RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: he distance from town A to town B is five miles. C is six miles from B. Which of the following could be the maximum distance from A to C?
A.11
B.77
C.51
D.16
Answer: A.11
Explanation: Explanation:
Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11
Answer:A
Question: The price of an item is discounted 7 percent on day 1 of a sale. On day 2, the item is discounted another 7 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
A.83.7%
B.85.2%
C.86.8%
D.78.8%
Answer: A.83.7%
Explanation: Let initial price be 100
Price in day 1 after 7% discount = 93
Price in day 2 after 7% discount = 86.49
Price in day 3 after 10% discount = 77.84
So, Price in day 3 as percentage of the sale price on day 1 will be = 77.84/93*100 => 83.7%
Answer will definitely be (A)
Question: Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying science?
A.52
B.65
C.115
D.158
Answer: D.158
Explanation: Given, boys and girls are in the ratio of 7 : 6,
So, Number of boys = 7/13 x 390 = 210
Number of girls = 390 - 210 = 180
Students studying Arts and Science are in the ratio of 3 : 7,
Number of students studying Arts = 3/10 x 390 = 117
Number of students studying Science = 390 - 117 = 273
Also boys and girls studying Arts are in the ratio of 4 : 5,
Number of boys studying arts = 4/9 x 117 = 52
Number of boys studying science = 210 - 52 = 158
ANSWER:D
Question: The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 5 ?
A.96
B.106
C.128
D.137
Answer: D.137
Explanation: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 * 20 = 640
Now increase in avg = 4 runs. So, new avg = 32+5 = 37 runs
Total runs = new avg x new no. of innings = 37 * 21 = 777
Runs made in the 11th inning = 777-640 = 137
ANSWER:D
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 9 is
A.3
B.7
C.21
D.189
Answer: D.189
Explanation: In that case, the Sophie prime numbers greater than 9 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be D
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 100 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
A.a. 0.96
B.b. 0.096
C.c. 0.0096
D.d. 0.00096
Answer: C.c. 0.0096
Explanation: Let total Production be 10000 units....
A produces 4000 units and 36 units are defective
B produces 6000 units and 60 units are defective
So, Out of total 10,000 units 96 units are defective...
So the required probability = 96/10000 => 0.0096
Answer will be (C)
Question: There are 3 people and 3 chairs. In how many different ways people can occupy the chairs?
A.6
B.15
C.24
D.36
Answer: A.6
Explanation: number of ways =3! = 6
Answer is A
Question: If a positive integer n is divisible by both 3 and 7, then n must also be divisible by which of the following?
I. 21
II. 10
III. 63
A.None
B.I only
C.II only
D.I and II
Answer: B.I only
Explanation: A multiple of 3 and 7 is also a multiple of 21, but not necessarily a multiple of 10 or 63.
The answer is B.
Question: A train passes a station platform in 40 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.177 m
B.300 m
C.240 m
D.187 m
Answer: B.300 m
Explanation: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 40 = 15
x + 300 = 600
x = 300 m.
Answer: B
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 8 different shirts, 10 different pairs of jeans, and 8 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
A.30
B.90
C.640
D.480
Answer: C.640
Explanation: Total # of outfits = 8 * 10 * 8 = 960
Answer - C
Question: X can finish a work in 30 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
A.3
B.10
C.6
D.8
Answer: B.10
Explanation: Work done by X in 1 day = 1/30
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/30) = 10
B
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.15,000 earned at the end of 2years from the startingof the business?
A.s. 5,000
B.s. 4,500
C.s. 5,700
D.s. 6,500
Answer: B.s. 4,500
Explanation: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 15000 x	3/10	= Rs. 4,500.
B
Question: If the weight of 10 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ?
A.7.2 kg.
B.10.8 kg.
C.14.04 kg.
D.18.0 kg
Answer: C.14.04 kg.
