RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?
A.1050
B.1060
C.1020
D.1048
Answer: C.1020
Explanation: 600- - 84
90
6 510
1--12
85---1020
ANSWER C
Question: The entry in the following sequence is determined by the rule if 1 is entry in the sequence the next three entries are n-1, entries are
A.0,1,2
B.0,-1,1
C.0,1,2
D.2,3,4
Answer: C.0,1,2
Explanation: at the starting point we have entry it just 1
now at the time of first entry we have n-1=1-1= 0
now we have two entries that is 1(default) , 0(first entry)
now at the time of second entry we have n-1=2-1=1
so we have 0,1 and now at the time of third entry
n-1=3-1=2;
so
0,1,2
ANSWER:C
Question: Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 10 phone numbers by using the readable digits followed by 10 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?
A.1/9
B.10/243
C.1/27
D.10/271
Answer: C.1/27
Explanation: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).
If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).
P = 10/(9*9*3+9*3) = 1/27.
Answer: C.
Question: three partners A, B, C start a business. Twice A’s capital is equal to thrice B’s capital and B’s capital is four times C’s capital. Out of a total profit of Rs. 16,500 at the end of the year, B’ share is:
A.2,000
B.4,000
C.5,000
D.6,000
Answer: D.6,000
Explanation: Sol.
Let C = x. Then, B = 4x and 2A = 3 * 4x = 12x or A = 6x.
∴ A : B : C = 6x : 4x : x = 6 : 4 : 1.
So, B’s capital = Rs. [16500 * 4/11] = Rs. 6000.
Answer D
Question: By selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 5% on the marked price. His gain percent during the sale is?
A.6%
B.2%
C.8%
D.3%
Answer: A.6%
Explanation: Marked price = Rs. 300
C.P. = 100/120 * 300 = Rs. 250
Sale price = 95% of Rs. 300 = Rs. 285
Required gain % = 15/250 * 100 =6%.
Answer: A
Question: John builds a square with a side of 12 cm from some wire. If from the same wire, he builds a rectangle with a width of 6 cm, what will be the length of the rectangle?
A.18 cm
B.19 cm
C.20 cm
D.21 cm
Answer: A.18 cm
Explanation: Solution:
If the side of the square is 12 cm, then its perimetre will be 48 cm. We build the rectangle from the same wire, so it will have the same perimetre. Its width is 6 cm, so its length will be (48-12) ÷ 2 = 36 ÷ 2 = 18 cm
Answer A
Question: The banker's discount on a sum of money for 3/2 years is Rs. 120. The true discount on the same sum for 2 years is Rs.150. What is the rate per cent?
A.3(1/3)%
B.4(1/3)%
C.3(2/3)%
D.4(2/3)%
Answer: A.3(1/3)%
Explanation: Explanation :
BD for 1(1/2) years = Rs. 120
=> BD for 2 years = 120 × (2/3) × 2 = Rs.160
TD for 2 years = Rs. 150
F = (BD ×TD)/(BD – TD) = (160 × 150)/(160 – 150) = (160 × 150)/10 = Rs. 2400
=> Rs.160 is the simple interest on Rs. 2400 for 2 years
⇒ 160 = (2400 × 2 × R)/100
⇒ R = (160 × 100)/(2400×2) = 160/48 = 10/3 = 3(1/3)% Answer A
Question: The average of 7 consecutive numbers is 20. The largest of these numbers is :
A.21
B.22
C.23
D.24
Answer: C.23
Explanation: Explanation:
Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.
or 7x + 21 = 140 or 7x = 119 or x =17.
Latest number = x + 6 = 23. Answer: C
Question: X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 20 days. How long will Y take to complete the work?
A.10
B.12
C.25
D.18
Answer: C.25
Explanation: Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 20 days
Whole work will be done by Y in 20*5/4 = 25days
Answer is C
Question: Which of the following are divisible by both 2 and 3?
I. 234,124,422
II. 88,865,544,264
III. 5,555,554,674
A.I​ only
B.I, II​ & III
C.II and III
D.II Only
Answer: B.I, II​ & III
Explanation: I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3
II. is divisible by 3 since sum of the digits is 60 , which is divisible by 3
III. is divisible by 3 since sum of the digits is divisible by 3
Thus among the given options only (B) holds true.
Question: Which value of x does statisfy the inequality 2x2 + x – 3 < 0?
