale: We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 36/4 = 9 cm
Area of third Square = 9*9 - 8*8
= 17 cm
So side of third square = 4.1 [because area of square = side*side]
Perimeter = 4*Side = 4*4.1 = 16.4 cm
Answer:A
Answer: (A) 16.4 cm
Question: In a class of 28 students in an examination in maths 4 students scored 95 marks each, 3 get zero each and the average of the rest was 45. What is the average of the whole class?
(A) A)47.3
(B) B)45.6
(C) C)44
(D) D)48
(E) E)49
Rationale: Explanation:
Total marks obtained by a class of 25 students
= 4*95 + 3*0 + 21 * 45 =1325
Average marks of whole class = 1325/28 =47.3
Answer: Option A
Answer: (A) A)47.3
Question: Find the average marks of all the students in classes A and B, if :
classes A = 43 students (average marks of students is 65)
classes B = 54 students (average marks of students is 72)
(A) 41.9
(B) 68.9
(C) 65.9
(D) 61.9
(E) 62.9
Rationale: Sum of the marks for the class of 43 students = 43 * 65 = 2795
Sum of the marks for the class of 54 students = 54 * 72 = 3888
Sum of the marks for the class of 97 students =
2795 + 3888 = 6683
Average marks of all the students = 6683/97
= 68.9
Answer:B
Answer: (B) 68.9
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.2 km?
(A) 600 m
(B) 200 m
(C) 300 m
(D) 400 m
(E) 100 m
Rationale: C
300 m
Distance covered by Amar = 18/4.8 (1.6km) = 3/8(1200) = 300 m
Answer is C
Answer: (C) 300 m
Question: Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 35 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?
(A) 17.5 minutes.
(B) 35 minutes.
(C) 52.5 minutes.
(D) 70 minutes.
(E) 105 minutes.
Rationale: Danny's time is 35 minutes. The time to reach halfway is 17.5 minutes.
Steve's time is 70 minutes. The time to reach halfway is 35 minutes.
The time difference is 35 - 17.5 = 17.5 minutes
The answer is A.
Answer: (A) 17.5 minutes.
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
(A) 3
(B) 3 9/11
(C) 3 9/17
(D) 4
(E) 4 1/7
Rationale: Net part filled in 1 hour 1	+	1	-	1 =	17	.
5	6	12	60
The tank will be full in	60/17	hours i.e., 3 9/17	hours.
C)
Answer: (C) 3 9/17
Question: The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 24 different signs. If the company used 22 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 24 signs?
(A) 246
(B) 248
(C) 92
(D) 15,128
(E) 30,256
Rationale: # of 2-letter codes possible from 24 different signs = 24*24.
# of 2-letter codes possible from 22 different signs = 22*22.
The difference = 24^2 - 22^2 = (24 - 22)(24 + 22) = 92.
Answer: C.
Answer: (C) 92
Question: Company T produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company T last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 5/17
(B) 7/17
(C) 4/17
(D) 3/17
(E) 5
Rationale: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 10*1=10 and total time for Deluxe would be 5*7/5=7 --> total time for both of them would be 10+7=17 --> deluxe/total=7/17.
B
Answer: (B) 7/17
Question: If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5) =
(A) 3^(a + 1)
(B) 2^(a + 1)
(C) 2a
(D) 2a^(a + 1)
(E) 63(2^a)
Rationale: If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5) =
2^a(1+2+4+8+16+32)
2^a(63)
E. 63(2^a)
Answer: (E) 63(2^a)
Question: Andrew purchased 10kg of grapes at the rate of 82 per kg and 6 kg of mangoes at the rate of 62 per kg. How much amount did he pay to the shopkeeper?
(A) 1000
(B) 1055
(C) 1378
(D) 1075
(E) 1080
Rationale: Cost of 10 kg grapes = 82 × 10 = 820.
Cost of 6 kg of mangoes = 62 × 6 = 558.
Total cost he has to pay = 820 + 558 = 1378
C
Answer: (C) 1378
Question: If log10 2 = 0.3010, then log2 10 is equal to:
(A) 1000/301
(B) 0.301
(C) 600/301
(D) 0.6992
(E) 0.7254
Rationale: log2 10 = 1/log10 2 = 1/0.3010 = 10000/3010 = 1000/301
ANSWER A
Answer: (A) 1000/301
Question: Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 2 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt?
(A) 12
(B) 15
(C) 20
(D) 24
(E) 28
Rationale: In the first 2 hours Lionel at the rate of 2 miles per hour covered distance=rate*time=2*2=4 miles. So, the distance between him and Walt was 48-4=44 miles when Walt left his house. Now, their combined rate to cover this distance was 2+6=8 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=44/8=5.5 hours. Total time that Lionel was walking is 2+5.5=7.5 hours, which means that he covered in that time interval distance=rate*time=2*7.5=15 miles.
Answer: B.
