RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: four concentric circles r given .the radius of 1st circle is x.next is 2x,then 3x and 4x. given that area b/w 2nd and 1st is A and 4th and 3rd circles being B.find ratio of A to B
A.2:7
B.1:7
C.3:5
D.3:7
Answer: D.3:7
Explanation: area of first circle = pi*(x)^2 = pi*x^2
area of second circle = pi*(2x)^2 = 4*pi*x^2
area of third circle = pi*(3x)^2 = 9*pi*x^2
area of fourth circle = pi*(4x)^2 = 16*pi*x^2
area b/w 1st and 2nd circles = 3*pi*x^2
area b/w 3rd and 4th circles = 7*pi*x^2
so ratio = 3:7
ANSWER:D
Question: A train is 385 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
A.42 seconds
B.30 seconds
C.40 seconds
D.50 seconds
Answer: A.42 seconds
Explanation: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 385+140 = 525 meter
Time = Distance/speed
=525∗2/25=42seconds
Option A
Question: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 21, then which of the following could be a value of x?
A.-4
B.-3
C.2
D.3
Answer: C.2
Explanation: 5%x = (5+x)(5-x)
25-x^2 = 21
x^2 = 4
x=-2,2
Ans: C
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
A.9:6
B.9:8
C.9:0
D.9:2
Answer: B.9:8
Explanation: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
Question: The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 60 kmph. Find the speed of the boat in still water and the speed of the stream?
A.50,10 kmph
B.78,10 kmph
C.70,70 kmph
D.78,10 kmph
Answer: A.50,10 kmph
Explanation: Speed of the boat in still water
= (40+60)/2
= 50 kmph. Speed of the stream
= (60-40)/2
= 10 kmph.
Answer:A
Question: The ratio of the ages of three people is 4:6:7. Six years ago, the sum of their ages was 67. Find their present ages.
A.12,18,21
B.16,24,28
C.20,30,35
D.24,36,42
Answer: C.20,30,35
Explanation: Let the present ages be 4x, 6x, 7x.
(4x-6) + (6x-6) + (7x-6) = 67
17x = 85
x = 5
Their present ages are 20, 30, and 35.
The answer is C.
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
A.33.8
B.33.7
C.33.3
D.33.2
Answer: C.33.3
Explanation: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer:C
Question: P,Q and R together earn Rs.1980 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
A.s.30
B.s.70
C.s.90
D.s.100
Answer: A.s.30
Explanation: Explanation :
Amount Earned by P,Q and R in 1 day = 1980/9 = 220 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120	---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130	---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-220 = 30
=>Amount Earned by R in 1 day = 30
Answer : Option A
Question: In John's School, there are 80boys of age 14 each, 70boys of age 15 each & 50boys of age 13 each and another 60boys of age 12each. The average age of the boys of the school is
A.13
B.13.6
C.13.8
D.14.6
Answer: B.13.6
Explanation: Average age of boys = Sum of the ages of all boys/ Total number of boys
= (80 x14)+(70x15)+(50x13)+(60x12)/(80+70+50+60)
= (1120+1050+650+720)/260
=3540/260 =13.6
B
Question: The ratio of the arithmetic mean of two numbers to one of the numbers is 4:7. What is the ratio of the smaller number to the larger number?
A.1:8
B.1:7
C.1:6
D.1:5
Answer: B.1:7
Explanation: For two numbers, the arithmetic mean is the middle of the two numbers.
The ratio of the mean to the larger number is 4:7, thus the smaller number must have a ratio of 1.
The ratio of the smaller number to the larger number is 1:7.
The answer is B.
Question: A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?
A.4.5 hrs
B.5 hrs
C.6.5 hrs
D.7.2 hrs
Answer: A.4.5 hrs
Explanation: Net part filled in 1 hour= 1/3 -1/9= 2/9
Therefore the cistern will be filled in 9/2 hours or 4.5 hours.
ANSWER:A
Question: Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability Q that Kate has more than $10 but less than $15?
A.5/16
B.1/2
C.Q=12/30
D.Q=15/32
Answer: D.Q=15/32
Explanation: For 21 heads Kate will end up with < $10 and we want her to win. Therefore, only possibilities are 3 or 4 heads.