A.-3⁄2 < x < 1
B.-1 < x < 3⁄2
C.x > 1
D.x < -2⁄5
Answer: A.-3⁄2 < x < 1
Explanation: 2x2 + x – 3 < 0
⇒ (x – 1)(2x + 3) < 0 or, -3⁄2 < x < 1
Answer A
Question: One half of a two digit number exceeds its one third by 4. What is the sum of the digits of the number?
A.A)3
B.B)6
C.C)7
D.D)9
Answer: B.B)6
Explanation: x/2 – x/3 = 4 => x =24
2 + 4 = 6
ANSWER:B
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
A.1244
B.1532
C.1349
D.1423
Answer: C.1349
Explanation: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 16, what is the sum of the first 15 terms of the progression?
A.80
B.100
C.105
D.120
Answer: D.120
Explanation: 4th term + 12th term = 16
i.e., (a+3d)+(a+11d) = 16
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 16 --------------- From (1)
=120
Answer : D
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and B quits 5 days before the project is completed, in how many days total will the project be completed?
A.10
B.12
C.14
D.16
Answer: C.14
Explanation: A's rate is 1/20 of the project per day.
B's rate is 1/30 of the project per day.
The combined rate is 1/12 of the project per day.
In the last 5 days, A can do 1/4 of the project.
Thus A and B must complete 3/4 of the project, which takes 9 days.
The total number of days is 9 + 5 = 14.
The answer is C.
Question: Compound interest earned on a sum for the second and the third years are Rs.12000 and Rs.13800 respectively. Find the rate of interest?
A.15% p.a.
B.22% p.a.
C.20% p.a.
D.24% p.a.
Answer: A.15% p.a.
Explanation: Rs.13800 - 12000 = Rs.1800 is the interest on Rs.12000 for one year.
Rate of interest = (1800/12000) * 100 = 15% p.a
ANSWER:A
Question: If a population of women in a town is 70% of men . What is the population of men as a % of population of women ?
A.A)200%
B.B)144%
C.C)50%
D.D)65%
Answer: B.B)144%
Explanation: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.
IF....
Men = 10
Women = 7
We're asked for the number of Men, as a percentage of the number of Women.
M/W = 10/7 = 144%
Answer is B
Question: S is the set of all fractions defined by the formula n/(n + 1), where n is a positive integer less than 20. What is the product Z of all the fractions that are in S?
A.1) 1/20
B.2) 1/21
C.3) 1/2
D.4) 19/40
Answer: A.1) 1/20
Explanation: 1/2 * 2/3 * 3/4 * ... 19/20
= 1/20
Answer - A
Question: If x is an integer and 6.1 × 10^x is less than 620 what is the greatest possible value for x?
A.2
B.6
C.5
D.4
Answer: A.2
Explanation: If x=2
6.1 × 10^2 = 610 < 620
So, x = 2
Answer : A
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the E odds that it is an ace?
A.1/52
B.1/26
C.1/13
D.1/4
Answer: C.1/13
Explanation: The question should ask about the probability not the odds.
There are 13 spades, the probability E that the spade we already have is an ace is therefore 1/13.
Answer: C.
Question: A bag contains 5 red, 4 blue and M green
balls if the probability of getting both the balls
green, when two balls are selected at
random is 1/7, find M
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: mC2/m+9C2=1/7
on solving
(m! / (m-2! * 2!) ) / (m+9! / (m+7! * 2!) ) =1/7 From nCr=n! / r!*(n-r)!
on solving
(m! / (m-2)! ) * ( (n-7)! / (n+7)!) =1/7
after solving and cross multiplication
m^2+4m-12=0
on solving
m=2,-6
so m will be 2.
ANSWER:B
Question: At a conference table, 7 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these 7 employees?
A.740
B.750
C.720
D.760
Answer: C.720
Explanation: Head's sit is fixed. Now 6 people is left with 6 seats.
6 people can sit on 6 seats in 6! ways or 720 ways.
Ans is C
Question: How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?
A.3587.51
B.3587.98
C.3587.5
D.3587.29
Answer: C.3587.5
Explanation: I = (8200 * 2.5 * 17.5)/100
= (8200 * 5 * 35)/(100 * 2 * 2)
= Rs.3587.50
Answer: C
Question: If a copier makes 2 copies every 4 seconds, then continues at this rate, how many minutes will it take to make 8,000 copies?
