mathewhe/aqua_rat huggingface dataset:
Question: . A car covers a distance of 390 km in 4 hours. Find its speed?
(A) 104
(B) 55
(C) 66
(D) 98
(E) 100
Rationale: 390/4 = 98 kmph
Answer: D
Answer: (D) 98
Question: If 40% of (x-y) = 20% of (x+y), then what percent of x is y?
(A) 50.5%
(B) 44.4%
(C) 22.2%
(D) 33.3%
(E) 25%
Rationale: 40% of (x-y) = 20% of (x+y)
40/100 (x-y) = 20/100 (x+y)
x = 3y
Required percentage = y/x *100 = y/3y * 100 = 33.3%
Answer is D
Answer: (D) 33.3%
Question: Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?
(A)  87
(B)  89
(C)  90
(D)  92
(E)  95
Rationale: Set X = {11, 13, 17,............., 83, 89, 97}
Set Y = {10, 20, 30,..............., 70, 80, 90}
Combining two sets, say Set Z
Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97}
Range = Max Value - Min Value
Range (Z) = 97 - 10 = 87
OA A is the answer.
Answer: (A)  87
Question: Prints a page 60 pg per min .If the printed for 1 hours except 10 min.Where there
was an paper jam,how many page did it print
(A) 10,880
(B) 12,880
(C) 3,000
(D) 8,880
(E) 18,880
Rationale: 60 pages ------->1 min
1 hrs except 10 mints means=1*60=60-10=50 mints
i.e.,50*60=3,000 pages printed.
ANSWER:C
Answer: (C) 3,000
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
(A) 10 2/8
(B) 10 2/9
(C) 10 2/3
(D) 10 2/2
(E) 10 2/5
Rationale: 2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3
Answer: C
Answer: (C) 10 2/3
Question: The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed six times, what is the probability that the coin turns up tails on at least one of the tosses?
(A) 15/16
(B) 21/32
(C) 31/32
(D) 63/64
(E) 51/64
Rationale: P(6 heads)= 1/2*1/2*1/2*1/2*1/2*1/2=1/64.
P(at least one tail)=1-1/64=63/64.
The answer is D.
Answer: (D) 63/64
Question: A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning?
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: 14x + 75 = 15(x + 3)
x = 30 + 3 = 33
Answer:C
Answer: (C) 33
Question: Which of the following equations represents a line that is perpendicular to the line described by the equation 2x + 3y = 12?
(A) 4x + 2y = 5
(B) 5x + y = 7
(C) 3x - 2y = 8
(D) 4x - 3y = 9
(E) x + y = 10
Rationale: Perpendicular lines have slopes which are negative reciprocals of each other.
The line 2x + 3y = 12 in slope-intercept form is y = -(2/3)x + 4
The slope of this line is -2/3.
The slope of a perpendicular line is 3/2.
3x - 2y = 8 in slope-intercept form is y = (3/2)x - 4
The answer is C.
Answer: (C) 3x - 2y = 8
Question: Manoj, Nayan and Ajit together started a software company. It was agreed that Manoj would invest Rs. 6500 for 6 months, Nayan, Rs. 8400 for 5 months and Ajit Rs. 10,000 for 3 months. Manoj wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of Nayan in the profit ?
(A) 2330
(B) 2660
(C) 3000
(D) none of the above
(E) Cannot be determined
Rationale: Explanation :
Manoj is a working member and for that, he receive 5% of the profit
= 5% of 7400 = 5*7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = 6500*6 : 8400*5 : 10000*3
= 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20
= 13 : 14 : 10
Share of Nayan in the profit = 7030 * (14/37) = 190*14 = 2660
Answer : B
Answer: (B) 2660
Question: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability R that the 2 apples selected will include the spoiled one?
(A) a. 1/5
(B) b. 3/10
(C) c. 2/5
(D) d. 1/2
(E) e. 3/5
Rationale: there can be two ways in which one can select a spoiled apple and a good apple.
1. you pick the spoiled one first and the good one later..
Prob of picking bad one = 1/5 (one bad apple)
Prob of picking a good one from the remaining 4 good apples (4/4 =1)
therefore the total prob for case 1 = i/5 * 1 = 1/5
Total prob R= porb1 + prob2 = 1/5+1/5 = 2/5.C
Answer: (C) c. 2/5
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 15
(B) 66
(C) 18
(D) 16
(E) 81
Rationale: Explanation:
90 * 10/60 = 15 kmph
Answer:A
Answer: (A) 15
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) 238
(B) 480
(C) 287
(D) 117
(E) 181
Rationale: Explanation:
SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer: B
Answer: (B) 480
Question: One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 300 of the attendees are neither female nor students, what is the total number of attendees at the convention?