I made an educated guess and it worked fine.
Ans- 'D'
MGMAT's anagram helped here as well.
HHHHT = 5!/4!*1! = 5
HHHTT = 5!/3!*2! = 10
Total acceptable cases = 15
Total cases = 32
P = 15/32.D
Question: Three unbiased coins are tossed. What is the probability of getting at least 2 heads?
A.1/4
B.1/2
C.1/3
D.1/8
Answer: B.1/2
Explanation: Here S={TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E=event of getting at least two heads = {THH, HTH, HHT, HHH}
P(E) = n(E)/n(S) = 4/8 = 1/2
Answer B.
Question: On a school’s Annual day sweets were to be equally distributed amongst 112 children. But on that particular day, 32 children were absent. Thus the remaining children got 6 extra sweets. How many sweets was each child originally supposed to get ?
A.17
B.18
C.29
D.15
Answer: D.15
Explanation: Let 'K' be the total number of sweets.
Given total number of students = 112
If sweets are distributed among 112 children,
Let number of sweets each student gets = 'L'
=> K/112 = L ....(1)
But on that day students absent = 32 => remaining = 112 - 32 = 80
Then, each student gets '6' sweets extra.
=> K/80 = L + 6 ....(2)
from (1) K = 112L substitute in (2), we get
112L = 80L + 480
32L = 480
L = 15
Therefore, 15 sweets were each student originally supposed to get.
Answer: D
Question: If one person completes a journey in 10 hrs. He travels 1st half of the journey at the rate of 21 km/hr and 2nd half at therate of 24 km/hr. Find the total journey in km.
A.200 km
B.212 km
C.224 km
D.230 km
Answer: C.224 km
Explanation: distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x
Distance covered in the the second half = 24(10 - x)
But distance covered in the the first half = Distance covered in the the second half
=> 21x = 24(10 - x)
=> 21x = 240 - 24x
=> 45x = 240
=> 9x = 48
=> 3x = 16
⇒x=163Hence Distance covered in the the first half = 21x=21×163=7×16=112 kmTotal distance = 2×112=224 km
C
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.
A.388
B.277
C.4312
D.2887
Answer: C.4312
Explanation: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m.Answer: C
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 150 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
A.800
B.1200
C.480
D.192
Answer: D.192
Explanation: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =150 => 16x = 1200 (2) 3x =150 => 16x = 800 (3) 5x =150 => 16x = 480 (4) 6x =150 => 16x = 400
Hence Answer is D 192 which can not be any of these.
Question: In a company 200 persons, working 6 hours per day complete 1/3 rd of the work in 7 days. Employee number of additional persons, working 4 hrs per day, required to complete the remaining work in 15 days is :
A.60
B.80
C.90
D.70
Answer: B.80
Explanation: Explanation :
Solution: Let the number of persons completing the work in 15 days be x.
Work done = 1/3, remaining work = (1-1/3) = 2/3.
less hours per day, more men required (IP)
more work, more men required (DP)
more days, less men required (IP)
hours per day 4 : 6
work 1/3 : 2/3 } : : 200 : x
days 15 : 7
.'. 4*1/3 * 15*x = 6 * 2/3 * 7 * 200
=> 60x = 16800
=> x = 16800/60 = 280.
Additional men required = (280-200) = 80.
Answer : B
Question: Find the odd man out. 24,36,52,72,96
A.52
B.72
C.36
D.24
Answer: A.52
Explanation: All except 52 are multiples of 6
Answer is A
Question: A village bank offers 5% compound interest calculated on half-yearly basis. A regular customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount the customer would have gained by the way of interest is:
A.121
B.130
C.125
D.135
Answer: A.121
Explanation: after 1 yr Rs 1600 at 5% at half yearly
P(1+(R/2)/100)^2T = 1600(1+(5/2)/100)^2*1 = 1600(1+1/40)^2--1
amt after 1/2 yr on Rs 1600 at 5%
==> 1600(1+(5/2)/100)^2*1/2 = 1600(1+1/40)--2
total amt after 1 yr from 1 and 2
1600(41/40)(81/40) = 41* 81 = 3321
Comp int = 3321- 3200 = Rs 121
ANSWER A
Question: The cost price of 12 articles is equal to the selling price of 8 articles. What is the profit percent?
