RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Calculate the circumference of a circular field whose radius is 8 centimeters.
A.17 π cm
B.18 π cm
C.1 π cm
D.16 π cm
Answer: D.16 π cm
Explanation: Circumference C is given by
C = 2πr = 2π*8 = 16 π cm
Answer: D
Question: If C and D are non-zero integers, and C/D > 1, then which of the following must be true?
A.CD > D
B.2C > D
C.C^2< D^2
D.C > D
Answer: A.CD > D
Explanation: MULTIPLICATION OF TWO INTEGER IS OBIVIOUSLY GREATER THAN EACH ONE OF THEM.
A
Question: Let the function Q(n) represent the product of the first n prime numbers, where n > 0. If x = Q(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
A.ii only
B.iii only
C.i and ii only
D.i and iii only
Answer: D.i and iii only
Explanation: Q(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of Q(n). Thus, Q(n) + 1 = even + 1 = odd. So, (i) is always true.
Now, use logic:
If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.
Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.
Answer: D.
Question: At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $7.50 per hour, how much less than a manager does a chef earn each hour?
A.$1.40
B.$3
C.$3.40
D.$4.40
Answer: B.$3
Explanation: Manager wages per hour = $7.50
Dishwasher wages per hour = half of manager's wages. = 1/2($7.50) ==> $3.75
Chef wages per hour = 20% greater than Dishwasher wages
--> 20% of $3.75 = (20*($3.75)) /100
--> ($75)/100
--> $0.75
Therefore,
Chef wages per hour = $3.75 + $0.75 ==> $4.5
Difference of wages between manager and chef = $7.50 - $4.5 ==> $3
ANSWER:B
Question: Which is greatest 33 1/3%, 4/15 and 0.35 ?
A.33 1/3%
B.4/15
C.0.35
D.Cannot be compared
Answer: C.0.35
Explanation: Answer
331/3% = (100/3) /100 = 1/3 =0.33;
4/15 = 0.26
Clearly 0.35>0.33>0.26
∴ 0.35 is greatest
Correct Option: C
Question: A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for ... days.
A.7 days
B.5 days
C.3 days
D.4 days
Answer: A.7 days
Explanation: The equation portraying the given problem is:
10 * x – 2 * (30 – x) = 216 where x is the number of working days.
Solving this we get x = 23
Number of days he was absent was 7 (30-23) days.
Answer:A
Question: What is the tenth digit to the right of the decimal point, in the decimal expansion of (1/5)^10
A.0
B.2
C.4
D.6
Answer: C.4
Explanation: Actually 1/5 = 0.2 = 2*10^-1
so 2^10 * 10^-10
2 has sequence 2,4,8,6.
Hence digit will be 4
Answer is C
Question: A is 1.5 times as fast as B. A alone can do the work in 30 days. If A and B working together in how many days will the work be completed?
A.23
B.18
C.21
D.24
Answer: B.18
Explanation: A can finish 1 work in 30 days
B can finish 1/1.5 work in 30 days - since A is 1.5 faster than B
This means
B can finish 1 work in 30*1.5 days = 45 days
Now using the awesome GMAT formula when two machines work together they can finish the job in = AB/ (A+B) = 45*30/(45+30) = 20*30/50 = 18 days
So answer is B
Question: Which of the following numbers is between 1⁄2 and 2⁄5?
A..45
B..35
C..29
D..22
Answer: A..45
Explanation: 1/2 = .5
2/5 = .4
The only number between these two is 0.45.
The answer is A.
Question: When a number is divided by 6 &then multiply by 12 the answer is 10 what is the no.?
A.4.5
B.5
C.5.5
D.5.8
Answer: B.5
Explanation: if $x$ is the number, x/6 * 12 = 10
=> 2x = 10
=> x = 5
B
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 2
II. y = 0
III. x = y
A.I only
B.II only
C.III only
D.I and III only
Answer: C.III only
Explanation: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer C
Question: A wildlife preserve is being planned for 7,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population?
