RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A one-foot stick is marked in 1/3 and 1/4 portion. How many total markings will there be, including the end points?
A.8
B.9
C.7
D.6
Answer: C.7
Explanation: LCM of 12 = 12
1/3 marking are (Table of 4) 0...... 4 ......8..... 12
(Total = 4)
1/4 marking are (Table of 3) 0 ....... 3 ...... 6...... 9........ 12 (Total = 5)
Overlapping markings are 0 ........ 12 (Total = 2)
Total markings = 4+5-2 = 7
Answer = C
Question: The ratio between the present ages of P and Q is 5:7 respectively. If the difference between Q's present age and P's age after 6 years is 2. What is the total of P's and Q's present ages?
A.48
B.277
C.65
D.15
Answer: A.48
Explanation: Let the present ages of P and Q be 5x and 7x years respectively.
Then, 7x - (5x + 6) = 2
2x = 8 => x = 4
Required sum = 5x + 7x = 12x = 48 years.
Answer:A
Question: A team has to design a flag. The team has three yellow strips of cloth and four green strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand?
A.24
B.35
C.42
D.84
Answer: B.35
Explanation: The # of permutations of total 3+4=7 strips where 3 are identical yellow and 4 are identical green is 7!/(3!*4!)=35 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).
Answer: B.
Question: John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/4 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?
A.45
B.62
C.70
D.77
Answer: B.62
Explanation: Rakesh : Rahul : Ranjan : Rohit = 1 / 4 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 4 x 60 ) = 15.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 15 x + 20 x + 15 x + 12 x) = 62 x.
For minimum number of pencils x = 1 .
The person should have at least 62 pencils.
B)
Question: In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 4 : 7 : 9. If the shop carries 364 dogs and bunnies total in stock, how many dogs are there?
A.42
B.66
C.98
D.112
Answer: D.112
Explanation: Let us assume the number of dogs, cats and bunnies to be 4x, 7x and 9x
Total dogs and bunnies = 13x.
And we are given that 13x = 364.
Hence x = 28.
Dogs = 4x = 4*28 = 112 (Option D)
Question: Find the area, diameter = 11m.
A.113.00 square meter
B.95.07 square meter
C.93.08 square meter
D.93.24 square meter
Answer: B.95.07 square meter
Explanation: Diameter = 11 meter.
Radius = diameter/2.
= 11/2.
= 5.5 meter.
Area of a circle = Ï€r2.
Here, pi (Ï€) = 3.14 meter, radius (r) = 5.5.
Area of a circle = 3.14 Ã— 5.5 Ã— 5.5..
= 3.14 Ã— 30.25.
= 95.07 square meter ANSWER : B
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.$448,000
B.$148,000
C.$248,000
D.$548,000
Answer: B.$148,000
Explanation: 6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x.
corect answer B
Question: If 10 lions can kill 10 deers in 10 minutes how long will it take 100 lions to kill 100 deers?
A.1 minutes
B.10 minute
C.100 minutes
D.10000 minutes
Answer: B.10 minute
Explanation: we can try the logic of time and work,our work is to kill the deers so 10(lions)*10(min)/10(deers)=100(lions)*x(min)/100(deers)hence answer is x=10
ANSWER:B
Question: There is a total of 84 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 2/7. What is the probability that the marble will be either red or blue?
A.3/7
B.11/14
C.13/28
D.19/28
Answer: C.13/28
Explanation: P(red or blue) = 1 - P(white) - P(green) = 28/28 - 7/28 - 8/28 = 13/28
The answer is C.
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:40 a.m., how long W will the conference last if there are a total of 6 seminars that day?
A.5 hours and 15 minutes
B.5 hours and 20 minutes
C.5 hours and 25 minutes
D.5 hours and 30 minutes
Answer: B.5 hours and 20 minutes
Explanation: Shouldnt the answer be 5 hours 20 mins?
Break = b
Seminar= 10b
9am to 11:40am= 160mins
3s+b=160
30b+b=160
b=160/31
6 seminar will take
6s+2b
=60b+2b
=62b
=62*160/31
=320
W=5 hours 20 mins.B
Question: Which of the following triples of numbers have the same standard deviation as the numbers a, b, and c?
I. a-2, b-2, c-2
II. 0, a-b, c-b
III. a-4, b+5, c-1
A.I only
B.II only
C.I and III only
D.II and I only
Answer: D.II and I only
Explanation: If we add or subtract a constant to each term in a set the standard deviation will not change.