Answer: (B) 15
Question: If pq = 3(p+ 1) + q and p and q are integers, p could be any of the following values EXCEPT:
(A) 2
(B) 4
(C) 3
(D) 7
(E) 9
Rationale: pq = 3(p + 1) + q
pq - q = 3(p + 1)
q = 3(p + 1)/(p-1)
q won't be an integer only if p = 8 (from the options).
Answer: E
Answer: (E) 9
Question: If by selling 110 apples, the cost price of 120 apples is realised. The gain % is?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 13%
Rationale: 1 apple=1 rup
cp of 110 app=110 rs
sp of 110 app=120 rs
gain=120-110=10
gain%=10/100*110=11%
ANSWER:C
Answer: (C) 11%
Question: If a:b=3:1 and b:c=1:4 find a:b:c?
(A) 1:6:2
(B) 3:1:4
(C) 2:3:4
(D) 2:3:3
(E) 1:4:2
Rationale: a:b = 3:1, b:c = 1:4
3:1
1:4
(a = a × b, b = b × b and c = b × c)
a:b:c = 3:1:4
B
Answer: (B) 3:1:4
Question: Anne earned $3 an hour baby-sitting, and $4 an hour working in the garden. Last week she did
baby-sitting for 5 hours and garden work for 3 hours. How much more money does she need to
buy a game that costs $35?
(A) $8
(B) $12
(C) $6
(D) $21
(E) $10
Rationale: 5 x $3 = $15 for baby-sitting
3 x $4 = $12 for garden work
$15 + $12 = $27 she has
$35 - $27 = $8 more needed to
buy the game
correct answer A
Answer: (A) $8
Question: What is the CP of Rs 100 stock at 6 discount, with 1/5% brokerage?
(A) 96.9
(B) 96.3
(C) 94.2
(D) 96.7
(E) 96.21
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-6+1/5
94.2
Thus the CP is Rs 94.2.
ANSWER: C
Answer: (C) 94.2
Question: Jack, Jill, and Sandy each have one try to make a basket from half court. If their individual probabilities of making the basket are 1/6, 1/7, and 1/8 respectively, what is the probability that all three will make a basket?
(A) 1/336
(B) 5/336
(C) 11/336
(D) 1/168
(E) 1/84
Rationale: The probability that all three will make a basket is 1/6*1/7*1/8=1/336.
The answer is A.
Answer: (A) 1/336
Question: A team scored a total of 154 points. If each player on the team scored at least 14 points, then what is the greatest possible number of players on the team?
(A) A)6
(B) B)7
(C) C)8
(D) D)9
(E) E)11
Rationale: 154/14=11 plus remainder.
The answer is E.
Answer: (E) E)11
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 21/112
(B) 36/145
(C) 3/115
(D) 2/115
(E) 3/116
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: If a + xy = a and x is not equal to 0, which of the following must be true?
(A) y=0
(B) x>y
(C) y<x
(D) x-y=0
(E) x+y=0
Rationale: a + xy = a --> xy=0. Since x is not equal to 0, thus y = 0.
Answer: A
Answer: (A) y=0
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.4, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.008
(B) 0.125
(C) 0.144
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.4
Therefore, probability of no rain = 0.6
0.6*0.6*0.4 = 0.144
Hence C
Answer: (C) 0.144
Question: If four cards are drawn at random from a well shuffled pack of cards, what is the probability that each card is an ace?
(A) 6/52C4
(B) 4/52C4
(C) 1/52C4
(D) 3/52C4
(E) 5/52C4
Rationale: Four cards can be drawn from a pack in 52C4 ways.
Let E be the event of each card being an ace.
This can be done in 4C4 i.e, 1 way.
So P(E) = 1/52C4
ANSWER:C
Answer: (C) 1/52C4
Question: A football team lost 5 yards and then gained 9. What is the team's progress?
(A) 1
(B) 3
(C) 2
(D) 4
(E) 5
Rationale: For lost, use negative. For gain, use positive.
Progress = -5 + 9 = 4 yards
correct answer is D)4
Answer: (D) 4
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate go?
(A) 57%
(B) 60%
(C) 65%
(D) 90%
(E) None
Rationale: Solution
Total no of votes polled
= ( 1136 + 7636 + 11628)
= 20400.
Required percentage	= [11628 / 20400 x 100]%
= 57%.
Answer A
Answer: (A) 57%
Question: Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?
(A) 3 pm
(B) 2 pm
(C) 1:00 pm
(D) 11 am
(E) 12 am
Rationale: Explanation :
Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the machines were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm
Answer : Option C
Answer: (C) 1:00 pm
Question: The distance from City A to City B is 200 miles. While driving from City A to City B, Glen drives at a constant speed of 40 miles per hour. Hannah leaves City A 108 minutes after Glen. What is the minimum constant speed in miles per hour that Hannah must exceed in order to arrive in City B before Glen?
