RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Jane Odd is the owner of Oddly Odd Book Store. Jane Odd loves odd things, but her book seller only sells books in even numbers. If there are an even number of books in the book store (b = an even number), and Jane divides the books into groups of 18 books, which results in an odd number of groupings (b/18 = an odd number). Now, if Jane doubles the number of books in the store, how can she divide the books up to keep an odd number of groupings (b^2/X = an odd number)?
A.b^2/12
B.b^2/18
C.b^2/9
D.b^2/6
Answer: A.b^2/12
Explanation: Divisible by 2 (Parity Mathematics) states: an even number is an integer of the form n = 2k, where k is an integer; an odd number is an integer of the form n = 2k + 1.
Since a is an even number, a = 2k, a^2 = 4k^2 = (2)(2)(k)^2, and a/18 is an odd number 2k/18.
18 = (2)(9). Now (2k)/((2)(9)) = k/9. So, we are looking for a (2)(2) factor in the denominator.
Factors are:
12 = (2)(2)(3)
18 = (2)(9)
9 = (3)(3)
6 = (2)(3)
2 = (2)
So, 12 has more than 1 (2).
Answer: A
Question: A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 3 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
A.8
B.16
C.21
D.22
Answer: A.8
Explanation: I treat such problems as work ones.
Work=Rate*Time
Mileage(m)=Rate(mpg)*Gallons(g)
X gallons is a full tank
{462=RX
{336=(R-3)X solve for R, R=11
11-3=8 mpg
A
Question: What is the remainder when 2^20 is divided by 10 ?
A.0
B.2
C.4
D.6
Answer: D.6
Explanation: 2^20 = 2^10 x 2^10
And 2^10 = 1024
4*4= 16, so the unit digit of this multiplication is 6
The remainder is 6
ANSWER:D
Question: If x/y = 2/7, then (x + y)/(x - y) = ?
A.5
B.1/5
C.-1/6
D.-9/5
Answer: D.-9/5
Explanation: Any x and y satisfying x/y = 2/7 should give the same value for (x + y)/(x - y).
Say x=2 and y=7, then (x + y)/(x - y) = (2 + 7)/(2-7) = -9/5.
Answer: D.
Question: A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?
A.20
B.36
C.48
D.60
Answer: C.48
Explanation: Question says they are both related linearly so they the relationships can be represented by standard linear definition y=mx+b.
Let S scale = y. and R scale = x.
30=6m+b EQN1
60=24m+b EQN2
EQN2-EQN1 => 30=18m => m=5/3
Solving for b using either equation gives us b=20
linear relationship is represented by y=(5/3)x+20
Solve for 100:
100=5/3x+20
80=5/3x
x=48
ANS = C
Question: 7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.
A.500
B.300
C.250
D.415
Answer: B.300
Explanation: 1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc
This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7)
You have 1*9*9 = 81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81 = 243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once.
In each of these numbers, 7 is written once. Therefore, 243 times.
2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77
In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7).
There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers.
In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.
3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it.
Therefore, the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300
Ans: B
Question: A tradesman by means of his false balance defrauds to the extent of 40%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
A.17%
B.77%
C.44%
D.96%
Answer: D.96%
Explanation: g% = 40 + 40 + (40*40)/100
= 96%
Answer: D
Question: A grocer has a sales of Euro 520 , Euro 320 , Euro 480 , Euro 120 and Euro 720 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Euro 620?
A.uro 4691
B.uro 1591
C.uro 2591
D.uro 1560
Answer: D.uro 1560
Explanation: D
Euro 1560
Total sale for 5 months = Euro (520 + 320 + 480 + 120 + 720) = Euro 2160.
Required sale = Euro [ (620 x 6) - 2160]
= Euro (3720- 2160)
= Euro 1560.
Answer is D
Question: If S is the sum of the reciprocals of the consecutive integers from 51 to 60, inclusive, which of the following is less than S?
I. 1/5
II. 1/6
III. 1/7
IV. 1/5>S >1/6
A.I
B.II
C.III
D.IV
Answer: D.IV
Explanation: Since we summarize the reciprocals from 60 to 51, we can say also that we add ten numbers who are all (with one exception 1/60) greater than 1/60, so that the sum must be greater than 1/6.
On the other side we can say that we add the reciprocals from 51 to 60, so that the sum has to be less than the sum of ten times 1/51.
sum has to be greater than 1/6 and less than 1/5
D
Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates X apply to what fraction of a week?