(A) 600
(B) 300
(C) 1200
(D) 1500
(E) 1800
Rationale: Let no. of Attendee are A.
Now As per the condition of the problem stated above .
We have following population in the convention as Attendee.
Total no. of females = [2/3]*A
Total no. of females as student : [1/6]*A
Total no. of students = [1/3]*A
Total no. of male as student = [1/6]*A
Total no. of males = A - [2/3]*A = [1/3]A
No. of males which are not student = [1/3]A - [1/6]*A = 300
Hence A = 1800
Total no of males who are not student will be the answer as it states it should be neither female nor student
So Answer is E
Answer: (E) 1800
Question: If a boat is rowed downstream for 200 km in 10 hours and upstream for 96 km in 12 hours, what is the speed of the boat and the river?
(A) 14 , 18
(B) 14 , 6
(C) 14 , 14
(D) 6 , 6
(E) 14 , 10
Rationale: Explanation:
If x: speed of boats man in still water
y: speed of the river
Downstream speed (Ds) = x + y
Upstream speed (Us) = x â€“ y
x = (Ds + Us) / 2
y = (Ds â€“ Us) / 2
In the above problem Ds = 20 ; Us = 8
x = (20 + 8) / 2 = 28/2 = 14 km/hr
y = (20 - 8) /2 = 12/2 = 6 km/hr
ANSWER: B
Answer: (B) 14 , 6
Question: On an order of 3 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: Clearly, the retailer gets 1 dozen out of 4 dozens free.
Equivalent discount = 1/4 * 100 = 25%.
Answer B) 25%
Answer: (B) 25%
Question: Ajith and Rana walk around a circular course 115 km in circumference, starting together from the same
point. If they walk at speed of 4 and 5 kmph respectively, in the same direction, when will they meet ?
(A) after 20 hours
(B) after 115 hours
(C) after 115 minutes
(D) after 20 minutes
(E) after 25 minutes
Rationale: Rana is the faster person. He gains 1 km in 1 hour. So Rana will gain one complete round over
Ajith in 115 hours. i.e. they will meet after 115 hours.
Answer: B
Answer: (B) after 115 hours
Question: If a Ã— b = 2a - 3b + ab, then 4 Ã— 5 + 5 Ã— 4 is equal to :
(A) 31
(B) 32
(C) 43
(D) 45
(E) 26
Rationale: Explanation:
4 Ã— 5 + 5 Ã— 4 = (2 Ã— 4 - 3 Ã— 5 + 4 Ã— 5) + ( 2 Ã— 5 - 3 Ã— 4 + 5 Ã— 4)
= (8 -15 + 20 + 10 - 12 +20) = 31.
Answer: A
Answer: (A) 31
Question: If ab-a-b=265
bc-b-c=155
ac-c-a=150
then find a?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: (A-1)(B-1)=AB-A-B+1=265+1=266..(1)
(B-1)(C-1)=BC-B-C+1=155+1=156..(2)
(C-1)(A-1)=CA-C-A+1=150+1=151..(3)
(1)/(2) gives..(A-1)/(C-1)=266/156..(4)
(3)*(4) gives..(A-1)^2=257.47...A=17.04
Solving other equations..B=17.58 and C=10.4
ANSWER:B
Answer: (B) 17
Question: A rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
(A) 144ft
(B) 88ft
(C) 22ft
(D) 112ft
(E) 146t
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
10 x Breadth = 680
Breadth = 68 feet
Area to be fenced = 2B + L = 2 (68) + 20 = 146 feet
Answer: E) 146ft
Answer: (E) 146t
Question: Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs.12 per square metre.
(A) 1824
(B) 1854
(C) 1872
(D) 1888
(E) 1999
Rationale: Explanation:
Area of the carpet = Area of the room = (13 × 9) m2 = 117 m2.
Length of the carpet = (area/width) = 117 ×(4/3) m = 156 m.
Therefore Cost of carpeting = (156 × 12) = Rs.1872
Answer: Option C
Answer: (C) 1872
Question: How many cubes of 10cm edge can be put in a cubical box of 1m edge
(A) 10
(B) 100
(C) 1000
(D) 10000
(E) 3000
Rationale: number of cubes=(100x100x100)/(10x10x10)=1000 Answer: C
Answer: (C) 1000
Question: A has 10000 chocolates.20% of the chocolates are Eaten.What percentage of the uneaten Chocolates must be eaten so that 3/2 of all chocolates are eaten?