Explanation: Answer
∵Weight of 10 m long rod = 23.4 kg
∴ Weight of 1 m long rod = 23.4 / 10 kg
∴ Weight of 6 m long rod = 23.4 x 6 / 10
= 14.04 kg
Option: C
Question: Two trains are moving in the same direction at 54 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
A.135
B.277
C.187
D.257
Answer: A.135
Explanation: Relative speed = (54 - 36) * 5/18 = 5 mps.
Distance covered in 27 sec = 27 * 5 = 135 m.
The length of the faster train = 135 m.
Answer: A
Question: Solution for 3.15+.014+.458
A.3.622
B.3.911
C.4.938
D.2.986
Answer: A.3.622
Explanation: 3.15+.014+.458=0
0=0-3.15-0.014-0.458
0=-3.622
answer :A
Question: If by selling twelve note-books, the seller earns profit equal to the selling price of two note-books, what is his percentage profit?
A.20%
B.25%
C.2163%
D.Data inadequate
Answer: A.20%
Explanation: Percentage profit= 2/12−2×100=20%
Answer A
Question: If x^2=x+2, then x^3 = ?
A.3x+2
B.3x-2
C.2x+1
D.2x-3
Answer: A.3x+2
Explanation: x^2 = x+2
x^3 = x*x^2 = x*(x+2) = x^2 + 2x = (x+2)+2x = 3x+2
The answer is A.
Question: Find the odd man out. 5,7,9,12,13
A.52
B.12
C.11
D.14
Answer: C.11
Explanation: Explanation :
5+2=7
7+2=9
9+2=11
11+2=13
Hence, it is clear that 11 should have come instead of 12
Answer : Option C
Question: It will take 16 days for Mary to complete a certain task alone. She worked for 8 days before she was joined by her sister. both of them completed the remaining task in 2 and half days. if her sister had joined her when she started the task, how many days would it have taken?
A.6
B.8
C.2
D.5
Answer: D.5
Explanation: Explanation:
Mary and her sister complete half work in 2.5 days
=> they can complete whole work in 5 days
Answer: Option D
Question: The radius of a cylindrical vessel is 7cm and height is 1cm. Find the whole surface of the cylinder?
A.352
B.771
C.440
D.767
Answer: A.352
Explanation: r = 7 h = 1
2πr(h + r) = 2 * 22/7 * 7(8) = 352
Answer:A
Question: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 12 ?
A.5
B.6
C.7
D.8
Answer: A.5
Explanation: Denote |x - 3| as y: y^2 + y = 12 --> y = -4 or y = 3. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.
y = |x - 3| = 3 --> x = 6 or x = -1. The sum = 5.
Answer: A.
Question: In the formula of converting temperature from Celsius to Fahrenheit F=9/5C+32, How many integer values(not fractional) of F will be there that lies between 100 to 200 for integer values of C.
A.9
B.10
C.11
D.12
Answer: C.11
Explanation: for c=40 ,F=((9/5) *40)+32=104
c=45 ,f=(9*9)+32=113
c=50 ,f=(9*10)+32=122
c=55 ,f=(9*11)+32=131
c=60 ,f=(9*12)+32=140
c=65 ,f=(9*13)+32=149
c=70 ,f=(9*14)+32=158
c=75 ,f=(9*15)+32=167
c=80 ,f=(9*16)+32=176
c=85 ,f=(9*17)+32=185
c=90 ,f=(9*18)+32=194
so ans is 11.
ANSWER:C
Question: A businessman earns $25800 in December, thus decreasing his average annual (January to December) earnings by $1000. His average annual earnings would be
Source: CMAT Preparation
A.$29000
B.$36800
C.$40200
D.$41000
Answer: B.$36800
Explanation: (x - 25,800)/11 - x/12 = 1,000
x = 441,600
x/12 = 36,800
Answer: B
Question: Which of the following data sets has the second smallest standard deviation?
A. {1, 2, 3, 4, 5}
B. {2, 3, 3, 3, 4}
C. {2, 2, 2, 4, 5}
D. {0, 2, 3, 4, 6}
Answer: C. {2, 2, 2, 4, 5}
Explanation: since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..
The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...
Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..
clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..