A.266.67
B.130
C.140
D.135
Answer: A.266.67
Explanation: 2 copies 4 seconds
8000 copies = (8000*4)/2 seconds
= 16000/60 minutes
= 266.67 minutes
Answer : A
Question: There are 32 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
A.6
B.12
C.16
D.24
Answer: C.16
Explanation: 32*2/3 *3/4= 16
Answer: C
Question: Given the equation e=-g^4, which of the following must be true?
I. If g is negative then e is negative.
II. e is negative.
III. g is non-negative.
A.II only
B.I only
C.II and III only
D.III only
Answer: B.I only
Explanation: If e=-g^4, which of the following must be true?
First of all notice g^2 is always non-negative, so -g^2 is non-positive (zero or negative), which means that e is zero when g=0 and e is negative for ANY other value of g.
I. e is negative --> not necessarily true, if g=0 then e=-m^2=0;
II. g is non-negative. g can take ANY value: positive, negative, zero. We don't have any restrictions on its value;
III. If g is negative then e is negative. m is negative means that m is not zero.
Answer: B (I only).
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
A.¹²C₅ * 10
B.¹²C₇ * 10
C.¹²C₇ * ¹⁰C₅
D.12 * ¹⁰C₅
Answer: C.¹²C₇ * ¹⁰C₅
Explanation: Here, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = ¹²C₅ * ¹⁰C₅ = ¹²C₇ * ¹⁰C₅
= ¹²C₅ = ¹²C₇
ANSWER:C
Question: The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 16. Find the sum :
A.4500
B.7500
C.5000
D.6400
Answer: D.6400
Explanation: Sol.(d) Let the sum be 100.
Therefore, SI = 100×5×2/100=10
and CI = 100(1+5/100)2−100
∴ =100×21×21/20×20−100=41/4
Difference of CI and SI = 41⁄4 - 10 = 1⁄4
If the difference is 1⁄4 , the sum = 100
=> If the difference is 16, the sum
= 400 × 16 = 6400 Answer D
Question: Stacy has a 12 page history paper due in 12 days. How many pages per day would she have to write to finish on time?
A.9
B.8
C.10
D.1
Answer: D.1
Explanation: 12/12=1
Answer : D
Question: Look at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?
A.II
B.IV
C.IX
D.14
Answer: B.IV
Explanation: Explanation: This is an alternating addition and subtraction series. Roman numbers alternate with Arabic numbers. In the Roman numeral pattern, each number decreases by 1. In the Arabic numeral pattern, each number increases by 1.
Answer: Option B
Question: The sum of two numbers is 50. Their difference is 10. The bigger number is
A.20
B.25
C.30
D.35
Answer: C.30
Explanation: X + Y = 50
X - Y = 10
Adding 2X = 60 ==> X = 30 and Y = 50 - 30 = 20
Bigger number is X = 30
Answer C.
Question: A bowl was filled with 10 ounces of water, and 0.08 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
A.0.004%
B.0.04%
C.40%
D.4%
Answer: C.40%
Explanation: Total amount of water evaporated each day during a 50-day period = .08 * 50
=.08 * 100/2
= 8/2
= 4
percent of the original amount of water evaporated during this period = (4/10) * 100%
= 40 %
Answer C
Question: Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
A.1200
B.3000
C.1000
D.3600
Answer: A.1200
Explanation: Let the additional invested amount for 8% interest be x;
Equation will be;
2400+0.05*2400+x+0.08x = 2400+x+0.06(2400+x)
0.05*2400+0.08x = 0.06x+0.06*2400
0.02x = 2400(0.06-0.05)
x = 2400*0.01/0.02 = 1200
Ans: "A"
Question: Ramu bought an old car for Rs. 45000. He spent Rs. 12000 on repairs and sold it for Rs. 80000. What is his profit percent?
A.16%
B.17%
C.40%
D.58%
Answer: C.40%
Explanation: Total CP = Rs. 45000 + Rs. 12000
= Rs. 57000 and SP = Rs. 80000
Profit(%)
= (80000 - 57000)/57000 * 100
= 40%
Answer: C
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.7 kmph
C.98 kmph
D.6 kmph
Answer: A.1 kmph
Explanation: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Question: A hall 36m long and 15m broad is to be paved with stones, each measuring 5dm by 5 dm. The number of stones required is:
A.180
B.1800
C.18
D.2160
Answer: D.2160
Explanation: Area of the hall= 3600*1500
Area of each stone= (50*50)
Therefore, number of stones= (3600*1500/ 50*50)= 2160
ANSWER:D
Question: Using all the letters of the word "LETTERS", how many words can be formed, which begin with L and end with S?