(A) 39.25
(B) 37.25
(C) 37.26
(D) 38.21
(E) 38.32
Rationale: Number of chocolates=10,000
Currently Eaten=10,000*20/100=2000
Uneaten Chocolates=10000-2000=8000
2/3 of all chocolates=5000
The number of chocolates to be eaten to make 2/3 of all chocolates Eaten =5000-2000=3000
So now the question remains - 3000 is how much percentage of uneaten chocolates (8000)
= 3000 * 100 /8000
=37.5
Answer (B)
Answer: (B) 37.25
Question: In Plutarch Enterprises, 60% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?
(A) $80,000
(B) $130,000
(C) $240,000
(D) $290,000
(E) $340,000
Rationale: For sake of ease, let's say there are 10 employees: 6 marketers, 2 engineers, and 2 manager.
Average company salary * Number of employees = Total company salary
>>> $80,000 * 10 = $800,000
Subtract the combined salaries for the marketers (6 * $50,000) and the engineers (2 * $80,000)
>>> $800,000 - $300,000 - $160,000 = $340,000.
The correct answer is E.
Answer: (E) $340,000
Question: A man walks from B to C, a distance of x miles, at 6 miles per hour and returns at 12 miles per hour. What is his average speed?
(A) 10 mph
(B) 9.6 mph
(C) 8.0 mph
(D) 8.4 mph
(E) 4 mph
Rationale: Total distance covered = 2x
Time taken12miles / hour = x/12 hrs
Time taken @ 6 miles / hour = x/6 hrs
Avg speed = 2x / (x/6 + x/12) = 8 mph
Ans is C
Answer: (C) 8.0 mph
Question: A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to
contradict each other, narraƟng the same incident
(A) 30%
(B) 35%
(C) 40%
(D) 45%
(E) 50%
Rationale: Explanation:
Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5
P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5
Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%
Answer: B
Answer: (B) 35%
Question: ♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠2.423 - ♠3.421 =
(A) 1.05
(B) 1.04
(C) -0.8
(D) -1.0
(E) -0.1
Rationale: ♠2.423 - ♠3.421
2.4 - 3.2 = -0.8
Answer : C
Answer: (C) -0.8
Question: In digging a pond 25 m * 10 m * 5 m the volumes of the soil extracted will be?
(A) 1750
(B) 1000
(C) 2866
(D) 2787
(E) 1121
Rationale: 25 * 10 * 5 = 1750
Answer: A
Answer: (A) 1750
Question: A zeebra chases a tiger 5 hours after the tiger runs. zeebra takes 6 hours to reach the tiger. If the average speed of the zeebra is 55 kmph, what s the average speed of the tiger?
(A) 35kmph
(B) 32kmph
(C) 30kmph
(D) 31kmph
(E) 20kmph
Rationale: tiger take 11 hours and zeebra take 6 hours...then Distance chased by them is 55*6.so speed of tiger is (55*6)/11=30kmph.
ANSWER IS C
Answer: (C) 30kmph
Question: The speed of a boat in upstream is 45 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 70,10 kmph
(B) 67.5,22.5 kmph
(C) 70.5,70.5 kmph
(D) 78.6,10.25 kmph
(E) 70,12 kmph
Rationale: Speed of the boat in still water
= (45+90)/2
= 67.5 kmph. Speed of the stream
= (90-45)/2
= 22.5 kmph.
Answer:B
Answer: (B) 67.5,22.5 kmph
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 7m
(B) 6m
(C) 5m
(D) 2m
(E) 4m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: D
Answer: (D) 2m
Question: From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Soln:-
15x=45 --> 23/20*x=45 --> x=45*20/23=900/23=~39.
Answer: B.
Answer: (B) 39
Question: A team of 11 member is to be formed from a group of 5 men and 8 women. At most 3 men are allowed. How many combination are possible.
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: At most 3 men means not more than 3,
Case 1 All women not possible
Case 2 10 women and 1men not possible
Case 3 9 women and 2 men not possible
Case 4 8 women and 3 men =5C3 * 8C8 = 10.
ANSWER:B
Answer: (B) 10
Question: A trader bought a car at 20% discount on its original price. He sold it at a 45% increase on the price he bought it. What percent of profit did he make on the original price?
(A) A)10%
(B) B)12%
(C) C)16%
(D) D)20%
(E) E)22%
Rationale: Original price = 100
CP = 80
S = 80*(145/100) = 116
100 - 116 = 16%
C)
Answer: (C) C)16%
Question: The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.
