RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 20 percent of the drive from the center, what percent of the round-trip has the technician completed?
A.60
B.50
C.40
D.70
Answer: A.60
Explanation: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 20% of 50% i.e 10%. so he completed 50 +10 =60 % of total trip
A
Question: A line that passes through (–3, –4) and (3, k) has a slope = k. What is the value of k?
A. 3/4
B. 1
C. 4/5
D. 2
Answer: C. 4/5
Explanation: Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(3+3)
=> 6k = k+4
=> k =4/5
Ans C it is!
Question: The monthly rent of a shop of dimension 18feet × 20feet is Rs.3600. What is the annual rent per square foot of the shop?
A.120
B.56
C.68
D.87
Answer: A.120
Explanation: Sol. Monthly rent per square feet = 3600/(18*20) = 10
& Annual rent per square feet
=12*10=120
Answer : A
Question: If A = {10, 15, 18, 22, 36, 44}, what is the product of mean and median of the numbers in A?
A.105
B.245
C.360
D.480
Answer: D.480
Explanation: Mean = (10 + 15 +18 + 22 + 36 + 43)/6 = 24
Median = (18+22)/2 = 20
product = 24*20 = 480
Option D
Question: In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
A.200
B.210
C.216
D.224
Answer: D.224
Explanation: The number must be a multiple of both 8 and 7 so the answer is 224.
The answer is D.
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 8 p.c?
A.36800
B.38000
C.32977
D.38128
Answer: A.36800
Explanation: CP + CP/8 = 45000
CP = 40000
SP = 40000*(92/100)
= 36800
Answer:A
Question: An observation is made on a clock and it is found that the hour hand is placed exactly at the minute mark while the minute hand is six minutes ahead it. After some time, the clock is observed again and it is found that the hour hand is exactly on another minute mark while the minute hand is seven minutes ahead of it.
Analyzing this data, can you calculate the total time that has elapsed between the two observations?
A.2hr 11min
B.1hr 11min
C.3hr 11min
D.2hr 15min
Answer: A.2hr 11min
Explanation: A
Now this question cannot be solved unless you know a fact i.e. the hour hand is exactly on the minute mark five times every hour - on the hour, 12 minutes past hour, 24 minutes past hour, 36 minutes past hour and 48 minutes past hour.
Denoting the number of hours with X and the number of minutes as Y, let us begin with the calculation.
When we have the hour hand on the minute mark, the position of hour hand:
5X + Y/12
And the position of the minute hand = Y
When the first observation was taken,
Y = Y = 5X + Y/12 + 6
Or, 60X = 11Y - 72.
With the given facts, we know for sure that Y can only be 0, 12, 24, 36 or 48.
According to which, the possible values for X and Y can be 1 and 12 respectively. Thus the time must be 1:12 when the first observation was taken.
Similarly, in the second observation, let's make the equation:
60X = 11Y - 84
Here, the possible values for X and Y here are 3 and 24 respectively. According to this, the time is 3:24 for sure.
From 1:12 to 3:24, two hours and eleven minutes have passed.
Question: The day of week on July 1,2000 was
A.Monday
B.Friday
C.Saturday
D.Tuesday
Answer: C.Saturday
Explanation: 1600 years:0 odd days
300 years=1 odd day
99 years=4 odd days
So till 1999 there are 5 odd days
now in 2000....2000 is a leap year
1 odd day till 1 july 2000 from jan 1 2000
so total odd days=5+1=6
So saturday
ANSWER:C
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases?
A.8:8
B.8:1
C.8:7
D.8:5
Answer: C.8:7
Explanation: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer:C
Question: The average waight of A,B,C is 45 Kg. The avgwgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.
A.23 KG
B.43 KG
C.21 KG
D.31 KG
Answer: D.31 KG
Explanation: Sol. Let A,B,c represent their individual wgts.
Then,
A+B+C=(45*3)Kg=135Kg
A+B=(40*2)Kg=80Kg & B+C=(43*2)Kg=86Kg
B=(A+B)+(B+C)-(A+B+C)
=(80+86-135)Kg
=31Kg.
ANSWER D
Question: If 6x^2 + x - 12 = (gx + b)(cx + d), then |g| + |b| + |c| + |d| =
For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/
A. 10
B. 12
C. 15
D. 18
Answer: B. 12
Explanation: 6x^2+x-12 = 6x^2 + 9x -8x -12
=> 3x(2x+3) -4(2x+3)
=> (2x+3)(3x-4) = (gx+b)(cx+d)
Hence g=2, b=c=3, d=-4
So, 2+3+3+ |-4| = 2+3+3+4 = 12
Answer B.
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 40% ?
A. 2.1
B. 1.9
C. 1.7
D. 1.5
Answer: D. 1.5
Explanation: Let x be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = x/10
Probability that the second contestant selected is also a male = x-1/9
Total probability = x(x-1)/ 90 < 1/40 (this probability is less than 40%)
Solving for x we get, x(x-1)< 9/4. This implies that the maximum value of x can be 1.5.
Answer D!
Question: What is the speed of the stream if a canoe rows upstream at 6km/hr and downstream at 10km/hr
A.1 kmph
B.4 kmph
C.3 kmph
D.2 kmph
Answer: D.2 kmph
Explanation: Sol.
Speed of stream = 1/2(10 -6) kmph = 2 kmph.
Answer D
Question: A is 30% more efficient than B .how much time they will working together take to complete a job which A alone could have done in 23 days?
A.25 days
B.13 days
C.14 days
D.20 days
Answer: B.13 days
Explanation: The ratio of times taken by A and B=100:130=10:13
suppose B can do work in x days
then 10:13::23:x
x=(23*13)/10
x=299/10
A's 1 day's work=1/23
B's 1 day's work=10/299
(A+B)'s 1 day's work =1/23+10/299 =23/299=1/13
A and B together can do work in 13 days
Answer(B)
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?