Set {a-2, b-2, c-2} is obtained by subtracting 2 from each term of {a, b, c}.
Set {0, a-b, c-b} is obtained by subtracting s from each term of {a, b, c}..
Set {a-4, b+5, c-1} is totally different from {a, b, c}.
Thus the answer is I and II only.
Answer: D.
Question: In a class of 5 students, average weight of the 4 lightest students is 40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is the difference between the the maximum and minimum possible average weight overall?
A.2.8 kgs
B.3.2 kgs
C.3 kgs
D.4 kilograms
Answer: D.4 kilograms
Explanation: DETAILED SOLUTION
If there are an odd number of terms, say, 2n + 1, then the median is the middle term. And if average is lesser than the middle term, there will at least be n + 1 terms greater than the average. So, there will be more terms above the average than below it.
However, this need not be the case when there are an even number of terms. When there are 2n distinct terms, n of them will be greater than the median and n will be lesser than the median. The average of these two terms can be such that there are n terms above the average and n below it.
For instance, if the numbers are 0, 1, 7, 7.5. The median is 4, average is 3.875. Average is less than the median. And there are more 2 numbers above the average and 2 below the average.
Correct Answer: Median is 4, average is 3.875.
Correct Answer: D
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 16 hours respectively after meeting each other. If the train A travels at 80kmph, find the rate at which the train B runs.
A.40
B.160
C.120
D.80
Answer: B.160
Explanation: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/16) = 2/4=1/2
This gives us that the ratio of the speed of A : speed of B as 1:2.
Since speed of A is 80 kmph, speed of B must be 80*(2/1) = 160 kmph
B
Question: The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is
A.64 sq.m
B.70 sq.m
C.78 sq.m
D.84 sq.m
Answer: B.70 sq.m
Explanation: Solution
Perimeter of the rhombus	= 56 m
Each side of the rhombus	= 56 / 4 m
= 14 m.
Height of the rhombus	= 5 m
Area	= (14 x 5) m²
= 70 m²
Answer B
Question: In a series of six consecutive odd numbers, the sum of the second and fifth numbers is 28. What is the third number?
A.9
B.11
C.17
D.13
Answer: D.13
Explanation: Let the numbers be x, x + 1, x + 3, x + 5 and x + 7.
Given (x + 1) + (x + 7) = 28
=> 2x + 8 = 28 => x = 10
The third number = x + 3 = 10 + 3 = 13.
Answer: D
Question: What will be the compound interest on a sum of Rs. 45,000 after 3 years at the rate of 12% p.a.?
A.s:10123.19
B.s:10123.29
C.s:10123.20
D.s:18221.76
Answer: D.s:18221.76
Explanation: Amount
= [45000 * (1 + 12/100)3]
= 45000 * 28/25 * 28/25 * 28/25
= Rs. 63221.76
C.I. = (63221.76 - 45000)
= Rs:18221.76
Answer: D
Question: 'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the addition of the maximum and minimum possible values of 'a + b'?
A.28
B.30
C.22
D.20
Answer: B.30
Explanation: possible values of a and b can be 5,4; 4,5 (which are same for a+b) and 1,20; 20,1 (same result for a+b)
so 21+9 = 30. ans B.
Question: Which of the following numbers doesn't have a divisor greater than 1 that is the square of an integer?
A.63
B.108
C.25
D.13
Answer: D.13
Explanation: Prime Factorization
63=7*3*3= 7*3^2. Includes the perfect square of 9.
108=2*3*2*3*3=6^2*3. Includes the perfect square of 36.
25=5*5=5^2. A perfect square of 25.
13=13*1. There are no perfect squares as factors.
36=2*2*3*3= 2^2*3^2. Includes the perfect squares of 4 and 9.
Only 13 does not have a perfect square as a factor so the correct answer is D.
Question: If g and f are both odd prime numbers andg < f, then how many different positive integer factors does2gfhave?
A. 3
B. 4
C. 6
D. 8
Answer: D. 8
Explanation: g and f are both odd prime numbers- It means either g or f is not 2
and since prime numbers have only two factors - 1 and the number itself
g and f each will have (1+1)= 2 factors
Hence 2gf will have (1+1)(1+1)(1+1)= 8 factors
D is the answer
Question: What is (25^7+25) / 25?