A. 340
B. 330
C. 320
D. 780
Answer: D. 780
Explanation: Number of rhinos = 7000
Watering area = 10,000 acres
Number of rhino to increase by 10 percent ,then number of rhino = 7700
Grazing area for a rhino = 100
Total grazing area for 7700 rhinos= 7700 * 100 = 7,70,000
Total area required for the wildlife preserve = 7,70,000 + 10,000 = 7,80,000 = 780 * 1000
Answer D
Question: Pipe P can fill a tank in 6 hours, pipe Q in 12 hours and pipe R in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
A.2 hours
B.2.4 hours
C.3 hours
D.3.4 hours
Answer: D.3.4 hours
Explanation: Explanation:
Part filled by (P + Q + R) in 1 hour = (1/6 + 1/12 + 1/24) = 7/24
All the three pipes together will fill the tank = 24/7 = 3.4 hours
ANSWER D
Question: In a shower, 7 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A.75 cu. m
B.1050 cu. m
C.7500 cu. m
D.75000 cu. m
Answer: B.1050 cu. m
Explanation: 1 hectare = 10000 sq mtr
The volume of water that falls on 1.5 hectares of ground = 0.07*1.5*10000 = 1050 cub mtr .
ANSWER:B
Question: What will come in place of the x in the following Number series? 5,28,57,88,125,166,209,256
A.309
B.159
C.166
D.170
Answer: A.309
Explanation: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
209=43+166
256=47+ 209
309 =53+ 256
=309
A
Question: The averge score of a cricketer for ten matches is 64 runs. If the average for the first six matches is 78. Then find the average for the last four matches?
A.48
B.49
C.40
D.43
Answer: D.43
Explanation: sum of last 4 matches = (10 × 64) – (6 × 78)= 172
Average =172/4
= 43
ANSWER:D
Question: The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. Find the second number.
A.10
B.20
C.30
D.40
Answer: C.30
Explanation: Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 × y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 × y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30.
Answer is C.
Question: The speed of a motor boat is that of the current of water as 30 : 5. The boat goes along with the current in 5 h 10 min. It will come back in
A.5 hour 15 minutes
B.6 hour
C.6 hour 50 minutes
D.12 hour 10 minutes
Answer: C.6 hour 50 minutes
Explanation: Let speed of motor boat is 30x and Current is 5X.
Speed of the boat along with current = 30X + 5X = 35X.
Given Time = 5h 10 min = 310/60 = 31/6 h.
Distance = (32/6) * 35X = 180.83X . . . . . (1)
Speed of the Boat in coming back = 30X - 5X = 25X.
Let time taken is T.
Now,
Distance = 25X *T
180.83X = 25X * T
T = 7.21 hours.
Note: If given ratio is 36:5 then answer would be 6 hours 50 minutes.
answer :C
Question: The perimeter of one face a of cube is 20 cm. Its volume must be
A.125 cm3
B.400 cm3
C.1000 cm3
D.8000 cm3
Answer: A.125 cm3
Explanation: Solution
Edge of the cube	= (20 / 4) cm
‹=›5 cm.
Volume	= (5×5×5)cm3
‹=›125 cm3.
Answer A
Question: Before being simplified, the instructions for computing income tax in country R were to add 6 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I?
A.50 + 13I/200
B.50 + 3I/100
C.50+ I/40
D.100+ I/50
Answer: A.50 + 13I/200
Explanation: Income of a person is I
6 percent of ones annual income = 6I/100
100 units of Country R's currency = 100
1 percent of one's annual income = I/100
Average of 100 units and 1 percent annual income = 50 + I/200
Sum of average and 6 percent = 6I/100 + 50 + I/200
= 50 + 13I/200
So answer is A
Question: George's drawer has 10 loose black socks, 12 loose blue socks, and 8 loose white socks. If George takes socks out of the drawer at random, how many would he need to take out to be sure that he had at least two matching pairs of socks in two different colors?
