RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
A.134600 m
B.235600 m
C.153600 m
D.153344 m
Answer: C.153600 m
Explanation: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Question: The product of the digits of the four-digit number W is 36. No two digits of are identical. How many different numbers are possible values of W ?
A.6
B.12
C.24
D.36
Answer: C.24
Explanation: The main question here is how can you arrange 4 different digits W. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.
Therefore no of ways to arrange 4 diff. digits is 4! which is 24
hence C
Question: Sachin is younger than Rahul by 18 years. If the ratio of their ages is 7:9, find the age of Sachin
A.24.5
B.63
C.65
D.36
Answer: B.63
Explanation: Explanation:
If Rahul age is x, then Sachin age is x - 18,
so,
9x - 162 = 7x
2x = 162
x = 81
So Sachin age is 81 - 18 = 63
Answer: B) 63
Question: In how many W ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
A.W=288
B.W=144
C.12
D.48
Answer: B.W=144
Explanation: 4 white chess pieces can be arranged in 4! ways and 4 black pieces can be arranged in 3 ! ways.
W_W_W_W
Number of ways = 4!*3! = 24 * 6 = 144
Answer B
Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A.3/4
B.4/7
C.1/8
D.3/7
Answer: B.4/7
Explanation: Solution
Total number of balls	=(6+8)
= 14.
Number of white balls	= 8.
P(drawing a white ball)	= 8/14
‹=› 4/7.
Answer B
Question: Express a speed of 16 kmph in meters per second?
A.10 mps
B.8 mps
C.4 mps
D.7 mps
Answer: C.4 mps
Explanation: 16 * 5/18
= 4 mps
Answer:C
Question: Find the odd man out. 742, 743, 633, 853, 871, 990, 532
A.532
B.990
C.633
D.742
Answer: D.742
Explanation: Explanation :
In all numbers except 742, the difference of third and first digit is the middle digit. Answer : Option D
Question: If p, q and r are positive integers and satisfy x = (p + q - r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?
A.81
B.1
C.9
D.8
Answer: B.1
Explanation: Hence, x = (p + q - r)/r = (p - q + r)/q = (q + r - p)/p
=> x = (p + q - r + p - q + r + q + r - p)/(r + q + p)
=> x = (p + q + r)/(r + q + p) = 1.
Answer: B
Question: A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: blue, green, yellow, or pink. The store packs notepads in packages that contain either 3 notepads of teh same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
A.6
B.8
C.16
D.24
Answer: C.16
Explanation: 1: 3 notepads of the same size and the same color = the first size in 4 ways + second size is also in 4 ways = 8
2: 3 notepads of the same size and of 3 different colors = the first size in 4c3 ways + second size is also in 4c3 ways = 4 = 4 = 8
so total = 16 ways
ANS:C
Question: What is the smallest no. which must be added to 8261955 so as to obtain a sum which is divisible by 11?
A.8
B.11
C.13
D.15
Answer: B.11
Explanation: For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.
For 8261955, Difference =(8+6+9+5) -(2+1+5)=28-8=20.
The units digit is at odd place. So we add 2 to the number
=> 8261955 +2 = 8261957
Now , (8+6+9+7) -(2+1+5)=30-8=22 => 22 is a multiple of 11 and hence 8261957 is also divisible by 11
B
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 10 minutes, how much time will she spend doing yoga? (rounded to minutes)
A.10 min.
B.41 min.
C.17 min.
D.23 min.
Answer: C.17 min.
Explanation: The ratio is 2:3 = gym:ride, so (10)(3/2) = 15 minutes at the gym, and 15 + 10 = 25 minutes exercise, so (2/3)(25) = 17 minutes yoga.
Answer: C
Question: The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 25 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?