(A) 33
(B) 88
(C) 48
(D) 77
(E) 27
Rationale: π * 12 * 4 = 48
Answer:C
Answer: (C) 48
Question: Two trains of length 400 m and 200 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 36 kmph. After how much time will the trains meet?
(A) 8 sec
(B) 20/7 sec
(C) 33/7 sec
(D) 21/7 sec
(E) 32/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 36)*5/18 = 25 mps.
The time required = d/s = 200/25 = 8 sec.
Answer : A
Answer: (A) 8 sec
Question: What is the greatest integer m for which the number 40!/14^m is an integer?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: 14^m = 2^m*7^m.
Let's figure out how many 7's are in the prime factorization of 40!
The multiples of 7 are: 7, 14, 21, 28, 35.
Thus 7^5 will divide 40! but 7^6 will not.
Clearly 2^5 will divide 40!
So m=5 is the largest possible integer.
The answer is D.
Answer: (D) 5
Question: If n = (33)^43 + (23)^33 what is the units digit of n?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: First of all, the units digit of (33)^23 is the same as that of 3^23 and the units digit of (23)^33 is the same as that of 3^33. So, we need to find the units digit of 3^23 + 3^33.
Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:
3^1=3 (the units digit is 3)
3^2=9 (the units digit is 9)
3^3=27 (the units digit is 7)
3^4=81 (the units digit is 1)
3^5=243 (the units digit is 3 again!)
...
Thus:
The units digit of 3^23 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).
The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (33)^23 + (23)^33 is 3 + 3 = 6.
Answer: D.
Answer: (D) 6
Question: If n = 2×3×5×7×11×13×17, then which of the following statements must be true?
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
IV . divisible by 35 only
(A) I only
(B) none and IV only
(C) III only
(D) I and III only
(E) e None
Rationale: n = 2×3×5×7×11×13×17 = 39270
I. not divisible by 600
II 39270+19=39289 not divisible by 19
III. 39270+4/2= odd= 19637
iv. divisible by 35
B
Answer: (B) none and IV only
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 255
(B) 267
(C) 235
(D) 277
(E) 211
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m.
Answer:C
Answer: (C) 235
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 101 players took part in that tournament. How many matches were played?
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 100 matches
(E) 87 matches
Rationale: D100 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 100 matches were played.
Answer: (D) 100 matches
Question: A room is 18 meters long, 15 meters wide 12 meters in height. The longest possible rod which can be placed in the room is
(A) 25.28 meters
(B) 24.28 meters
(C) 23.28 meters
(D) 26.28 meters
(E) 20.28 meters
Rationale: Square root of 18^2+15^2+12^2...(Diognal) which is square root of 639 that lies 25<√639<26. Hence the answer should be A
Answer: (A) 25.28 meters
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train.
(A) 175 m
(B) 145 m
(C) 140 m
(D) 200 m
(E) 155 m
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12 = 200 meter
ANSWER: D
Answer: (D) 200 m
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 1% p.a. in 5 years. What is the sum?
(A) 82762
(B) 12877
(C) 82882
(D) 80925
(E) 80325
Rationale: Principal = (100 * 4016.25) / (1 * 5)
= Rs.80325.
Answer:E
Answer: (E) 80325
Question: A vendor bought 6 toffees for a rupee.How many for a rupee he must sell to gain 20%.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: SP=(100+20)*1/100=1.20
1.20 rupees=6 toffees
so for 1 rupee=6/1.2=5
ANSWER:C
Answer: (C) 5
Question: A roofing crew can roof the house in 10 hours. Another crew can roof the house in 15 hours. How many hours will it take for both of them working together to roof the house?
(A) 6
(B) 5
(C) 8
(D) 4
(E) 9
Rationale: Work hrs=AB/(A+B)= 150/25 =6
Answer is A
Answer: (A) 6
Question: A number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z. What is the greatest two digit prime saturated integer ?
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95
Rationale: Clearly D A number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z.
96 has more number of smaller prime factor thats the clue !!=D
Answer: (D) 96
Question: The marked price of a radio is Rs 1,600. Rahul gives successive discount of 10%, r% to the Pradeep. If Pradeep pays Rs 1.224 for the radio, find the value of r.