A. 1/2
B. 5/8
C. 9/14
D. 16/21
Answer: C. 9/14
Explanation: Number of hours between 8 PM to 8 AM = 12
Number of hours with reduced rates = (12*5)+(24*2)
Hours with reduced rates X/Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14
Answer: C
Question: For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $8 and the price of a student ticket was $4. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
A.$20960
B.$21920
C.$22680
D.$28500
Answer: C.$22680
Explanation: From 9:00 in the morning to 5:55 in the afternoon, inclusive there are 9*12=108 five-minute intervals, thus total of 108*30 tickets were sold.
Say x student and 3x regular tickets were sold, then x+3x=108*30 --> x=27*30 and 3x=3*(27*30)=27*90.
Therefore, the total revenue from ticket sales that day was 27*30*4+27*90*8=$22,680.
Answer: C.
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
A.22
B.25
C.77
D.99
Answer: B.25
Explanation: 800 --- 200
100 --- ? => 25%
Answer: B
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Two pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
A.5
B.12
C.24
D.32
Answer: B.12
Explanation: The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 12.
Answer: option B
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
A.285
B.665
C.999
D.255
Answer: D.255
Explanation: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285.
Answer: D
Question: Sara bought both German chocolate and Swiss chocolate for some cakes she was baking. The Swiss chocolate cost $3.5 per pound, and German chocolate cost $2.5 per pound. if the total the she spent on chocolate was $70 and both types of chocolate were purchased in whole number of pounds, how many total pounds of chocolate she purchased?
A.7
B.8
C.10
D.24
Answer: D.24
Explanation: If there were all the expensive ones,3.5....
There would be 70/3.5 or 20 of them but since 2.5$ ones are also there, answer has to be >20....
If all were 2.5$ ones, there will be 70/2.5 or 28..
So ONLY 24 is left
Ans D..
Question: A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 225,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
A.a) 500
B.b) 750
C.c) 1,000
D.d) 1,250
Answer: B.b) 750
Explanation: Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 225,000 = 56,250
So required ratio = 56,250/75 = 750
Answer B
Question: What was the day of the week on, 17th July, 1776?
A.Tuesday
B.Wednesday
C.Monday
D.Saturday
Answer: B.Wednesday
Explanation: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 3 days)
Total number of odd days = (0 + 3) = 3.
Required day was 'Wednesday'.
Answer:B
Question: Two trains 110 meters and 140 meters long are running in the same direction with speeds of 102 km/hr, 66 km/hr. In how much time will the first train cross the second
A.22 sec
B.25 sec
C.27 sec
D.23 sec
Answer: B.25 sec
Explanation: Explanation:
Relative speed of the trains = (102 - 66) km/hr = 36 km/hr
= (36Ã— 5/18) m/sec = 10 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (110 + 140) m at 10 m /sec = (250/10) sec = 25 sec.
Answer: Option B
Question: f (x + y)/(2x + y) = 4/5, then find (2x + y)/(3x + y) ?
A.5/9
B.5/6
C.5/7
D.5/4
Answer: B.5/6
Explanation: (x + y)/(2x + y) = 4/5
=> 5x + 5y = 8x + 4y => y = 3x
Now, (2x + y)/(3x + y) = 5x/6x = 5/6.
Answer: B
Question: Rectangular tile each of size 20cm by 30cm must be laid horizontally on a rectangular floor of size 100cm by 150cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
A.40
B.15
C.25
D.32
Answer: C.25
Explanation: Area of tile = 20*30 = 600
Area of floor = 100*150 = 15000
No of tiles = 15000/600 =25
So, the no of tile =25
ANSWER:C
Question: How many integers between 300 and 1200 are there such that their unit digit is odd?
A.250
B.350
C.450
D.550
Answer: C.450
Explanation: There are 900 numbers from 301 to 1200 (inclusive).
Half of the numbers are odd, so there are 450 odd numbers.
The answer is C.
Question: A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 7,000 meters of fabric?
A.$13,360
B.$14,450
C.$15,720
D.$16,780
Answer: A.$13,360
Explanation: For first 2000 meters he does not get any discount.
The price is 2*2000 = $4000
For next 1500 meters, he gets a 5% discount.
The price is 1.9*1500 = $2850
For the next 1500 meters, he gets a 7% discount.