A.75%
B.25%
C.10%
D.45%
Answer: D.45%
Explanation: Let length of each side of square A be 10
Area of A = 10^2 = 100
Since , length of each side of square A is increased by 100 percent to make square B
length of each side of square B = 2*10 = 20
Area of B = 20^2 = 400
Since , length of the side of square B is increased by 25 percent to make square C
length of each side of square C= 1.25*20 = 25
Area of C= 25^2 = 625
Difference in areas of C and cummulative areas of A and B = 625 -(400+100) = 225
percent is the area of square C greater than the sum of the areas of squares A and B = (225/500) * 100 % = 45%
Answer D
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 40 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 4 hours, how many machines of type R were used?
A.11/3
B.10/3
C.8/3
D.13/3
Answer: B.10/3
Explanation: Rate of machine R =1/40
Rate of machine S =1/20
since same no of machines used for R and S to do the same work in 4 hrs
So collective rate needed to finish the work in 4 hrs= 1/4
Let the no of machine be x
So, x/40 +x/20 =1/4
3x/40=1/4
x=10/3
So no of machine R is 10/3
Answer B
Question: Fred has $200. If he wants to give each of his nine grandkids the same amount of money as a gift, how much money will Fred have left over for himself out of the $200?
A.$1
B.$2
C.$4
D.$7
Answer: B.$2
Explanation: $200 is not divisible by 9 (2+0+0 does not = a multiple of 9). Counting down from $200, $199 is not divisible by 9 (1+9+9 = 19, which is not a multiple of 9), but $198 is (1+9+8 = 18, which is dividible by 9). This means that Fred has $200 - $198 = $2 left over, hence answer : B
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction.
A.1/12
B.1/19
C.1/16
D.1/12
Answer: A.1/12
Explanation: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
Answer:A
Question: Divide Rs. 1400 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
A.346
B.368
C.350
D.337
Answer: C.350
Explanation: A+B+C = 1400
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1400 => 350
Answer:C
Question: A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 18%?
A.17 per kg
B.17.70 per kg
C.16.5 per kg
D.16 per kg
Answer: B.17.70 per kg
Explanation: C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)
= 3000.
S.P. = 118% of 3000 = (118⁄100 × 3000) = 3540
∴ Rate of S.P. of the mixture = (3540⁄200) per kg
= 17.70 per kg.
Answer B
Question: A start walking from a place at a uniform speed of 3 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B.
A.4.7 kmph
B.3.6 kmph
C.4 kmph
D.7 kmph
Answer: B.3.6 kmph
Explanation: Distance covered by A in 30 min = 1 Km
B covers extra 1km in 1 hour 48 minutes (9/5 hr)
i.e. Relative speed of B over A = 1/(9/5) = 5/9
So the speed of B = Speed of A + 5/9
= 3 + 5/9
= 3.55
Answer B
Question: A watch passes through three hands and each person gains 25%. If the third person sells it for $62.50, what did the first person pay for it?
A.$24
B.$28
C.$32
D.$36
Answer: C.$32
Explanation: 1.25*1.25*1.25 * original price = 62.5
(5/4)^3 * original price = 62.5
original price = 64*62.5 / 125 = $32
The answer is C.
Question: List L: ABC, BCA, CAB
In list L above, there are 4 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
A.47
B.114
C.152
D.161
Answer: C.152
Explanation: Let's try to sum the 3 given numbers taking their place values into account:
(100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)
= 100(A + B + C) + 10(A + B + C) + (A + B + C)
= 111*(A + B + C)
We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152
Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.
Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3
A, B and C are all even. 2+4+8 = 14. Factors 2 and 7
Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.
C
Question: At 30 minutes past 5 o'clock, what is the angle between the two hands?
A.45
B.60
C.30
D.15
Answer: D.15
Explanation: The hour hand moves 360 degrees in 12 hours.
The hour hand moves 30 degrees in 1 hour and 15 degrees in 30 minutes.
The minute hand moves 360 degrees in 60 minutes and 180 degrees in 30 minutes.
At 30 minutes past 5, the hour hand has moved 165 degrees.
At 30 minutes past 5, the hour hand has moved 180 degrees.