A.40%
B.45%
C.50%
D.55%
Answer: C.50%
Explanation: 8*SP = 12*CP
SP = 1.5*CP
The profit percent is 50%.
The answer is C.
Question: A box contains 12 pairs of shoes (24 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
A.1/190
B.1/23
C.1/19
D.1/10
Answer: B.1/23
Explanation: The problem with your solution is that we don't choose 1 shoe from 24, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/23(as after taking one at random there are 23 shoes left and only one is the pair of the first one)=1/23
Answer: B
Question: In a group of ducks and cows, the total number of legs are 20 more than twice the no. of heads. Find the total no.of buffaloes.
A.10
B.12
C.13
D.15
Answer: A.10
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 20
=> 2x = 20 => x = 10
A
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 5 cm, and the point of contact is 7 cm above the ground, what is the radius of the other ball?
A.10 cm
B.25/2 cm
C.35/3 cm
D.15 cm
Answer: C.35/3 cm
Explanation: similar triangle properties..
2/r+5 = 5/r-5
giving r = 35/3.
Answer: C
Question: In a factory, an average of 50 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 45 sets/day . The average production per day for day last 5days is ?
A.20
B.36
C.48
D.50
Answer: A.20
Explanation: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 45 - 25 x 50
= 100
∴ Average for last 5 days = 100 / 5
= 20
A
Question: A machine is bought for Rs.4000/- and sold at a loss of 20% find its selling price?
A.s.4600/-
B.s.4560/-
C.s.4880/-
D.s.4800/-
Answer: D.s.4800/-
Explanation: 100 % ------> 600 (100 * 40 = 4000)
120 % ------> 4800 (120 * 40 = 4800)
Selling price = Rs.4800/-
Option 'D'
Question: Deepa bought a calculator at 30% discount on the listed price. Had she not got the discount, she would have paid 82.50 extra. At what price did she buy the calculator ?
A.192.5
B.275
C.117.85
D.Cannot be determined
Answer: A.192.5
Explanation: List price of calculator
82.50/30×100= 275
Deepa bought calculator in
275 × 0.70 = 192.50
Answer A
Question: If the sum of the interior angles of a regular polygon measures up to 720 degrees, then how many sides does the polygon have?
A.10
B.6
C.12
D.11
Answer: B.6
Explanation: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=720
180n - 360 = 720
180n = 1080
n = 1080/180 = 6
ANSWER:B
Question: A train covers a distance in 50 min, if it runs at a speed of 48 kmph on an average. The speed at which the train must run to reduce the time of journey to 40 min will be.
A.60 kmph
B.45 kmph
C.50 kmph
D.55 kmph
Answer: A.60 kmph
Explanation: Time = 50/60 = 5/6 hr
dist = S * T = 48*5/6 = 40 km
Time = 50/60 => new speed = 40*3/2 = 60 kmph
ANSWER A
Question: The workforce of Company X is 60% female. The company hired 26 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
A.160
B.220
C.312
D.360
Answer: C.312
Explanation: Let's xx be total quantity of employees
0.6x=females before adding men
0.55(x+26)=females after adding men
as quantity of women doesn't change we can make an equation:
0.6x=0.55(x+26)
0.05x=14.3
x=286 - this is quantity of employees before adding 26 men
So after adding it will be 312
Answer is C
Question: If Jack walked 7 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?
A. 4
B. 4.5
C. 5.6
D. 6.25
Answer: C. 5.6
Explanation: Distance walked in 1 hour and 15 mins = 7 miles
Speed per hour = Distance/Time = 7/(5/4) = 5.6 miles per hour
Answer C
Question: A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used
A.12 months
B.10 months
C.14 months
D.16 months
Answer: B.10 months
Explanation: Explanation :
B received 2/3 of the profit
=> A : B = 1 : 2
Let the total capital = x
Then A's capital = x/4
B's capital = x – x/4 = 3x/4
Assume B's money was used for b months
Then A:B = (x/4)*15 : (3x/4)*b = 1 : 2
=> 15/4 : 3b/4 = 1 : 2
=> 15 : 3b = 1 : 2
=> 5 : b = 1 : 2
=> 5/b = 1/ 2
=> b = 5*2 = 10. Answer : Option B
Question: Sachin borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends money to Rahul at 25/4% p.a. for 2 years. Find the gain of one year by Sachin.