A.244140626
B.243120617
C.242580531
D.241230438
Answer: A.244140626
Explanation: (25^7+25) / 25 =
25*(25^6+1) / 25 =
25^6 + 1
Clearly this is a number which ends with a 6 in the units place.
The answer is A.
Question: A started a business with an investment of Rs. 70000 and after 9 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 76000, then the share of B is?
A.33008
B.24000
C.28000
D.48000
Answer: D.48000
Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 3) = 7 : 12
Total profit = Rs. 76000
Share of B = 12/19 (76000) = Rs. 48000
Answer: D
Question: If s,t ,and u are positive real numbers such that s(t+u) = 152, t(u+s) =162 , and u(s+t) = 170, then stu is
A.a) 672
B.b) 688
C.c) 704
D.d) 720
Answer: D.d) 720
Explanation: st+su = 152 ----------------------------- tu+ts = 162-------------------------------- su+ut= 170---------------------------------------3)
Re-writing equation 3 as follows:
su+ut = 162 + 8
su+ut = tu+ts + 8
su = ts + 8 ............... (4)
Adding (1)(4)
2su = 160
su = 80
stu has to be multiple of 80, only 720 fits in
Answer = D
Question: During a Thanksgiving weekend, a car rental company rented six-tenths of their vehicles, including two-fifths of the 4WDs that it had. If 40% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
A.20%
B.30%
C.40%
D.50%
Answer: C.40%
Explanation: 4/10 of all the vehicles were not rented.
(3/5)(2/5) = 6/25 of all the vehicles are 4WDs that were not rented.
(6/25) / (4/10) = 3/5 is the fraction of non-rented vehicles that were 4WDs
1 - 3/5 = 40% of non-rented vehicles were not 4WDs.
The answer is C.
Question: Jack needs to arrive at the flower shop before 2 p.m, and the car rental by 3:30 pm, before he picks Sally up for their date at 5:30. It is now 12 p.m. the flower shop is 1.2 miles from Jacks house. He walks at a pace of 3.1 miles per hour. The flower shop is about .6 miles from the car rental shop, where Jack must walk to next. He can then drive the last 4.3 miles to Sallys house with an approx speed of 35 mph. When should he leave for each destination, in order based on the distance between stops Jack's walking speed, and finally the travel in the car?
A.1:56 p.m, 3:21pm, 5:21 p.m
B.1:59 p.m, 3:17p.m, and 5:24 p.m
C.1:57 p.m., 3.19 p.m, and 5:26pm
D.1:52 pm, 3:11 p.m, and 5:18 pm
Answer: D.1:52 pm, 3:11 p.m, and 5:18 pm
Explanation: 1.2 m/3.2 mph= 38 minutes to travel to flower shop
Needs to leave home at: 1:52 pm bc 2pm-38minutes=1:52 pm
Needs to leave flower shop at: .6Ã·3.1=approx 19 minutes 3:30 pm- 19 minutes= 3:11pm
Needs to leave car rental by: 4.3/35mph= approx 12 minutes 5:30-12 minutes= 5:18pm
Correct answer is D
Question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 743.095 + ?
A.870
B.790
C.780
D.770
Answer: C.780
Explanation: ? = 285 + 1895 – 655 – 745 or, ? = 780
Answer C
Question: The cost of producing x tools by a company is given by
C(x) = 1000 x + 5500 (in $)
a) What is the cost of 100 tools?
A.125500 $
B.125800 $
C.105900 $
D.105500 $
Answer: D.105500 $
Explanation: Solution
C(100) = 1000*100 + 5500 = 125500 $
Answer D
Question: A person buys an article at Rs.400. At what price should he sell the article so as to make a profit of 40%?
A.600
B.277
C.560
D.261
Answer: C.560
Explanation: Cost price = Rs.400
profit = 40% of 400 = Rs.160
Selling price = Cost price + Profit
= 400 + 160 = 560
Answer: C
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.8, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
A.4.2
B.4.4
C.4.6
D.5.6
Answer: A.4.2
Explanation: Sum of the remaining two numbers = (3.95 * 6) - [(3.8 * 2) + (3.85 * 2)]
= 8.4.
Required average = (8.4 / 2) = 4.2.
A
Question: Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability Q that Jane will be on the same committee as Albert?
A. 12%
B. 20%
C. 33%
D. 40%
Answer: D. 40%
Explanation: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20
No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8
Probability Q= (8/20) *100 =40%.