The angle between the two hands is 15 degrees.
The answer is D.
Question: As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 40%, what is the probability that Karen will be accepted to at least one project?
A.317/500
B.141/250
C.98/125
D.67/100
Answer: C.98/125
Explanation: Since the probability of Karen's being accepted to each individual project is 40%, the probability of her not being accepted to each project is 60%. The probability that she will be accepted to none is, therefore, (3/5)*(3/5)*(3/5)=27/125.
P(Karen will be accepted to at least one project) = 1 - (27/125) = 98/125.
The answer is C.
Question: N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?
A.5
B.7
C.9
D.None
Answer: B.7
Explanation: Explanation :
Each person sings with everyone else other than the ones standing near him and “himself”.
So, each person sings with (n-3) persons. Also, they stand in form of a circle, so we can avoid 1 side of the circle, as all the others would have already sung.
Total number of songs, hence is n * (n – 3 ) / 2.
Total song time = 28 minutes, and 2 minutes per song.
So, total number of songs is 14.
So, n*(n – 3) / 2 = 14. n*(n-3) = 28 => n = 7.
Answer : B
Question: Vikas can cover a distance in 1 hr 24 min by covering (left(dfrac{2}{3}right)^{rd})of the distance at 4 kmph and the rest at 5kmph. The total distance is?
A.4 km
B.5 km
C.6 km
D.9 km
Answer: C.6 km
Explanation: Let total distance be SS
total time = 1 hr 24 min = 84 min
= 8460=21158460=2115 hr
Let Vikas travels from A−>T−>SA−>T−>S
A ------------------------ T ------------ S
<---------- (2S3)(2S3)---------><----(S3)(S3)---->
AA to TT :: speed = 4 kmph
Distance = (23)×S(23)×S
T to S :: speed = 5 km =
Distance = (1−23)S=13S(1−23)S=13S
Total time:
2115=2/3S4+1/3S42115=2/3S4+1/3S4
84=10S+4S84=10S+4S {Multiply both sides by 15×415×4}
S=8414=6S=8414=6 km
Option(C) is correct
Question: A money lender lent Rs. 1000 at 3% per year and Rs. 1200 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.
A.3.5
B.3.75
C.3.88
D.4.25
Answer: C.3.88
Explanation: (1000xtx3/100) + (1200xtx5/100) = 350 â†’ t =3.88 answer C
Question: 5 points are marked on a straight line and another 6 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
A.91
B.5
C.196
D.21
Answer: B.5
Explanation: assuming that the top line can have either 2 points or 1 point...
5! / 1!4! - 5! / 2! 3! yields 5.
B
Question: Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm.
A.45
B.47
C.49
D.42
Answer: A.45
Explanation: Required length = H.C.F. of 495 cm, 900 cm and 1665 cm.
495 = 3^2 x 5 x 11, 900 = 2^2 x 3^2 x 5^2, 1665 = 3^2 x 5 x 37.
Therefore, H.C.F. = 32 x 5 = 45.
Hence, required length = 45 cm.
Answer is A.
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 47 kg, then the weight of B is:
A.39 kg
B.32 kg
C.33 kg
D.34 kg
Answer: A.39 kg
Explanation: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (47 x 2) = 94 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 174 …. (iv)
Subtracting (i) from (iv), we get : B = 39.
B’s weight = 39 kg.
Answer: A
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.288
B.266
C.245
D.298
Answer: C.245
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X
= 245 m.