Next is D, which has a range of 6-0 or 6..
and has smallest standard of deviation.
and (C) {2, 2, 2, 4, 5} has second smallest standard of deviation.
ans C
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
A.20 hours
B.25 hours
C.35 hours
D.Cannot be determined
Answer: C.35 hours
Explanation: If c takes x hrs, B takes 2x hrs and A takes 4x hrs,
then
1/x +1/2x = 1/4x = 1/5
7/4x = 1/5
x= 7*5/4 hrs = 35/4 hrs
So A alone will take 4*35/4 = 35 hrs
ANSWER:C
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
A.2/9
B.5/7
C.1/7
D.1/9
Answer: D.1/9
Explanation: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 × 6 = 36
E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Hence, n(E) = 4
P(E) = n(E)/n(S)
=4/36
=1/9
Answer : Option D
Question: What is the least number which when divided by 8, 12, 15 and 20 leaves in each case a remainder of 5
A.110
B.125
C.75
D.170
Answer: B.125
Explanation: LCM of 8, 12, 15 and 20 = 120
Required Number = 120 + 5 = 125
Answer: Option B
Question: Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 12 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
A.20
B.21
C.22
D.23
Answer: D.23
Explanation: Check two extreme cases:
Jane = 18, child = 9, years ago = 32-18 = 14 --> child's age now = 9+14 = 23;
Jane = 20, child = 10, years ago = 32-20 = 12 --> child's age now = 10+12 = 22.
Answer: D.
Question: Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in the train approaching the place hears the second shot 10 minutes after the first. The speed of the trian (in km/hr), supposing that speed travels at 330 metres per second, is:
A.50.4
B.111.8
C.19.88
D.59.4
Answer: D.59.4
Explanation: Sol.
Let the speed of the train be x m/sec. Then,
Distance travelled by the train in 10 min. = Distance travelled by sound in 30 sec.
∴ Speed of the train = 16.5 m/sec = [16.5*18/5] km/hr = 59.4 km/hr
Answer D
Question: In how many ways can an answer key for a quiz be written if the quiz contains 4 true-false questions followed by 3 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
A.512
B.656
C.740
D.896
Answer: D.896
Explanation: There are 2^4 = 16 possibilities for the true-false answers.
However we need to remove two cases for TTTT and FFFF.
There are 4*4*4 = 64 possibilities for the multiple choice questions.
The total number of possibilities is 14*64 = 896.
The answer is D.
Question: A train covers a distance of 10 km in 20 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.50
B.80
C.120
D.100
Answer: A.50
Explanation: Speed = (10/20 * 60) km/hr = (30 * 5/18) m/sec = 8.333333 m/sec.
Length of the train = 8.333333 * 6 = 50 m.Answer: A
Question: Simplify (4^y + 4^y + 4^y + 4^y) (4^y + 4^y + 4^y + 4^y)
A. 4^4y * 3^3y
B. 12^y+1
C. 16^y+1
D. 12^y
Answer: C. 16^y+1
Explanation: C
(4^y + 4^y + 4^y + 4^y) (4^y + 4^y + 4^y + 4^y)
(4*4^y)(4*4^y)
16*16^y=16^(y+1)..
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam?
A.22
B.26
C.25
D.28
Answer: C.25
Explanation: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25
Answer: C
Question: If x and y are perfect squares, then which three of the following is not necessarily a perfect square?
A.x^2
B.xy
C.4x
D.x+y
Answer: A.x^2
Explanation: If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square.
Answer: A.
Question: Two heavily loaded sixteen-wheeler transport trucks are 787 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
A.90
B.131
C.150
D.320
Answer: B.131
Explanation: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:
Short version:
Truck A travels for an hour.
Distance remaining = 787-90 = 697k
Ratio of speeds 9:8 -> 697/17 = 41
Truck A = 90 + 41*9 = 459
Truck B = 41*8 = 328
Delta = 131km
Answer B
Question: A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?
A.8 km
B.4 km
C.6 km
D.1 km
Answer: C.6 km
Explanation: Average speed = (2 * 3 * 2) / (3 + 2) = 12/5 km/hr.