+1 for me.. :D
Question: A car traveling at a certain constant speed takes 10 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 40 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
A.35
B.35.5
C.36
D.36.5
Answer: C.36
Explanation: 40 * T = 1 km => T = 1/40 km/h
V*(T+10/3600) = 1
V (1/40 + 10/3600) = 1
V (100/3600) = 1
V = 36 km/h
The answer is C.
Question: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit and remaining 60% at 20% profit. Find his % profit on total.
A.24%
B.20%
C.26%
D.28%
Answer: B.20%
Explanation: If the total quantity was 100
Then 40X 20% + 60 X20%= 20
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'B' is the answer
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?
A.8 1/9 %
B.8 7/3 %
C.8 1/3 %
D.2 1/3 %
Answer: C.8 1/3 %
Explanation: C.P. of 1 kg = 420/7 = Rs. 6
S.P. of 1 kg = Rs. 6.50
Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %.Answer: C
Question: The average of 25 result is 18.The average of 1st 12 of them is 14 & that of last 12 is 17.Find the 13th result.
A.18
B.68
C.58
D.78
Answer: D.78
Explanation: Clearly 13th result=(sum of 25 results)-(sum of 24 results)
=(18*25)-(14*12)+(17*12)
=450-(168+204)
=450-372
=78.
ANSWER D 78
Question: There are ten players in the basketball team. If the average height of the players is 170 cm, what will be the new average height if a 192 cm player will join the team?
A.168.
B.172.2
C.172
D.181
Answer: C.172
Explanation: Given ( X1 + X2 + .......... X10 ) / 10 =170
Now ( X1 + X2 + .......... X10 ) = 1700 ---> Eq 1.
Now one new person added and the person be A and height is 192 and the total no of players will be 11 and let's say the new average is B.
=> ( X1 + X2 + .......... X10 + 192 ) / 11 = B --Eq 2
Sub X1 + X2 + .......... X10 from Eq 1 in Eq 2.
=> 1700 + 192 = 11 B
B = 172.
Answer: C is the correct option
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
A.15
B.99
C.77
D.55
Answer: A.15
Explanation: Speed of the boat in still water = (60+90)/2 = 75 kmph. Speed of the stream
= (90-60)/2
= 15 kmph.
Answer: A
Question: The total age of A and B is 18 years more than the total age of B and C. C is how many years younger than A ?
A.12
B.27
C.21
D.18
Answer: D.18
Explanation: (A+B) - (B+C) = 18
A - C = 18.
C is younger than A by 18 years.
Answer: D
Question: Working individually, Emma can wrap presents for 6 hours and Troy can wrap presents in 8 hours. If Emma and Troy work together but independently at the task for 2 hours, at which point Troy leaves, how many remaining hours will it take Emma to complete the task alone?
A.30/12
B.5/12
C.3/4
D.2/12
Answer: A.30/12
Explanation: In first 2 hrs Troy will finish 2/8 = 1/4 of work and Emma will finish 2/6 work so total 1/4 + 1/3 = 7/12 work is finished and 1-7/12 = 5/12 work remaining. Now Emma will take (5/12)*6 = 30/12 hrs to finish it.
So answer is A.
Question: A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 140 billion gallons. If the storm increased the amount of water in the reservoirs to 80 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
A.51
B.48
C.55
D.63
Answer: A.51
Explanation: Let total capacity be x
we know 140 = 0.80x
x = 140/0.80 = 175
Prior to storm, we had 124 bn gallons
175-124 = 51
Answer : A
Question: An inspector rejects 15% of the meters as defective. How many will he examine to reject 15?
A.A)100
B.B)120
C.C)250
D.D)200
Answer: A.A)100
Explanation: Then, 15% of x= 15
(15/100)x = 15
x = (15*100*)/15= 100
Answer is A
Question: If f(x) = x - 4, then (f o f)(3) = ?
A.-5
B.-4
C.-6
D.-3
Answer: A.-5
Explanation: (f o f)(3) = f(f(3)) = f(3 - 4) = f(-1) = - 5
correct answer A
Question: A 40-liter solution of alcohol and water is 5 percent alcohol. If 2.5 liters of alcohol and 7.5 liters of water are added to this solution, what percent of the solution produced is alcohol?
A.9%
B.12%
C.15%
D.18%
Answer: A.9%
Explanation: The percent of alcohol in the solution is (0.05(40) + 2.5) / 50 = 4.5/50 = 9%
The answer is A.