Answer: C
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
A.6
B.5
C.4
D.3
Answer: A.6
Explanation: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Question: A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5 hours, then the distance covered at 40 kmph is
A.130 km
B.120km
C.100km
D.140km
Answer: C.100km
Explanation: Let the partial distance covered at 40 kmph be X
Let the another partial distance covered at 60 kmph be (250 - x)
Thus, x/40 - (250 - x)/60 = 5
or, x/40 + (250 - x)/60 = 5
or, (3x + 500 - 2x)//120 = 5
or 500 + x = 600
x=100
ANSWER:C
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
A.Sunday
B.Saturday
C.Friday
D.Monday
Answer: A.Sunday
Explanation: Explanation:
Given that 8th Feb, 2005 was Tuesday
Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)
366 days = 2 odd days
Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday
Answer: Option A
Question: If log10 7 = a, then log10 (1/70)is equal to:
A.- (1 + a)
B.(1 + a)-1
C.a /10
D.1 /10a
Answer: A.- (1 + a)
Explanation: Explanation:
log10 (1/70)= log10 1 - log10 70
= - log10 (7 x 10)
= - (log10 7 + log10 10)
= - (a + 1).
ANSWER IS A
Question: Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 5 miles per hour, what is his average rate for the entire trip in miles per minute?
A.1/9
B.2/15
C.3/15
D.1/4
Answer: A.1/9
Explanation: Dan travels 4 miles round trip.
Running part: (2/10 = 1/5*60 = 12 minutes)
Swimming Part: (2/5 = 2/5*60 = 24 minutes)
4 miles in (12+24) minutes
4/36 = 1/9 mile per minute
Answer: 1/9 mile per minute
Question: A heap of coconuts is divided into groups of 2, 3 and 11 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
A.A)31
B.B)41
C.C)51
D.D)67
Answer: D.D)67
Explanation: LCM = 66
=> 66 + 1 = 67
ANSWER:D
Question: If the average marks of three batches of 65, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
A.53.33
B.54.41
C.55
D.57
Answer: B.54.41
Explanation: Sol.
Required average = [65x50 + 60x55 + 45x60 / 65 + 60 + 45]
= [3250 + 3300 + 2700 / 160]
=9250 / 170 = 54.41.
Answer B
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
A.409
B.400
C.428
D.427
Answer: B.400
Explanation: 441 = P(21/20)2
P = 400
Answer:B
Question: A certain bag contains 60 balls — 22 white, 18 green, 2 yellow, 15 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
A.0.7
B.0.15
C.0.54
D.0.85
Answer: A.0.7
Explanation: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 18 + 2)/60 = 42/60 = 0.7.
Answer: A.
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
A.17 days
B.11 days
C.12 days
D.15 days
Answer: B.11 days
Explanation: (5 + x)/20 + 5/25 = 1 => x = 11 days
ANSWER:B
Question: The average height of 35 boys in a class was calculated as 185cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
A.187.89 cm
B.183.29 cm
C.123.98 cm
D.149.98 cm
Answer: B.183.29 cm
Explanation: Calculated average height of 35 boys = 185 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 185 cm - (166 cm - 106 cm)/35
= 185 cm - 60 /35 cm
= 185 cm - 1.71 cm = 183.29 cm.
Answer: B
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :
A.35
B.38
C.90
D.88
Answer: B.38
Explanation: Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 130
=> 5x = 190
=> x = 38
Answer:B
Question: A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 61⁄4% p.a for 2 years. Find his gain in the transaction per year.
A.167.5
B.150
C.225
D.112.5
Answer: D.112.5
Explanation: Explanation :
The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×4×2/100=400
He also lends it at 6 1⁄4% p.a for 2 years
Simple interest that he gets = PRT/100=5000×254×21/00=625
His overall gain in 2 years = Rs.625 - Rs.400 = Rs.225
His overall gain in 1 year = 2252 = Rs.112.5
Answer : Option D
Question: Excluding stoppages, the speed of a bus is 80 km/hr and including stoppages, it is 70 km/hr. For how many minutes does the bus stop per hour?
A.11 min
B.10 min
C.8 min
D.6 min
Answer: C.8 min
Explanation: Due to stoppages, it covers 10 km less.
Time taken to cover 10 km = 10/80 * 60
= 8 min.
Answer:C
Question: In a group of 50 people, 25 have visited Iceland and 23 have visited Norway. If 21 people have visited both Iceland and Norway, how many people have visited neither country?
