RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: if 6 coins are tossed simultaneously what is the probability of getting atleast four heads
A.11/32
B.12/32
C.13/32
D.15/32
Answer: A.11/32
Explanation: n(S)= 2^6= 64
n(E)= 6C4 + 6C5 + 6C6 = 15+6+1= 22
p(E)= n(E)/n(S)= 22/64= 11/32
ANSWER:A
Question: The average of temperatures at noontime from Monday to Friday is 40; the lowest one is 30, what is the possible maximum range of the temperatures?
A.20
B.25
C.50
D.45
Answer: C.50
Explanation: Average=40, Sum of temperatures=40*5=200
As the min temperature is 30, max would be 200-4*30=80 --> The range=80(max)-30(min)=50
Answer: C
Question: List L: ABC, BCA, CAB
In list L above, there are 5 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: D.161
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.
D
Question: One copy machine can make 30 copies a minute, and a second copy machine makes 20 copies a minute. If the two copiers work together, how long would it take them to make 2,000 copies?
A.20 minutes
B.40 minutes
C.45 minutes
D.50 minutes
Answer: B.40 minutes
Explanation: Total work done by both machines in a minute = 30 + 20 = 50 copies
Total number of copies required = 2000
Time = 2000/50 = 40 mins
Answer B
Question: if log 2 = 0.30103, the number of digits in 2128 is
.
A.38
B.39
C.40
D.41
Answer: B.39
Explanation: log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4
ie, its characteristic = 38
Hence, number of digits in 2128 = 38+1 = 39
Answer: Option B
Question: The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?
A.3:9
B.3:0
C.3:5
D.3:2
Answer: C.3:5
Explanation: Let the present ages of the two brothers be x and 2x years respectively.
Then, (x - 5)/(2x - 5) = 1/3
3(x - 5) = (2x - 5) => x = 10
Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5
Answer: C
Question: There are 5,280 feet in 1 mile and 11 inches in one foot. How many inches are in a mile?
A.5,280 - 12
B.5,280/12
C.12(5,280)
D.11(5,280)
Answer: D.11(5,280)
Explanation: 1 feet = 11 inches
1 mile = 5280 feet
1 mile = 5280*11 inches
Ans: D
Question: How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
A.256
B.24
C.12
D.None of these
Answer: B.24
Explanation: Solution:
Let the 3 boys be B1, B2, B3 and 4 prizes be P1, P2, P3 and P4.
Now B1 is eligible to receive any of the 4 available prizes (so 4 ways).
B2 will receive prize from rest 3 available prizes(so 3 ways).
B3 will receive his prize from the rest 2 prizes available(so 2 ways).
So total ways would be: 4*3*2*1=24 Ways.
Hence, the 4 prizes can be distributed in 24 ways.
Answer B
Question: A reduction of 40% in the price of bananas would enable a man to obtain 60 more for Rs.40, what is reduced price per dozen?
A.1.2
B.2.2
C.3.2
D.4.2
Answer: C.3.2
Explanation: 40*(40/100) = 16 --- 60
? --- 12 => Rs.3.2
Answer: C
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 30%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
A.15%
B.25%
C.33.33%
D.40%
Answer: A.15%
Explanation: Say 100g pure butter costs $100
But; $100 is his 25% profit because he just used 80gram pure butter.
80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.30(85)
so;
total weight=100g
fat=20g
20%
A
Question: If a drawing has an outer circle of diameter 30 and an inner circle of diameter 24, then what fraction of outer circle's surface is not covered by the inner circle?
A.3/6
B.8/24
C.14/16
D.9/25
Answer: D.9/25
Explanation: The questions asks us to find the surface which is not covered by the inner circle i.e., area of the surface not covered.
Where as circumference is the length along the edge of the circle,
2*pi*r implies the length of the curve
pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem
Area of the inner circle=pi* r^2, where r=12
=>pi*144
Area of the outer circle=pi*225
Surface not covered by the inner circle=pi*225-pi*144=Pi*81
fraction of outer circle's surface is not covered by the inner circle= Pi*81/total area of the outer circle
=>Pi*81/Pi*225=9/25
Answer is D
Question: In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 2/3 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight
A.1/6
B.1/8
C.1/4
D.3/4
Answer: A.1/6
Explanation: Good question.
So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).
we're told that 2/3 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/3 are yellow. We're also told there is an equal probability of straight or curved, 1/2.
We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).
So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 1/3 * 1/2 = 1/6, or A.