(A) 10%
(B) 20%
(C) 25%
(D) 15%
(E) 30%
Rationale: Marked price of the article = Rs 1,600
Therefore, Selling price = (100 - 10)% x (100 - r%) x 1600
= (90/100) x [(100 - r) / 100] x 1600
Given, 1224 = 9/10 x (100 - r) x 16
=> 1224 x 10 / (9 x 16) = (100 – r)
85 = 100 - r
r = 15%
ANSWER:D
Answer: (D) 15%
Question: On my sister's birthday, she was 132 cm in height, having grown 10% since the year before. How tall was she the previous year?
(A) 130 cm
(B) 126 cm
(C) 120 cm
(D) 116 cm
(E) 112 cm
Rationale: Let the previous year's height be x.
1.1x = 132
x = 120
The answer is C.
Answer: (C) 120 cm
Question: How many different ways are possible to arrange the letters of the word “MACHINE” so that the vowels may occupy only the odd positions?
(A) 800
(B) 125
(C) 348
(D) 576
(E) None
Rationale: Solution
MACHINE has 4 consonants and 3 vowels.The vowels can be placed in position no. 1, 3, 5, 7
⇒ Total number of ways possible = 4P3 = 24.
For each of these 24 ways the 4 consonants can occupy the other 4 places in 4P4 ways
⇒ Total = 24 × 24 = 576
Answer D
Answer: (D) 576
Question: If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions Q represents the final price of the item?
(A) Q=(10,000z + 100z(x – y) – xyz)/10,000
(B) Q=(10,000z + 100z(y – x) – xyz)/10,000
(C) Q=(100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: -A-
z=Original Price
x=MU
y=MD
New price with MU:
z(x/ 100+1)
New price with MD:
z[(x/100+1)(-y/100+1)]
Solvingâ€¦
=z[((x+100)/100)((-y+100)/100)]
=z(x100-xy+10000-100y)/10000
=(zx100-xyz+10000z-100yz)/10000 --> similar to A
Answer: (A) Q=(10,000z + 100z(x – y) – xyz)/10,000
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 5/8
(B) 5/5
(C) 5/4
(D) 5/6
(E) 5/1
Rationale: P(at least one graduate)
= 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer:D
Answer: (D) 5/6
Question: If a lies in the range (-3,2) then which of the following statements must be true?
(A) a^4 >a^3 > a^2 > a
(B) a > a^2 > a^3 > a^4
(C) a^4 > a^2 > a^3 >a
(D) a^2 > a^4 > a^3 >a
(E) a^2 > a^4 > a > a^3
Rationale: consider any number from the given range (-3,+2)..let a=-1/2
then a^2= 1/4
a^3=-1/8
a^4=1/16
so we have a^2>a^4>a^3>a
Ans D
Answer: (D) a^2 > a^4 > a^3 >a
Question: In a group of 2 boys and 8 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?
(A) 120
(B) 140
(C) 160
(D) 180
(E) 200
Rationale: Number of ways to select four children is 10C4 = 210
Number of ways to choose only girls is 8C4 = 70
Number of ways that at least one boy is selected is 210 - 70 = 140
The answer is B.
Answer: (B) 140
Question: Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?
(A) 60,87
(B) 60,86
(C) 60,89
(D) 60,84
(E) 60,81
Rationale: (5x-25):(7x-25) = 35:59
x = 12 => 60,84
Answer: D
Answer: (D) 60,84
Question: If 6 different numbers are to be selected from integers 0 to 6, how many 6-digit even integers greater than 300,000 can be composed?
(A) 1080
(B) 1180
(C) 1280
(D) 1480
(E) 1680
Rationale: Starting with number n >= 3and last number = {0,2,4,6}
case I :
Even number
4 or 6 in 100 thousands digit
the units digit can be any one of {0,2,4(if 6 is considered), 6 (if 4 is considered)}
so IF 4 is considered in 100 thousands digit
1*5*4*3*2*3 = 360
So if 6 is considered in 100 thousands digit
1*5*4*3*2*3 = 360
Hence in Case I we have 720
Case II
3 or 5 in 100 thousands digit
So if 3 is considered in 100 thousands digit
1*5*4*3*2*4 = 480
So if 5 is considered in 100 thousands digit
1*5*4*3*2*4 = 480
Hence For case II we have 480+480= 960
Total we have 960+720 = 1680 cases:
Final Answer:E
Answer: (E) 1680
Question: If a - b = 3 and a(power 2) + b(power 2) = 29, find the value of ab.
(A) 5
(B) 8
(C) 4
(D) 10
(E) 3
Rationale: 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 29 - 9 = 20
ab = 10.
Answer is D.
Answer: (D) 10