The price is 1.86*3500 = $6510
The total price is $4000 + $2850 + $6510 = $13,360
The answer is A.
Question: 8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 4 women and 30 children together complete the piece of work?
A.5 days
B.15 days
C.28 days
D.4 days
Answer: D.4 days
Explanation: Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
4 women’s 1 day’s work = 1/192 × 4 = 1/48
1 child’s 1 day’s work = 1/240
30 children’s 1 day’s work = 1/8
Therefore, (10 men + 4 women + 30 children)’s 1 day’s work = 5/48 + 1/48 + 1/8
=1/4
The required No. of days = 4 days
Answer: Option D
Question: Abi decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If abi's savings by the end of the year from these monthly savings were six times the amount she spent per month, what should be the fraction of her salary that she spent each month?
A.6/9
B.5/3
C.2/3
D.4/3
Answer: C.2/3
Explanation: Let Abi 's monthly savings = S
Abi 's monthly pay = P
Abi 's monthly expenditure = P-S
Abi 's savings by the end of the year from these monthly savings were six times the amount she spent per month
12S = 6*(P-S)
=>2S = P-S
=> P = 3S
Abi 's monthly expenditure = P-S = 3S-S = 2S
fraction of her salary that Abi spent each month = 2S / 3S=P-S/P = 2/3. Answer is C
Question: A present value of a machine is $148000. Its value depletiation rate is 25% per annum then find the machine value after 3 years?
A.A)$54000
B.B)$48000
C.C)$36520
D.D)$62437.5
Answer: D.D)$62437.5
Explanation: P= $148000
R = 25%
T = 3 years
Machine value after 3years = P/(1-R/100)^T
=148000*3/4 * 3/4 * 3/4
=$62437.5
Answer is D
Question: A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current?
A.8kmph
B.6kmph
C.4kmph
D.5 kmph
Answer: D.5 kmph
Explanation: Explanation:
Speed of the boat in still water: 15 km/hr
Speed of boat downstream: (15+x)km/hr where x is speed of the current.
The boat travels 30 km downstream and then 30 km upstream and takes 9/2 hours.
Total time= Time taken to travel downstream + Time taken to travel upstream
=> 4/5= (30/(15+x))+(30/(15-x))
=>x= 5
ANSWER:D
Question: How long will a train 100m long travelling at 72kmph take to overtake another train 200m long travelling at 54kmph ?
A.60 sec
B.70 sec
C.80 sec
D.50 sec
Answer: A.60 sec
Explanation: 72 kmph=72*5/18 mps=20mps.
54 kmph=54*5/18 mps=15 mps.
The train has to travel (200+100)m=300m to overtake the other one.
Resultant velocity=(20-15)mps=5 mps
time it takes to travel 300m at a velocity of 5 mps is 60 sec..
Ans 60 sec.
ANSWER:A
Question: 3,6,13,26,33,66,?
A.70
B.71
C.72
D.73
Answer: D.73
Explanation: 3*2=6
6+7=13
13*2=26
26+7=33
33*2=66
so next will be
66+7=73
ANSWER:D
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
A.180°
B.154°
C.160°
D.170°
Answer: A.180°
Explanation: We know that angle traced by hour hand in 12 hrs = 360°
From 8 to 2, there are 6 hours.
Angle traced by the hour hand in 6 hours = 6×36012=180°
Answer is A.
Question: Find the slope of the line perpendicular to the line y = x - 7
A.1
B.2
C.-1
D.4
Answer: C.-1
Explanation: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1. If m is the slope of the line perpendicular to the given line, then
m × 1 = -1
Solve for m
m = - 1
correct answer C) -1
Question: In one alloy there is 12% chromium while in another alloy it is 8%. 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
A.8.8%
B.9.75%
C.9.2%
D.8.6%
Answer: B.9.75%
Explanation: The amount of chromium in the new 35+45=80 kg alloy is 0.12*35+0.08*45=7.8 kg, so the percentage is 7.8/80*100=9.75%.
Answer: B.
Question: Look at this series: 55, 55, 40, 40, 25, 25, ... What number should come next?
A.14
B.15
C.17
D.10
Answer: D.10
Explanation: In this series, each number is repeated, then 15 is subtracted to arrive at the next number.