Question: Simple interest on a sum at 5% per annum for 2 years is Rs.140. The C.I. on the same sum for the same period is?
A.141.5
B.142.5
C.143.7
D.144.6
Answer: A.141.5
Explanation: SI = 70 + 70
CI = 70 + 70 + 1.5 = 141.5
Answer: A
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
A.11.9
B.11.2
C.11.6
D.11.5
Answer: D.11.5
Explanation: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
Answer: D
Question: At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 16th highest price and the 23rd lowest price among the prices of the items sold, how many items were sold at the garage sale?
A.35
B.36
C.37
D.38
Answer: D.38
Explanation: There were 15 items sold at a higher price than the radio and 22 items sold at a lower price than the radio. Including the radio, there were 15 + 22 + 1 = 38 items sold.
The answer is D.
Question: In a pond 100 fish were caught and examined for levels of mercury. Of this sample, 25 fish were found to have unhealthy levels of mercury. If we use this sample as an estimate, and we know the population of the pond to be 5,000 fish, what is the approximate number of fish in the pond that have healthy levels of mercury?
A.2,150
B.750
C.1,250
D.3,750
Answer: D.3,750
Explanation: Let D = fish population of the pond = 5,000,
B = fish population of the sample = 100,
A = fish sample with healthy level of mercury = 100 - 25 = 75, and
C = fish population with healthy level of mercury, then:
Proportion: A/B = C/D
Proportion: 75/100 = C/5,000
C = 3,750. There are approximately 3,750 healthy fish in the pond.
Answer is D
Question: In a group of ducks and cows, the total number of legs are 12 more than twice the no. of heads. Find the total no.of buffaloes.
A.6
B.8
C.10
D.4
Answer: A.6
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 12
=> 2x = 12=> x = 6
A
Question: A shop owner sells 40 Pencils and gains SP of 15 pencils. Find the gain %?
A.55%
B.40%
C.50%
D.60%
Answer: D.60%
Explanation: Gain=15 orangesTotal 40 orangesCP 40-15=25(15/25)*100=60%Ans D
Question: How much did Rohit get as profit at the year-end in the business done by Nitin, Rohit and Kunal?
I.Kunal invested Rs. 8000 for nine months, his profit was times that of Rohit’s and his investment was four times that of Nitin.
II.Nitin and Rohit invested for one year in the proportion 1 : 2 respectively.
III.The three together got Rs. 1000 as profit at the year end.
A.Only I and II
B.Only I and III
C.Question cannot be answered even with the information in all the three statements.
D.All I, II and III
Answer: D.All I, II and III
Explanation: Explanation:
I and II give:
K = Rs. (8000 x 9) for 1 month = Rs. 72000 for 1 month.
N = Rs. ( 1/4 x 8000 x12 ) for 1 month = Rs. 24000 for 1 month.
R = Rs. 48000 for 1 month.
K : N : R = 72000 : 24000 : 48000 = 3 : 1 : 2.
III gives, total profit = Rs. 1000.
Rohit’s share = Rs. (1000 x 2/6 )= Rs. 333 1/3
answer is (D).
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
A.1 kmph
B.5 kmph
C.8 kmph
D.3 kmph
Answer: A.1 kmph
Explanation: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
ANSWER:A
Question: How many different 6 letter combinations can be created from the letters A,B,C,D,E and F?
A.216
B.36
C.46656
D.1296
Answer: C.46656
Explanation: This is a case of number of arrangements possible with repetition.
Thus you have 6 options each for the 1st,2nd,3rd,4th,5th and 6th letter giving you a total of 6*6*6*6*6*6 = 46656 number of possible combinations.
Answer : C
Question: man is 21 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A.14years
B.26 years
C.19 years
D.18 years
Answer: C.19 years
Explanation: Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 21) + 2 = 2(x + 2)
x + 23 = 2x + 4
x = 19.
answer :C
Question: Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
A.Rs. 17,000
B.Rs. 20,000
C.Rs. 25,500
D.Rs. 38,000
Answer: D.Rs. 38,000
Explanation: Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then,	2x + 4000/	3x + 4000=40/57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
ANSWER IS D
Question: A certain rectangular crate measures 12 feet by 16 feet by 18 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
A.4
B.5
C.6
D.8
Answer: D.8
Explanation: For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 18x16 i.e. of radius 16/2 = 8
D
Question: The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.9. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?
A.1/5
B.2/5
C.3/10
D.4/5
Answer: C.3/10
Explanation: p(m) =0.2
p(r) =0.1
p(m intersection r) = 0 (If events M and R cannot both occur)
p(m or r) = 0.2+0.1 =0.3
Corrected !!