A.11
B.13
C.15
D.17
Answer: C.15
Explanation: The worst case scenario is choosing 12 blue socks. Then he would need 3 more socks to be sure of a matching pair of black socks or white socks.
The answer is C.
Question: The avgof marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15, the no.of candidateswho passed the examination is?
A.70
B.80
C.100
D.120
Answer: C.100
Explanation: Let the number of candidate who passed = y
Then, 39y + 15(120 - y) =120 x 35
⇒ 24y= 4200 -1800
∴ y= 2400 / 24 = 100
C
Question: Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fifth widget, starting with the fifth, and Steven inspects every third, starting with the third, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector?
A.91
B.59
C.53
D.47
Answer: C.53
Explanation: Widgets inspected by Lauren: ((95-5)/5)+1=18+1=19
Widgets inspected by Steven: ((96-3)/3)+1 =31+1 =32
Widgets inspected by both: ((90-15)+1 =6
Total : 19+32 -6=45
hence, widgets not inspected: 98-45=53
ANSWER:C
Question: A question paper has 2 parts, A & B, each containing 6 questions. If a student has to choose 4 from part A &3 from part B, in how many ways can he choose the questions?
A.100
B.200
C.350
D.150
Answer: D.150
Explanation: There 6 questions in part A out of which 4 question can be chosen as = 6C4.
Similarly, 3 questions can be chosen from 6 questions of Part B as = 6C3.
Hence, total number of ways,
=6C4*6C3
=[6!/(2!4!)]*[6!/(3!*3!)]
= {15}*{6*5*4*3/(3*2*1)}
= 300.
D
Question: Anand starts from a point P towards point Q, where PQ = 50 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
A.(45/7) kmph
B.(100/21) kmph
C.(40/7) kmph
D.(30/7) kmph
Answer: B.(100/21) kmph
Explanation: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (50-x) km
Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph
So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km
And between their first meeting point and second, they both together covered a distance of 2(90-x) km.
2x+3x=2(50-x)
5x=100-2x
7x=100
x=100/7 km
Anand's speed=x/3=100/(3*7)=100/21 kmph
Ans:B
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 2 second to produce a bolt but 1 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?
A.1,250 seconds
B.1,500 seconds
C.1,750 seconds
D.2,000 seconds
Answer: B.1,500 seconds
Explanation: To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.
Two machines to produce 1,000 bolts will need (1,000*2)/2 = 1,000 seconds.
Two machines to produce 1,000 nuts will need (1,000*1)/2 = 500 seconds.
Total = 1,000 + 500 = 1,500.
Answer: B.
Question: An automobile financier claims to be lending money at S.I., 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 becomes?
A.10.29
B.10.25
C.10.27
D.10.24
Answer: B.10.25
Explanation: Let the sum be Rs. 100. Then,
S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5
S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25
So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 - 100) = %.
Answer: B
Question: total num of pupiles in 3 grades of scholl is 333 . the no of pupiles in grades 1 and 2 are un 3:5 ratio and 2 and 3 grades are 7:11 ratio .what is the strength of class that has highest no of pupils
A.145
B.155
C.165
D.175
Answer: C.165
Explanation: Ratio G1:G2=3:5 and G2:G3=7:11
So G1:G2:G3=21 : 35 : 55
Let the strength of three classes are 21x, 35x and 55x respectively, then 21x+35x+55x= 333
=> 111x= 333 or x=3
So strength of the class with highest number of pupils=55x=55*3= 165
ANSWER:C
Question: What is the CP of Rs 100 stock at 4 discount, with 1/5% brokerage?
A.96.9
B.96.3
C.96.2
D.96.7
Answer: C.96.2
Explanation: Explanation:
Use the formula,
CP= 100 – discount + brokerage%
CP= 100-4+1/5
96.2
Thus the CP is Rs 96.2.