Question: Timmy and Tommy Pumpernickel are leaving home for college today. Peter and Patty Pumpernickel stand and wave goodbye as their pride and joy head off to schools at opposite ends of the state. If Timmy drives a slow 45 miles/ hour and Tommy "the lead foot" Pumpernickel drives a jaw dropping 75 miles per hour, how long until they are 500 miles away from one another?
A.4 hours
B.4.5 hours
C.4.24 hours
D.4.17 hours
Answer: D.4.17 hours
Explanation: The Pumpernickel brothers are traveling 120 miles per hour in opposite directions.
500 miles/ 120 miles/hour= 4.17 hours
Answer is D
Question: There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:
A.5
B.6
C.21
D.33
Answer: C.21
Explanation: 6 Green - 1 way
5 green - 2 ways
4 green - 3 ways
3 green - 4 ways
2 green - 5 ways
1 green - 6 ways
total = > 21 ways
Answer C
Question: A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 8 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?
A.258
B.584
C.774
D.624
Answer: B.584
Explanation: Pretty simple actually
Number of 1 letter symbols = 8
Number of 2 letter symbols = 8*8
Number of 3 letter symbols = 8*8*8
The answer is sum of the 3. =584
So the answer is B.
Question: What approximate value should come in place of the a in the following equation?
10% of 6275 + 20% of 7584 = a
A.2180
B.2160
C.2140
D.2130
Answer: C.2140
Explanation: a = 10% of 6275 + 20% of 7584
a = 10/100* 6275 + 20/100* 7584
a =2144.3
≈ 2140
Answer C
Question: The mark up between "normal plan" price and "premium plan" price is 30 percent of the "normal plan" price. The markup is what percent of the "premium plan" price ?
(markup = difference between normal and premium price plans)
A. 8%
B. 20%
C. 33 1/3%
D. 45%
Answer: C. 33 1/3%
Explanation: A = price for normal plan
B = price for premium plan
MP = 0.5 A
B = A + 0.5 A = 1.5 A
hence Markup = B-A = 0.5/1.5 B = 1/3 B. Hence MP is 33.33% of B
Answer C
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 42 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
A.105
B.140
C.175
D.210
Answer: D.210
Explanation: In 72 minutes, car X travels 42 miles.
Car Y gains 7 miles each hour, so it takes 6 hours to catch car X.
In 6 hours, car X travels 210 miles.
The answer is D.
Question: The ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan?
A.17
B.16
C.18
D.15
Answer: D.15
Explanation: Let the school ages of Neelam and Shaan be 5x and 6x years respectively.
Then, (1/3 * 5x)/(1/2 * 6x) = 5/9
15 = 15
Thus, Shaan's age cannot be determined.
Answer:D
Question: let p be the product of the positive integers between 1 and 7 inclusive. How many distinct prime factors does p have?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: There are 4 primes between 1 and 7, inclusive: 2, 3, 5, and 7, therefore p=1*2*...*7=7! has 4 distinct prime factors.
Answer: D.
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
A.19 months
B.10 months
C.11 months
D.81 months
Answer: B.10 months
Explanation: 7*5: 5*x = 7:10
x = 10
Answer: B
Question: If abc ≠ 1 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =
A.(1 + bc)/(b + c)
B.(1 – bc)/(b + c)
C.(1 + b + c)/(bc)
D.(1 – b – c)/(bc)
Answer: C.(1 + b + c)/(bc)
Explanation: Answer is C though it took me around 4 minutes to get that.
Question: g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(z) is divisible by 4^11, what is the smallest possible value for z?
A. 22
B. 24
C. 28
D. 32
Answer: B. 24
Explanation: g(z)=4^11=2^22. So we have to find a product with atleast 22 2's in it.
in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
Question: A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 301 test scores with a standard deviation less than d?
A. 75 and 80
B. 80 and 85
C. 70 and 75
D. 75 and 75
Answer: D. 75 and 75
Explanation: Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 75 and 75 are the most close numbers and they will increase the number of elements in the set without changing the median value.
D
Question: In Town X, 96 percent of the population are employed, and 24 percent of the population are employed males. What percent of the employed people in Town X are females?
A.16%
B.25%
C.32%
D.75%
Answer: D.75%
Explanation: Total employed people 96%, out of which 24 are employed males, hence 72% are employed females.
(employed females)/(total employed people)=72/96=3/4=75%
Answer: D.