A.50
B.120
C.160
D.100
Answer: B.120
Explanation: There are five letters in the given word.
Consider 7 blanks ....
The first blank and last blank must be filled with L and S all the remaining three blanks can be filled with the remaining 5 letters in 5! ways.
The number of words = 5! = 120.
Answer: B
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
A.2
B.3
C.166
D.288
Answer: C.166
Explanation: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Question: In one hour a boat goes 14 km long the stream and 6 km against the stream.The speed of the boat in still water is?
A.7
B.10
C.12
D.11
Answer: B.10
Explanation: Speed in still water A = ½ ( 14+6) km/hr A= 10 kmph
Answer: B
Question: In the infinite sequence 27, 36, 45, 54, 63, . . . , where each term is 9 greater than the previous term, the 55th term is
A.783
B.513
C.198
D.963
Answer: B.513
Explanation: T(n) = a + (n-1) d
Here d =9, a=27, n=55
Solving we get T(n) = 513.
Answer: B
Question: If the positive integer y is divisible by 3, 8, and 16, then which of the following must y be divisible by?
I. 21
II. 32
III. 48
A.III only
B.II only
C.I and II only
D.II and III only
Answer: A.III only
Explanation: Answer = A
LCM of 3, 8, 16 = 48
Answer = 48
Answer : A
Question: An article is bought for Rs.700 and sold for Rs.900, find the gain percent?
A.33 1/8%
B.33 8/3%
C.28 4/7%
D.35 1/3%
Answer: C.28 4/7%
Explanation: 700 ---- 200
100 ---- ? => 28 4/7%
Answer: C
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 57?
A.s.3876
B.s.3948
C.s.3942
D.s.3965
Answer: A.s.3876
Explanation: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 57
= Rs.3876.
Answer: A
Question: The paragraph can start only with the sentence E. The opening words of the sentence of ‘B’ – ‘these two parties’ is a continuation of the last words of the sentence E– ‘two parties’. There are only two options with EB; in the option 4, D follows B; but whom the opening pronoun ‘he’ of D does refer to? F is the further explanation of B. Hence EBFCAD.
A.11
B.77
C.26
D.99
Answer: B.77
Explanation: Answer:	B
Question: 1604 x 1604 = ?
A.A)2572816
B.B)3624216
C.C)3624316
D.D)3625116
Answer: A.A)2572816
Explanation: 1604 x 1604 = (1604)2
= (1600 + 4)2
= (1600)2 + (4)2 + (2 x 1600 x 4)
= 2560000 + 16 + 12800.
= 2572816.
A)
Question: Arrange 4boys and 4girls in a row such that all the 4 girls are together.
A.1240
B.1440
C.2880
D.3200
Answer: C.2880
Explanation: Treat all the 4 girls as G
4boys and G can be arranged in 5!ways
G can be arranged among them in 4!ways
total = 5!*4! = 2880
correct option is C
Question: If s and t are positive integers such that s/t = 43.18, which of the following could be the remainder when s is divided by t ?
A.44
B.17
C.54
D.20
Answer: C.54
Explanation: s/t= 43.18
s = 43.18t
s = (43 + 0.18)t
s = 43t + (18/100)t
s = 43t + (9/50)t
So remainder will be multiple of 9. The only multiple of 9 is 54.
Ans. C
Question: he number of sequences in which 8 players can throw a ball, so that the youngest player may not be the last is?
A.43288
B.23770
C.43200
D.35280
Answer: D.35280
Explanation: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 7 players. The first 7 players can throw the ball in 7p7₆ ways.
The required number of ways = 7(7!) = 35280
Answer:D
Question: Find the number of square tiles to cover the floor of a room measuring 6 m * 11 m leaving 0.50 m space around the room. A side of square tile is given to be 50 cms?
A.187
B.476
C.200
D.208
Answer: C.200
Explanation: Area of the room =5 * 10 =50
Area of the tile = 0.5 *0.5=0.25
No. of tiles =50/0.25 =200
Answer : C
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
A.276
B.299
C.322
D.345
Answer: C.322
Explanation: Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer: Option C
Question: The sector of a circle has radius of 14 cm and central angle 108o. Find its perimeter?