A.110.5
B.111.5
C.112.5
D.113.5
Answer: C.112.5
Explanation: Explanation:
Two things need to give attention in this question, First we need to calculate gain for 1 year only.
Second, where we take money at some interest and lends at other, then we use to subtract each other to get result in this type of question. Lets solve this Simple Interest question now.
Gain in 2 year = [(5000×25/4×2/100)−(5000×4×2/100)]
=(625−400)=225
So gain for 1 year = 225/2=112.50
Option C
Question: How many real solutions does the equation x5 + 2x3 + 8x2 + 16 = 0 have?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: Note that x5+2x3+8x2+16 = (x3+8)(x2+2) = (x+2)(x2-2x+4)(x2+2).
Since the quadratic equations x2 - 2x + 4 = 0 and x2 + 2 = 0 have no real solutions, the
original equation has just one real solution, x = -2.
correct answer B
Question: The bankers discount and the true discount of a sum at 20% per annum simple interest for the same time are Rs.80 and Rs.40 respectively. What is the sum and the time?
A.Sum = Rs.80 and Time = 5 years
B.Sum = Rs.100and Time = 5 years
C.Sum = Rs.60 and Time = 5 years
D.Sum = Rs.120 and Time = 5 years
Answer: A.Sum = Rs.80 and Time = 5 years
Explanation: Explanation :
BD = Rs.80
TD = Rs.40
R = 10%
F = BD ×TD/(BD – TD)=80×40/(80–40)=80×40/40=Rs. 80
BD = Simple Interest on the face value of the bill for unexpired time =FTR/100
⇒80= (80×T×20)/100
⇒80 = 8 × T × 2 ⇒10= 2 × T
⇒ T = 10/2 = 5 years Answer : Option A
Question: The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 55 terms of set X?
A.1
B.3
C.5
D.7
Answer: C.5
Explanation: 55*4 + 54*40 + 53*400 = 220 + 2160 + 21200 = 23580
The hundreds digit is 5.
The answer is C.
Question: In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?
A.90
B.105
C.168
D.420
Answer: B.105
Explanation: You need to choose 4 groups of 2 from 8 people: That's 8/!2!2!2!2!, then divided by 4!, since any ordering of these 4 groups is the same.
Total = 8/2!2!2!2!4!=8!/8∗2∗4!=7!/2∗4!=7∗6∗5∗4∗3∗2/4∗3∗2∗2=7∗6∗5/2=35∗3=105.
Answer: B
Question: The sum t of prime numbers that are greater than 60 but less than 70 is
A. 67
B. 128
C. 191
D. 197
Answer: B. 128
Explanation: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum t of 61 and 67 is 128.
Answer B.
Question: John took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If he paid Rs. 540 as interest at the end of loan period, what was the rate of interest?
A.2 %
B.3 %
C.4 %
D.6 %
Answer: D.6 %
Explanation: Explanation:
Simple interest is same as the rate of interest.
Hence,
Rate of interest = R% and Time = R years
Simple Interest =	(P × R × T)/100
60 =	(1500 × R2)/100
15R2 = 540
R2 = 36
R=6 %
Rate of Interest = 6 %
ANSWER IS D
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
A.3888
B.2988
C.2777
D.8925
Answer: D.8925
Explanation: Principal = (100 * 4016.25) / (9 * 5) = Rs. 8925.Answer: D
Question: A person travels from K to L a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?
A.55 kmph
B.58 kmph
C.60 kmph
D.66 kmph
Answer: C.60 kmph
Explanation: Explanation:
Speed on return trip = 150% of 50 = 75 km/hr.
Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.
ANSWER IS C
Question: How many plants will be there in a circular bed whose outer edge measure 34 cms, allowing 4 cm2 for each plant ?
A.18
B.750
C.23
D.120
Answer: C.23
Explanation: Circumference of circular bed = 34 cm
Area of circular bed = (34)2â„4Ï€
Space for each plant = 4 cm2
âˆ´ Required number of plants
= (34)2â„4Ï€ Ã· 4 = 22.98 = 23(approx)
Answer C
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,260 ?