ANSWER: C
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many F cents does a liter of kerosene cost? [One dollar has 100 cents.]
A. 0.33
B. 0.44
C. 0.55
D. 44
Answer: D. 44
Explanation: Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $
Just multiply by 100, Answer F= 44.D
Question: If 60% of 3/5 of a number is 18, then the number is?
A.80
B.100
C.75
D.50
Answer: D.50
Explanation: Let the number be x. Then 60% of 3/5 of x=18
60/100*3/5*x=18
x=(18*25/9)=50
Required number=50.
Correct Option: D
Question: A diner is having lunch at a salad bar. There are two types of lettuce to choose from, as well as four types of tomatoes, and five types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad?
A.10
B.20
C.30
D.40
Answer: D.40
Explanation: 2*4*5 = 40
The answer is D.
Question: A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
A.$150.000
B.$160.000
C.$132.000
D.$148.000
Answer: D.$148.000
Explanation: 6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x.
Question: With an average speed of 40 km/hr a car takes 7 hrs to reach a certain distance. With what speed will it be able to cover the same distance in 5 hours ?
A.46 km/hr
B.56 km/hr
C.58 km/hr
D.48 km/hr
Answer: B.56 km/hr
Explanation: 40:x= 5:7, x being the speed of the car. ie) 5x =40*7/5 =56 The speed of the car =56 km/hr Answer : B
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
A.22
B.66
C.30
D.77
Answer: C.30
Explanation: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
== (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Question: A box contains 2 red, 3 yellow. 2 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
A.2/3
B.3/5
C.2/5
D.1/3
Answer: B.3/5
Explanation: Total number of balls = 3+2 = 5
n(S) = 5C2 = 5*4 / 2 = 10
n(E) = 2C1 * 3C1 = 2*3 = 6
Probability = 6/10 = 3/5
Answer is B
Question: If 6 boys can color 48 m long cloth in 2 days, then 6 boys can color 36 m long cloth in
A.day
B.days
C.days
D.days
Answer: A.day
Explanation: The length of cloth painted by one boy in one day = 48 / 6 × 2 = 4 m
No. of days required to paint 36 m cloth by 6 boys = 36/ 4 × 6 = 3/2 day.
A)
Question: A certain amount earns simple interest of Rs. 1750 after 7 years.Had the interest been 2% more,how much more interest would it have earned ?
A.Rs. 35
B.Rs. 245
C.Rs. 350
D.Cannot be determined
Answer: D.Cannot be determined
Explanation: Solution
We need to know the S.I. , Principal and time to find the rate.Since the principal is not given,so, data is inadequate.
Answer D
Question: Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 57.2 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
A.1.3
B.1.0
C.1.1
D.10.5
Answer: A.1.3
Explanation: Change in production of motor vehicles = 57.2 - 3.9 = 53.3 million in 41 years (1987 - 1946)
average increase per year = 53.3/41 = 1.3 million (apporx.)
Answer (A)
Question: 3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
A.11/4 days
B.16/4 days
C.18/4 days
D.15/4 days
Answer: D.15/4 days
Explanation: D
15/4 days
3M = 6W ---- 20 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 20 32 -----?
6 * 20 = 32 * x => x = 15/4 days
Question: The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit H on the height of vehicles that are allowed to use the tunnel?
A.5½ ft
B.7½ ft
C.8 ½ ft
D.9½ ft
Answer: B.7½ ft
Explanation: Let's label the midpoint of the circle O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10.
We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Let's call the leftmost point on the base of the traffic lane A. So, the distance OA is 6.
Now draw a line straight up from A to the top of the tunnel. Let's label the point at which the line intersects the circle B. The answer to the question will, therefore, be the height AB - .5 feet (we need to leave .5 feet of clearance).
Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).
Finally: AB=8, so the correct answer H is 8 - .5 = 7.5... choose (B)!