Distance traveled = 12/5 * 5 = 12 km.
Distance between house and school = 12/2 = 6 km.
Answer: C
Question: John is traveling to a meeting that is 20 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
A.40 mph
B.37 mph
C.41 mph
D.49 mph
Answer: A.40 mph
Explanation: Well 40mph. A. Time*rate=distance --> 0.5*rate=20 --> rate=40
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
A.3098
B.3000
C.2878
D.2899
Answer: B.3000
Explanation: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
AnswerB
Question: In the first 20 overs of a cricket game, the run rate was only 4.6. What should be the run rate in the remaining 30 overs to reach the target of 396 runs?
A.10.13
B.9.13
C.8.13
D.11.13
Answer: A.10.13
Explanation: Required run rate = 396 - (4.6 x 20)	/30	=	304/30 = 10.13 Option A
Question: What will be the vulgar fraction of 0.60
A.3/7
B.3/5
C.3/2
D.3/7
Answer: B.3/5
Explanation: Explanation:
0.6 = 60/100 = 3/5
Option B
Question: which of the following options is a multiple of 5!-20?
A.4!+76
B.5!+80
C.4!-10
D.5!+10
Answer: A.4!+76
Explanation: The factorial 5! is same as 5*4*3*2
Therefore 5!-20 =(5*4*3*2)-20
This gives you 120-20=100
A is the correct option.
Question: If r > a and L < a, which of the following cannot be true?
A. d + L = 14
B. d - L = 7
C. d - L = 1
D. a - r = 9
Answer: D. a - r = 9
Explanation: Is the answer D?
If r>a, then r-a>0 (always positive). The converse would be a-r<0 (always negative). Option D states that a-r=9, which can never be true.
Question: If 5 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
A. -8
B. -4
C. -3
D. 1
Answer: A. -8
Explanation: The phrase “5 is one solution of the equation” means that one value of x is 5. Thus, we first must plug 5 for x into the given equation to determine the value of k. So we have
5^2 + (3)(5) + k = 10
25 + 15 + k = 10
40 + k = 10
k = -30
Next we plug -30 into the given equation for k and then solve for x.
x^2 + 3x – 30 = 10
x^2 + 3x – 40 = 0
(x+8)(x-5) = 0
x = -8 or x = 5
Thus, -8 is the other solution. Answer A.
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 16% less than the price each head sold for the day before.what was the gross profit on this shipment?
A.$100
B.$110
C.$125
D.$130
Answer: B.$110
Explanation: Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 84% of the previous price: 84/100 * 1/2 = $(21/50)
Total revenue by selling 500 heads = 21/50 * 500 = 210
Total revenue after selling 1500 cabbage heads - 210+500 = $710
Money spent on the purchase: $600
Profit = 710-600 = $110
Ans: B
Question: A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
A.7500
B.7522
C.2789
D.3677
Answer: A.7500
Explanation: P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8
= Rs.7500
Answer:A
Question: A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were?
A.1009
B.1110
C.1111
D.1112
Answer: A.1009
Explanation: 999919 = 1000000 - 81 = 1000^2 - 9^2 = (1000+9)(1000-9) = 1009*991.
Since there were more mice than there were cats, 991 cats killed 1009 mice each.
ANSWER:A
Question: A student is ranked 13th from right and 8th from left. How many students are there in totality ?
A.18
B.19
C.20
D.21
Answer: C.20
Explanation: From right 13 , From left 8
Total = 13+8-1 = 20
ANSWER:C
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
A.40 %
B.50 %
C.60 %
D.70 %
Answer: B.50 %
Explanation: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50 %
B
Question: In a group of 100 adults, 60 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
A.40
B.52
C.54
D.60
Answer: A.40
Explanation: 12 left-haded women compose 100-60=40% (or 2/5) of all women, so there are total of 5*12=60 women --> 100-60=40 men.
Answer: A.
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 2?