A.$12
B.$14
C.$16
D.$17
Answer: B.$14
Explanation: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,260, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,260 --> (5+x)(20-x)=126 --> x=2 or x=13 --> price=10+$2*2=$14 or price=10+$2*13=$36.
Answer: B.
Question: The average of Suresh’s marks in English and History is 55. His average of marks in English and Science is 65. What is the difference between the marks which he obtained in History and Science?
A.40
B.60
C.20
D.Data inadequate
Answer: C.20
Explanation: E + H = (55 × 2) = 110;
E + S = (65 × 2) = 130
∴ Reqd difference = 130 – 110 = 20
Answer C
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
A.27
B.29
C.31
D.32
Answer: C.31
Explanation: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
C
Question: Tim and Élan are 60 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
A.30 miles.
B.35 miles.
C.40 miles.
D.60 miles.
Answer: C.40 miles.
Explanation: Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.
Plugging in the answer choice Only Answer Choice C meet the 2:1(Tim:Elan=40:20) ratio of maintaining total distance traveled 60 miles
So Correct answer C
Question: James has 300 roses, and he decided to make booke with 50 flowers in each. After that he packed these bookes and wanted to sent some friends. He he decide to arrange the bookes in every possible combination and moved just one booke every 1/4 minute, how long would it taken by him ?
A.200 minutes
B.180 minutes
C.250 minutes
D.160 minutes
Answer: B.180 minutes
Explanation: Explanation:
No of bookes = 300/50 = 6
Clearly, number of ways of arranging 6 bookes = 6 ! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
So, total time taken = 720*1/4 minutes = 180 minutes
Answer: B
Question: The sum and the product of two numbers are 16 and 64 respectively, the difference of the number is?
A.0
B.6
C.7
D.8
Answer: A.0
Explanation: Explanation:
x + y = 16
xy = 64
(x- y)2 = (x + y)2 - 4xy
(x- y)2 = 256- 256 => (x - y) = 0
Answer: A
Question: A survey of n people in the town of badaville found that 50% of them prefer brand A. Another survey of 100 people in the town of chottaville found that 60% prefer brand A.In total 55% of all the people surveyed together prefer Brand A.What is the total number of people surveyed?
A.138
B.100
C.128
D.278
Answer: B.100
Explanation: 50% (n) + 60% (100 ) = 55% (n + 100)
Solving we get n = 100
Answer:B
Question: Which of the following is a factor of 18!+1?
A.15
B.17
C.19
D.33
Answer: C.19
Explanation: 18! and 18!+1 are consecutive integers and so they do not have any common factor except 1.
15, 17, 33 (=3*11), and 39 (=3*13) are factors of 18! and none of those can be a factor of 18!+1.
So, only 19 can be a factor of 18!+1
Answer:C
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $10.00 per hour and a standard tip rate of 40% of the cost of the orders she serves. If she worked four 16-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
A.280
B.300
C.1664
D.350
Answer: C.1664
Explanation: Jill earns 10 dollars/hour and the hourly tip is (2/5)*40.
Jill thus earns 10*16+16*16 per day(or 10(16)+16(16)=26(16)=416).
Jill has worked for 4 days -> 416*4=1664.
This matches answer choice C.
Question: If 7 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
A.7 × 6 × 5 × 4 × 3 × 2 × 1
B.7 × 6 × 5 × 4 × 3 × 2 × 1
C.7 x 8
D.21
Answer: D.21
Explanation: 1st person will have 6 handshakes, 2nd will have 5, ....6th will have 1 and 7th will have 0
= 6+5+4+3+2+1 = 21
if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.
Ans.D)
Question: A man on tour travels first 100 km at 50 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 260 km of tour.
A.60.11 km/hr
B.61.11 km/hr
C.62.11 km/hr
D.65.00 km/hr
Answer: D.65.00 km/hr
Explanation: Explanation:
We know Time = Distance/speed
So total time taken =
(100/50+160/80)=4hours
Time taken for 260 Km = 260/4=65km/hr
Option D
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.298
B.288
C.120
D.776
Answer: C.120
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer:C