A.20
B.21
C.22
D.23
Answer: D.23
Explanation: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:
50= 25 + 23 - 21 + (# in Neither Group)
=23
The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.
D
Question: The cost price of a radio is Rs.4800 and it was sold for Rs.4400, find the loss %?
A.8
B.9
C.7
D.6
Answer: A.8
Explanation: 4800 ---- 400
100 ---- ? => 8%
Answer: A
Question: What is the sum of the greatest common factor and the lowest common multiple of 36 and 16?
A.148
B.210
C.314
D.320
Answer: A.148
Explanation: Prime factorization of 36 = 2 x 2 x 3 x 3
Prime factorization of 16 = 2 x 2 x 2 x 2
GCF = 4
LCM = 144
Sum = 148.
Answer A.
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
A.12
B.45
C.77
D.88
Answer: B.45
Explanation: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3)
= 45 kmph.
Answer: B
Question: In the following alphabet second half is written first and then the first half is arranged in reverse order.
Then which of the following will be the 5th letter to the left of 16th letter from the right?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A.S
B.Y
C.U
D.H
Answer: A.S
Explanation: N O P Q R S T U V W X Y Z M L K J I H G F E D C B A
(16 + 5) = 21th letter from your right is S.
Answer: A
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more?
A.49
B.40
C.21
D.79
Answer: B.40
Explanation: 760 ---- 22
760 ---- 20
x ----- 19
x*19 = 760*20
x = 800
760
-------
40
Answer: B
Question: The sum of two numbers is 90 and their difference is 10. Find their product.
A.104
B.2000
C.315
D.325
Answer: B.2000
Explanation: Let the numbers be x and y.
Then x + y = 90 and x - y = 10
x = 50; y = 40
xy = 50 * 40 = 2000
ANSWER:B
Question: If |4x+6| = 36, then find the sum of the values of x?
A.-3
B.4
C.3
D.-5
Answer: A.-3
Explanation: |4x+6| = 36
4x+6 = 36 or 4x+6 = -36
4x = 30 or 4x = -42
x = 7.5 or x = -10.5
sum = 7.5-10.5 = -3
Answer is A
Question: A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 10 months and 7 months respectively. What was the ratio of their investments?
A.10:12:14
B.12:24:28
C.20:22:12
D.25:49:80
Answer: D.25:49:80
Explanation: Explanation :
Ratio in which A,B and C shared the profit = 5 : 7 : 8
Assume that the ratio of their investment = a:b:c
Then 14a : 10b : 7c = 5 : 7 : 8
Good to go, we got the equation. Now it's a matter of time to find a, b and c
14a/10b = 5/7
=> 98a = 50b
=> b = 98a/50 = 49a/25 ---(1)
14a/7c =5/8
=> 2a/c =5/8
=> 16a = 5c
=> c = 16a/5 ---(2)
a : b : c = a : 49a/25 : 16a/5 = 1 : 49/25 : 16/5 = 25 : 49 : 80. Answer : Option D
Question: The population of a village is 6000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?
A.5000
B.4860
C.5400
D.4800
Answer: B.4860
Explanation: Formula :
( After =100 denominator
Ago = 100 numerator)
6000 Ã— 90/100 Ã— 90/100 = 4860
B
Question: If u+5/v is a prime integer, which of the following must be true?
1.v=5u
2. v is a prime integer
3. u+5/v is ODD.
A.None
B.1 only
C.2 only
D.1 and 2 only
Answer: A.None
Explanation: I would pick up numbers and do .
i hope the question is (u+5)/v....
let u = 3 , v = 4
3+5/4 = 2 = Prime
1. v is not equal to 5u
2.v is not a prime number
3. (u+5)/v is not odd.
hence A
Question: There are between 110 and 120 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.111
B.113
C.115
D.117
Answer: B.113
Explanation: The numbers with the form 4n+1 are 113 and 117.
Only 113 has the form 3k+2.
The answer is B.