A.$0.50
B.$0.75
C.$1.25
D.$1.50
Answer: B.$0.75
Explanation: Salary grade of 5 is p(5)=9.50+0.25(5–1)=9.50+0.25*4;
Salary grade of 2 is p(2)=9.50 + 0.25(2–1)=9.50+0.25;
p(5)-p(2)=9.50+0.25*4-9.50-0.25=0.75.
Answer: B.
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 45% play football, how many play both?
A.120
B.150
C.200
D.180
Answer: A.120
Explanation: n(A) = 75*600/100 = 450
n(B) = 45*600/100 = 270
n(AUB) = 600
n(AnB) = 450+270-600 = 120
Answer is A
Question: Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio A of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job?
A.5 to 1
B.10 to 7
C.1 to 5
D.7 to 10
Answer: D.7 to 10
Explanation: Solutioning this exercise can be facilitated by using a R T W (rate time work) table:
We translate the exercise into the table:
R T W
X t/2 1
Y t 1
Z (t/2*3/2 =3t/4) 1
From this table we find the rates
Rx = 2/t
Ry = 1/t
Rz = 4/3t
The Q is what is the ratio of (Tx + Ty) / (Ty + Tz)
Rx + Ry = 2/t + 4/3t = 6/3t+4/3t = 10/3t
Ry+Rz = 1/t + 4/3t = 3/3t + 4/3t = 7/3t
The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7
Since Time Ratio A is the inverse of work, the the answer is 7 to 10
CORRECT ANSWER D
Question: An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest after one year becomes:
A.10.25%
B.10.5%
C.10.75%
D.10%
Answer: A.10.25%
Explanation: Explanation :
Let the automobile financier lends Rs.100
Simple Interest for first 6 months = PRT/100=100×10×12/100=Rs. 5
After 6 months, he adds the simple interest to principal
i.e., after 6 months, principal becomes Rs.100 + Rs.5 = Rs.105
Simple Interest for next 6 months = PRT/100=105×10×1/2 /100=Rs. 5.25
Amount at the end of 1 year = Rs.105 + Rs. 5.25 = Rs.110.25
i.e., Effective Simple Interest he gets for Rs.100 for 1 year = 110.25 - 100 = 10.25
i.e, the Effective Rate of Interest = 10.25%
(∵R = 100×SI/PT=100×10.25/100×1=10.25%)
Answer : Option A
Question: What percent of the different arrangements of the letters of the word ADACUS are those in which the vowels appear together?
A.20%
B.25%
C.30%
D.40%
Answer: A.20%
Explanation: let's determine the number of total possibilities in arranging the letters. There are six spaces, so the total number of arrangements is 6!, or 360.
Next, we need to figure out how to determine the number of ways that we can arrange the 3 vowels together - simply place them together (as in AAU) and call that a single place.
Next, we must determine the number of ways to arrange the now 4 units (i.e., AAU, B, C, S). Like above, there are 4 units and 4 places so the number of arrangements is 4!, or 24.
Finally, we need to account for the number of ways we can arrange AAU. We can either write out each unique iteration (AAU, AUA and UAA) or calculate as 3!/2! and get 3.
Putting this all together, we get the number of ways to arrange the letters so that the vowels are together is 4! x 3 ==> 72
the number of total arrangements of all the letters is 6! ==> 360
72/360 = 1/5, or 20%
Correct answer is A
Question: Which digits should come in place of * and $ if the number 62684*$ is divisible by both 8 and 5 ?
A.8,5
B.4,0
C.1,4
D.0,8
Answer: B.4,0
Explanation: Since the given number is divisible by 5, so 0 or 5 must come in place of $. But, a number ending with 5 is never divisible by 8. So, 0 will replace $.
Now, the number formed by the last three digits is 4*0, which becomes divisible by 8, if * is replaced by 4.
Hence, digits in place of * and $ are 4 and 0 respectively.
ANSWER B 4,0
Question: If a and b are even numbers, which of the following CANNOT be the value of ab?
A.6
B.14
C.21
D.24
Answer: C.21
Explanation: 21 is a odd number. The multiple of two even number should be an even number
ans C