From a strategic guessing point of view, as soon as we realize that the height of the tunnel is 10 in the middle, we should quickly eliminate (D) and (E) as too big; worse case you have a 1/3 shot at picking up the points.B
Question: Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners.
Conclusions:
1) 80% of the team consists of spinners.
2) The opening batsmen were spinners.
A.Only conclusion I follows
B.Only conclusion II follows
C.Either I or II follows
D.Neither I nor II follows
Answer: D.Neither I nor II follows
Explanation: According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow.
D
Question: In 1982 and 1983, Company B’s operating expenses were $13.0 million and $15.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
A.3%
B.46 1/6%
C.25%
D.33 1/3%
Answer: B.46 1/6%
Explanation: Profit in 1982 = 15.6 - 13 = 2.6 million $
Profit in 1983 = 18.8 - 15 = 3.8 million $
Percentage increase in profit = (3.8-2.6)/2.6 * 100 %
= 46 1/6 %
Answer B
Question: In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.815 per pound?
A.1:3
B.1:2
C.6:1
D.2:1
Answer: C.6:1
Explanation: Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.815
0.9 – 0.1x = 0.815
x = 0.85
Thus ratio of both flours is 6:1
C
Question: A tradesman by means of his false balance defrauds to the extent of 15%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
A.37.5
B.32.25
C.24.45
D.26.46
Answer: B.32.25
Explanation: Explanation:
g% = 15 + 15 + (15*15)/100
= 32.25%
Answer: B
Question: Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 450 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day?
A.$ 1.50
B.$ 1.88
C.$ 2.25
D.$ 2.50
Answer: D.$ 2.50
Explanation: 7 regular days --> sales = 7*32*x = 224x;
3 hot days --> sales = 3*32*(1.25x) = 120x;
Total sales = 224x+120x = 344x.
Total cost = 10*32*0.75 = 240.
Profit = 344x - 240 = 450 --> x=2.
1.25x=~2.50.
Answer: D.
Question: In a 2 digit no unit's place is halved and tens place is doubled. diff bet the nos is 37.digit in unit's place is 2 more than tens place.
A.36
B.46
C.56
D.66
Answer: B.46
Explanation: let tenth place digit be x & unit place be y
then no. is = 10x + y
if unit place is halved and tens place is doubled
then no. is = 10*2x + y/2
10*2x + y/2 -(10x+y)=37
=> 10x - y/2 = 37 .....(1)
and, y-x=2 ....(2)
solving, x=4,y=6
no. is 46
ANSWER:B
Question: The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 294 square centimeters, what is the length of the rectangle in centimeters?
A.19
B.20
C.21
D.22
Answer: C.21
Explanation: Perimeter = 2(W+L) = 5W
3W = 2L
W = 2L/3
WL = 294
2L^2/3 = 294
L^2 = 441
L = 21 cm
The answer is C.
Question: Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 7 books, how many shelves does the bookcase have?
A.5
B.6
C.7
D.8
Answer: A.5
Explanation: Let x be the number of shelves.
12x - 21 = 8(x-1) + 7
4x = 20
x= 5
The answer is A.
Question: 2, 5, 10, 17, 26, 37, 50, 64
A.50
B.26
C.37
D.64
Answer: D.64
Explanation: Solution
The pattern is x2 +1,where x=1,2,3,4,5,6,7,8 etc.But,64 is out of pattern. Answer D
Question: In the first M games of a team's season, the ratio of the team's wins to its losses was 3:1. In the subsequent N games, the ratio of the team´s wins to losses was 1:4. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games?
A.1:2
B.2:3
C.3:4
D.4:5
Answer: D.4:5
Explanation: M = 4/9 of total games
N = 5/9 of total games
Wins = 3/4*4/9 + 1/5*5/9 = 3/9 + 1/9 = 4/9
Losses = 1 - 4/9 = 5/9
The ratio of wins to losses is 4:5.
The answer is D.
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
A.1500
B.2000
C.300
D.8000
Answer: D.8000
Explanation: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
Answer : D