The next number should be 10
Answer : D
Question: In order to obtain an income of Rs. 1250 from 10% stock at Rs. 210, one must make an investment of
A.5363
B.26250
C.28678
D.29002
Answer: B.26250
Explanation: To obtain Rs. 10, investment
= Rs. 210.
To obtain Rs. 1250, investment =
= Rs. 26250.
Answer: B
Question: In a certain city each of 17 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)
A.5
B.10
C.6
D.20
Answer: C.6
Explanation: B.6:
if we have 5 colors we can choose pairs in 5C2 ways = 10 and single color flags are 5. Therefore total number of flags = 15. This is less than the number of girl scout groups.
if we have 6 colors we can choose pairs in 6C2 ways = 15 and single color flags are 6. Therefore total number of flags = 21.
ANS C.
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
A.11
B.8
C.12
D.99
Answer: C.12
Explanation: T = 9/45 * 60
= 12
Answer: C
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
A.331/8%
B.331/3%
C.338/3%
D.391/3%
Answer: B.331/3%
Explanation: 100
150
------
150-------50
100-------? => 331/3%
Answer: B
Question: In a group of ducks and cows, the total number of legs are 48 more than twice the no. of heads. Find the total no.of buffaloes.
A.28
B.12
C.24
D.16
Answer: C.24
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 48
=> 2x = 48 => x = 24
C
Question: 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
A.84 m
B.88 m
C.120 m
D.137 m
Answer: A.84 m
Explanation: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m.
Answer A
Question: A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 4 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
A.27
B.36
C.72
D.18
Answer: D.18
Explanation: {1}{2}{greater than 6}{divisible by 4}{3x}{x}:
The third digit can take 3 values: 7, 8, or 9.
The fourth digit can take 2 values: 4, or 8.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 3*2*3 = 18.
Answer: D.
Question: Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many H miles will Tom drive before Karen wins the bet?
A.15
B.18
C.21
D.24
Answer: D.24
Explanation: Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him H: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer.
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 25 percent during the third year. What is the value of the account today?
A.$10,350
B.$8,662.50
C.$10,500
D.$11,500
Answer: B.$8,662.50
Explanation: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.75 = 10,395
Answer B is correct.
Question: Markov bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?
A.$10
B.$11
C.$12
D.$13
Answer: B.$11
Explanation: From the given information,we can conclude that Markov bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for 1000*.90 = $900 . With the remaining money ($1000 - $900 = $100), he can buy 10 more shares. So, the reduced price per share = $100/10 = $10.
Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=B
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
A.33
B.20
C.28
D.36
Answer: D.36
Explanation: (9*12)/3 = 36
Answer: D
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is?
A.1/8
B.1/7
C.1/0
D.1/6
Answer: B.1/7
Explanation: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: B
Question: Five boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
A.A)5^30
B.B)2^30
C.C)1^30
D.D)3^30
Answer: A.A)5^30
Explanation: Each Mango can be given to any one of the five people or in other words..1 mango can be divided into 5 ways...so all 30 can be divided in 5^30 ways
ANS:A
Question: The value of x + x(xx) when x = 2 is:
A.8
B.10
C.12
D.14
Answer: B.10
Explanation: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
ANSWER : (B) +10
Question: It takes Jim three hours to wash the gym and it takes Julia two hours to wash the gym. Working together, how many minutes will it take them to wash the gym?
A.70
B.72
C.74
D.76
Answer: B.72
Explanation: Jim can wash (1/3) of the gym per hour.
Julia can wash (1/2) gym per hour.
Together they can wash 1/3+1/2=5/6 of the gym per hour.
1 gym / (5/6) of the gym per hour = 6/5 hours = 72 minutes.
The answer is B.
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is
A.4/15
B.4/18
C.4/16
D.4/13
Answer: D.4/13
Explanation: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
= 4/13
Answer: D
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
A.1/39
B.1/36
C.1/35
D.1/34
Answer: B.1/36
Explanation: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216
= 1/36
Answer: B
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $52 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
A.$5
B.$10
C.$14
D.$28
Answer: D.$28
Explanation: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $52
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 52
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 52
i.e. x = 24
i.e. Fixed Monthly Charge, y = 28
Answer: Option
D
Question: If a sum of money doubles itself in 10 years at simple interest, the ratepercent per annum is
A.10
B.12.5
C.13
D.13.5
Answer: A.10
Explanation: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 10) = 10
Option A