A.52cm
B.54.4cm
C.60cm
D.65cm
Answer: B.54.4cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (108/360 * 2 * 22/7 * 14) + 2(14)
= 26.4 + 28 = 54.4 cm
Answer:B
Question: What percent is 520 gm of 1 kg?
A.25%
B.40%
C.52%
D.8%
Answer: C.52%
Explanation: 1 kg = 1000 gm
520/1000 Ã— 100 = 52000/1000
=52 %
Answer is C
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is :
A.19
B.29
C.39
D.49
Answer: C.39
Explanation: Explanation:
Let B's present age = x years. Then, A's present age = (x + 9) years.
(x + 9) + 10 = 2(x - 10)
=> x + 19 = 2x - 20
=> x =39. Answer: C
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
A.33
B.12
C.18
D.19
Answer: C.18
Explanation: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100 = 18%
Answer: C
Question: An amount of Rs. 85000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
A.s. 53125; Rs. 31875
B.s. 62500; Rs. 37500
C.s. 72500; Rs. 27500
D.s. 82500; Rs. 17500
Answer: A.s. 53125; Rs. 31875
Explanation: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (85000 - x). Then,
(x * 9 * 1)/100 + [(85000 - x) * 11 * 1]/100 = (85000 * 39/4 * 1/100)
(9x + 935000 - 11x)/100 = 39000/4 = 16575/2
x = 53125
Sum invested at 9% = Rs. 53125
Sum invested at 11% = Rs. (85000 - 53125) = Rs. 31875.
ANSWER:A
Question: Of the three numbers, the sum of the sum of the first two is 45; the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. the third number is :
A.20
B.25
C.30
D.3
Answer: C.30
Explanation: Solution
Let the numbers be x,y, and z. then, x + y = 45, y + x = 55 and 3 x + z = 90
⇒ y = 45 - x, z = 55 - y = 55 - (45 - x) = 10 + x.
∴ 3 x + 10 + x = 90 or x = 20.
y = (45 - 20) = 25 and z = (10 + 20) = 30.
∴ third number = 30
Answer C
Question: In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number?
A.26
B.28
C.32
D.36
Answer: A.26
Explanation: Solution
Let the ten digits be x. Then,units digit=3x
Therefore x + 3x = 8
‹=›4x = 8
‹=›x= 2.
So, ten's digit = 2, unit's digit = 6.
Hence, the required number is 26.
Answer A
Question: If 8m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
A.2m −1
B.3m
C.6m
D.m/5
Answer: B.3m
Explanation: 8m - n = p
Add n to both sides:
8m = n + p
Add m to both sides:
9m = n + p + m
Now, divide both sides by 3
3m = (n + p + m)/3 = the average of n, p, and m
B
Question: A merchant marks goods up by 75% and then offers a discount on the marked price. The profit that the merchant makes after offering the discount is 22.5%. What % discount did the merchant offer?
A.20%
B.25%
C.30%
D.35%
Answer: C.30%
Explanation: Let P be the original price of the goods and let x be the rate after the markup.
(1.75P)*x = 1.225P
x = 1.225/1.75 = 0.7 which is a discount of 30%.
The answer is C.
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability W that a + b is prime?
A. 0
B. 1/12
C. 5/12
D. 7/18
Answer: C. 5/12
Explanation: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
W=15/36.
Answer: C.
Question: Calculate the value of 2.34 x 10^7 ?
A.2340
B.2340000
C.23400000
D.23400
Answer: C.23400000
Explanation: 3.14 x 10^7 = 2.34 x 10000000 = 23400000.
Answer = C
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.31/32
B.31/38
C.31/31
D.61/38
Answer: A.31/32
Explanation: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: A
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 12 years?
A.3 : 2
B.1 : 3
C.1 : 6
D.3 : 1
Answer: C.1 : 6
Explanation: Explanation :
Simple Interest = PRT/100
Here Principal(P) and Rate of Interest (R) are constants
Hence, Simple Interest ∝ T
Required Ratio = Simple Interest for 2 years/Simple Interest for 12 years
=T1/T2
=2/12
=1/6
=1:6
Answer : Option C
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 18%, then the cost price of the article is:
A.500
B.474.6
C.222
D.297
Answer: B.474.6
Explanation: Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (100 * 560)/118 = Rs. 474.6
Answer:B