Answer C
Question: Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.1,20,000 earned at the end of 3 years from the start of the business in 1999 ?
A.Rs.40,000
B.Rs.50,000
C.Rs.70,000
D.Rs.75,000
Answer: A.Rs.40,000
Explanation: Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(12000x2/6) = Rs. 40,000. Answer A
Question: The slant height of a cone is 22 cm and radius of the base is 7cm, find the curved surface of the cone?
A.426
B.284
C.483
D.256
Answer: C.483
Explanation: π * 22 * 7
= 483
Answer:C
Question: If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 170 pounds. What is Leo's current weight?
A.80
B.86
C.92
D.98
Answer: D.98
Explanation: L+K = 170 and so K = 170-L
L+10 = 1.5K = 1.5(170-L)
2.5L = 245
L = 98
The answer is D.
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 56 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
A.70
B.400
C.150
D.35
Answer: B.400
Explanation: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 56, so 0.14*{total} = 56 --> {total} = 400.
Answer: B.
Question: In six successive games, a baseball team scored 3 runs once, 6 runs twice, and 7 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?
A.8
B.7
C.6
D.5
Answer: C.6
Explanation: 3 runs once (one game)
6 runs twice (two game)
7 runs three times (three games)
SO we have (3*1 + 6*2 + 7*3)/6 = 36/6 = 6.
ANS: C.
Question: A man divides $8600 Among 5 Sons, 3 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
A.A)$200
B.B)$716.67
C.C)$800
D.D)$1200
Answer: B.B)$716.67
Explanation: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 5*5X+3*3X+2*X=8600
25X+9X+2X=8600
36X=8600, X=238.89
Daughter receives four times of nephew so 3 *238.89 = 716.67.
So Each Daughter receives $800. answer is option B) $716.67.
Question: If x+y=300, x-y=200, for integers of x and y, y=?
A.200
B.250
C.50
D.115
Answer: B.250
Explanation: x+y = 300
x-y = 200
2x = 100
x = 50
y = 250
Answer is B
Question: The sale price sarees listed for Rs.550 after successive discount is 18% and 12% is?
A.298
B.237
C.342
D.396
Answer: D.396
Explanation: 550*(88/100)*(82/100)
= 396
Answer: D
Question: In a school 10% of the boys are same in number as 1/6th of the girls. what is the ratio of boys to the girls in the school?
A.5:3
B.2:3
C.1:4
D.3:7
Answer: A.5:3
Explanation: 10% of B = 1/6 G
10B/100 = G/6
B = 5G/3
B/G = 5/3
B:G = 5:3
Answer is A
Question: A taxi charges u dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.
A.un – c/8(100)
B.cu + 4n-8/200
C.u + (4cn-8c)/100
D.u + 100cn/4
Answer: C.u + (4cn-8c)/100
Explanation: This is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost u is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost u, or subtract the additional cost from u. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C).
Question: If the selling price of 10 articles is same as the cost price of 12 articles. Find the gain or loss percentage?
A.10%
B.20%
C.30%
D.32%
Answer: B.20%
Explanation: Let the C.P of each article be Re 1. Then,
S.P of 10 articles = C.P of 12 articles = Rs. 12
Now, C.P of 10 articles = Rs. 10, S.p of 10 articles = Rs 12
Gain = Rs ( 12 - 10 ) = Rs 2.
Gain% = ( 2/10 × 100 ) % = 20%
B)
Question: Three numbers are in the ratio 2 : 3 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
A.A)24
B.B)75
C.C)48
D.D)46
Answer: A.A)24
Explanation: Let the numbers be 2x, 3x, 7x.
Largest number = 7x.
Smallest number = 3x.
Third number = 6x.
7x + 2x = 3x + 48
6x = 48 =>x=8
3x=24=> third number is 24.
Answer:A
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 2/7 % his yearly income diminishes by Rs.61.50. his capital is
A.22.378
B.87.86
C.246.0
D.78.88
Answer: B.87.86
Explanation: Explanation:
Capital = Rs.x , then
5/7x = 61.5
x = 87.86
Answer: B) Rs.87.86
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers W are there between 6* + 2 and 6* + 6, inclusive?
A.None
B.One
C.Two
D.Three
Answer: A.None
Explanation: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes W in this range.
Answer: A.