(A) 52.5
(B) 55
(C) 57.5
(D) 60
(E) 62.5
Rationale: The time it takes Glen to drive to City B is 200 / 40 = 5 hours.
Hannah needs to take less than 3.2 hours for the trip.
Hannah needs to exceed a constant speed of 200 / 3.2 = 62.5 miles per hour.
The answer is E.
Answer: (E) 62.5
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
(A) 87
(B) 67
(C) 23
(D) 75
(E) 25
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer: C
Answer: (C) 23
Question: The value for A=(0.889 × 55)/9.97 to the nearest tenth is
(A) 0.5
(B) 4.63
(C) 4.9
(D) 7.7
(E) 49.1
Rationale: if we read the Q, we can easily home on to the answer,,
the numerator is clearly between 40 and 50..
denomiator is close to 10..
so A=(0.889 × 55)/9.97 is between 4 and 5..
It may tempt us to solve it since ther are two values between 4 and 5..
but the catch is innearest tenth
4.63 can be called nearest to hundreth and no tenth, so can be eliminated..
4.9 is our answer...
C
Answer: (C) 4.9
Question: The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 87 cm2
(B) 28 cm2
(C) 98 cm2
(D) 26 cm2
(E) 40 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 32/2
= 40 cm2
Answer:E
Answer: (E) 40 cm2
Question: A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 9000 interest. The principal amount borrowed by him was.
(A) Rs 14000
(B) Rs 25000
(C) Rs 16000
(D) Rs 17000
(E) None of these
Rationale: Explanation:
S.I.=Pâˆ—Râˆ—T/100
=>P=S.I.âˆ—100/Râˆ—T
=>P=9000âˆ—100/12âˆ—3=Rs25000
Option B
Answer: (B) Rs 25000
Question: A motor pool has 500 vehicles of which 30 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
(A) 165%
(B) 90%
(C) 53%
(D) 55%
(E) 10%
Rationale: Trucks = 30% of 500 = 150
Other Vehicles (Excluding Trucks) = 500-150 = 350
Diesel Vehicle = 20% of 500 = 100 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 100-15 = 85
Trucks that are NOT diesel = 150 - 15 = 135
Other Vehicles that are NOT diesel Vehicles = 350-85 = 265
Required % = (265/500)*100 = 53%
Answer: option C
Answer: (C) 53%
Question: Find the average of all prime numbers between 30 and 50.
(A) 30
(B) 33.6
(C) 39.8
(D) 44.9
(E) None
Rationale: Sol.
There are five prime numbers between 30 and 50.
They are 31, 37, 41, 43 and 47
∴ Required average = [31 + 37 + 41 + 43 + 47 / 5] = 199/ 5 = 39.8
Answer C
Answer: (C) 39.8
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
(A) 4.1%
(B) 4.04%
(C) 4.35%
(D) 5.04%
(E) 4%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Answer: (B) 4.04%
Question: A man can row at 5 kmph in still water. If the velocity of current is 2 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(A) 2.1 km
(B) 2.9 km
(C) 3.4 km
(D) 4.4 km
(E) 5.6 km
Rationale: Explanation:
Speed in still water = 5 kmph
Speed of the current = 1 kmph
Speed downstream = (5+2) = 7 kmph
Speed upstream = (5-2) = 3 kmph
Let the required distance be x km
Total time taken = 1 hour
â‡’ x/7+x/3=1
â‡’3x+7x=21
â‡’10x=21
â‡’x=2.1 km
Answer: Option A
Answer: (A) 2.1 km
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
(A) 0.14
(B) 0.26
(C) 0.49
(D) 0.55
(E) 0.86
Rationale: probability of adams approval = 0.7
baker approval =0.5
corfu approval=0.4
proabability of approval is must adam approval and atleast one approval
= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval
= 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4
=0.14+0.21+0.14
=0.49
so answer C sufficient
Answer: (C) 0.49
Question: If the odd numbers between 20 to 40 are arranged in a row, what will be the 6th number from the right?
(A) 27
(B) 31
(C) 33
(D) 25
(E) 29
Rationale: 21,23,25,27,29,31,33,35,37,39 these are odd numbers between 20 to 30. The question is 6th number from the right is 29
ANSWER:E
Answer: (E) 29
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a black and the second card is a spade is?
(A) 1/16
(B) 1/8
(C) 1/13
(D) 1/26
(E) 1/52
Rationale: Probability of a black card= 26/52 = 1/12
Probability of a jack = 13/52 = 1/4
Probability of both = P1*P2 = 1/(2*4) = 1/8
Answer is B.
Answer: (B) 1/8
Question: What would be the seventh rung of the following pyramid?
1
11
21
1211
111221
312211
13112221
(A) 1113213211
(B) 1223213211
(C) 1527321321
(D) 1112343211
(E) 1532213211
Rationale: A
1113213211. After the first line, each line describes the previous line as follows:
One 1
2 Ones
One 2, One 1
(and so on...)
Answer: (A) 1113213211