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
A.600
B.277
C.269
D.261
Answer: A.600
Explanation: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600.Answer: A
Question: On his first 4 tests, John received an average score of X points. If on his fifth test, he exceeds his previous average score by 30 points, what is his average score for his first 5 tests?
A.X +6
B.X +5
C.X +4
D.X
Answer: A.X +6
Explanation: Total of 1st 4 tests= 4X
5th test score = X + 30
Total of all 5 tests = 5X + 30
Average = X +6
Answer : A
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 3 years ago?
A.11
B.10
C.12
D.14
Answer: A.11
Explanation: Let's say
Age of Richard is "R"
Age of David is "D"
Age of Scott is "S"
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 3 years ago?
i.e. D-4 = 14-3 = 11 years
ANSWER:A
Question: What is the ratio of Arun's monthly income in the year 2006, Suman's monthly income in the year 2007 and Jyothi's monthly income in the year 2005?
A.22
B.67
C.26
D.18
Answer: A.22
Explanation: Answer:	A
Question: A square with sides of 15 units each. What would be the area of the square. Consider a square as a combination of two right angled triangles.
A.100
B.256
C.225
D.81
Answer: C.225
Explanation: A square can be considered as a set of two right angled triangles joined from the hypotenuse.
Since the sides are 10 units each. The height and base of both the triangles is 10 each.
Area of a right angled triangle is 1/2 * base * height
Area of both the triangles is 2 * 1/2 * base * height. Since both triangles are similar.
= base * height
= 15*15 =225
Ans: C
Question: 4 men can check exam papers in 8 days working 5 hours regularly. What is the total hours when 2 men will check the double of the papers in 20 days?
A.8
B.9
C.6
D.1
Answer: A.8
Explanation: Let a man can do 1 unit of work in 1 hour.
Total units of work = 4 x 8 x 5 = 160 units.
Now work = 2 x 160 = 320 units.
Now 2 men work for 20 days. Let in x hours they have to work per day.
Now total work = 2×x×20 = 40 x
40x = 320 So x = 320/40 = 8 hours.
Answer:A
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
A.10
B.18
C.16
D.14
Answer: B.18
Explanation: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Question: Which is the least number that must be subtracted from 1100 so that the remainder when divided by 7, 12, 16 is 4?
A.58
B.68
C.78
D.88
Answer: D.88
Explanation: First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,16) = 48*7 = 336
The numbers which will leave remainder 4 will be {336+4, 336x2 +4, 336x3 +4,...}
The largest such number less than or equal to 1100 is 336x3+4 or 1012
To obtain this you need to subtract 88
D
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
A.680
B.700
C.720
D.800
Answer: C.720
Explanation: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER : C
Question: On average, Machine A will produce a completed item once every six minutes, and Machine B will produce a completed item once every ten minutes. The number of items Machine A produces in a 24-hour period is approximately what percent greater than the number of items Machine B would produce in that same period?
A.100%%
B.67%
C.25%
D.125%
Answer: B.67%
Explanation: Machine A: 1 item in 6 minutes --> 1/6 items in 1 minute;
Machine B: 1 item in 10 minutes --> 1/10 items in 1 minute.
In the same time period, Machine A produces (1/6-1/10)/(1/10)*100=~67% more items than machine B.
Answer: B.
Question: What inequality represents the condition 1<x<8?
A.|x|<3
B.|x+5|<4
C.|x-9/2|<7/2
D.|-5+x|<4
Answer: C.|x-9/2|<7/2
Explanation: 1<x<8 represents segment with
length: 8-1 = 7
center: (8+1)/2 = 9/2
For any |x-a|<b a is a center and b is a half of length. So, |x-9/2|<7/2 represents our inequality (answer C)
Question: . In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 55 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
A. 50%
B. 53%
C. 54%
D. 41%
Answer: D. 41%
Explanation: Registered voters = 100
D = 60
R = 40
55% of D ( 60) = 33
20% of R ( 40 ) = 8
Total voter% of registered voters = 41 / 100
41% Ans D
Question: A meal cost $ 37.25 adn there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
A.42-45
B.41-43
C.39-41
D.37-39
Answer: B.41-43
Explanation: 10%(37.25) = 3.725
15%(37.25) = 5.5875
total amount could have been 37.25+3.725 and 37.25+5.5875
=> could have been between 40.975 and 42.8375
=> approximately between 41 and 43
Answer is B.
Question: sue has 3 apples. Billy has 5 apples. If billy steals all of sues apples and eats 2 how many does he have left?
A.2
B.5
C.6
D.4
Answer: C.6
Explanation: 6 C