A.278
B.277
C.960
D.278
Answer: C.960
Explanation: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer:C
Question: The traffic lights at three different road crossings change after every 48 sec., 72 sec and 108 sec.respectively .If they all change simultaneously at 8:20:00 hours,then at what time they again change simultaneously .
A.8:29:12 hrs
B.8:22:12 hrs
C.8:25:12 hrs
D.8:27:12 hrs
Answer: D.8:27:12 hrs
Explanation: Interval of change = (L.C.M of 48,72,108)sec.=432sec.
So, the lights will agin change simultaneously after every 432 seconds i.e,7 min.12sec
Hence , next simultaneous change will take place at 8:27:12 hrs
Answer is D.
Question: Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
A.300
B.992
C.772
D.552
Answer: A.300
Explanation: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300
Answer: A
Question: Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil.
A.12
B.10
C.15
D.19
Answer: A.12
Explanation: Let the cost of a pen ands a pencil be Rs. X and Rs. Y respectively.
Then, 2x + 3y = 86 ….(i) and 4x + y =112.
Solving (i) and (ii), we get: x = 25 and y = 12.
Cost of a pen =Rs. 25 and the cost of a pencil =Rs. 12.
Answer is A.
Question: The cost price of an article is 70% of the marked price. Calculate the gain percent after allowing a discount of 10%.
A.13.6%
B.28.6%
C.35.6%
D.42.3%
Answer: B.28.6%
Explanation: Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 70. S.P = Rs. 90.
âˆ´ Gain % = [20/70 * 100]% = 28.6%.
Answer B
Question: Solve the quickfire maths brain teaser âˆš49% = ?
A.30%
B.40%
C.70%
D.19%
Answer: C.70%
Explanation: âˆš49%
=> âˆš49/âˆš100
=> 7/10
=> 70/100
=> 70%
C
Question: There are 13person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
A.4!*2!
B.7!*2!
C.6!*1!
D.10!*2!
Answer: D.10!*2!
Explanation: Total number of ways = 10!*2!.
D
Question: The probability of selecting face card of any color from 52 cards
A.1/13
B.2/13
C.3/13
D.4/13
Answer: C.3/13
Explanation: king queen and jack are the face cards
there are totally 12 face cards in a suit
probability = 12/52 = 3/13
ANSWER:C
Question: If a certain number is divisible by 36 and 52, it is NOT necessarily divisible by which of the following?
A.4
B.6
C.13
D.16
Answer: D.16
Explanation: If a certain number is divisible by 36 and 52, it is NOT necessarily divisible by which of the following?
let the certain number be 468, which is both divisible by 36 and 52.
468/16 =117/4
D. 16
Question: A lady builds 8cm length, 15cm width, and 5cm height box using 10cubic cm cubes. What is the minimum number of cubes required to build the box?
A.107
B.60
C.70
D.89
Answer: B.60
Explanation: Number of cubes required = Volume of box/Volume of cube
= 8*15*5/10
=60 cubes
ANSWER:B
Question: A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random form this box. The probability that at least one of these is defective is:
A.10/19
B.7/19
C.17/19
D.19/19
Answer: B.7/19
Explanation: P(none is defective)=16c2/20c2
=12/19
P( at least one is defective)= 1-12/19
=7/19
ANSWER B 7/19
Question: Working together at their respective constant rates, Machine A and Machine B can produce 600 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 600 unit total would it produce?
A.25
B.37
C.50
D.30
Answer: D.30
Explanation: 1/A+1/B= 1/T
1/A +1/12= 1/8 (50% more of 8 is 12)
1/A= 1/24
Machine A can produce 600 units in 24 hrs, so it can produce 600*8/24= 200 units is 8 hrs.
200 is 30% of 600.
D is the answer
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
A.150m
B.159m
C.750m
D.180m
Answer: A.150m
Explanation: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
A.$1
B.$1.84
C.$2.54
D.$2.65
Answer: B.$1.84
Explanation: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Question: NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day.if in 25 days they completed 1/3 part of work .than how many more emploies should NHAI hire to finish it in time working 10 hours a day
A.60
B.70
C.80
D.50
Answer: A.60
Explanation: (M1*D1*H1)/W1 = (M2*D2*H2)/W2
(100*25*8)/(1/3) =((100+a)*25*10))/(2/3)
160=100+a
a=60
ANSWER:A
Question: n what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
A.2/7
B.5/6
C.3/4
D.1/5
Answer: B.5/6
Explanation: Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Correct Option :B
Question: The wages earned by Robin is 38% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?
A.23%
B.27.53%
C.30%
D.50%
Answer: B.27.53%
Explanation: Explanatory Answer
Let the wages earned by Erica be $100
Then, wages earned by Robin and Charles will be $138 and $160 respectively.
Charles earns $38 more than Robin who earns $138.
Therefore, Charles' wage is 38/138*100 = 27.53%.
The correct choice is (B)
Question: There are three departments having students 68,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
A.73
B.74
C.75
D.76
Answer: C.75
Explanation: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 68/2 = 34
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 34+12+29 = 75
ANSWER:C
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o'clock noon?
A.30
B.60
C.90
D.120
Answer: D.120
Explanation: The hour hand will move 4/12 of a circle.
(4/12)*360 = 120 degrees.
The answer is D.
Question: Which of the following integers is the square of an integer?
A.73,410,624
B.63,398,748
C.54,113,892
D.42,785,337
Answer: A.73,410,624
Explanation: CONCEPT: The unit digit of any Perfect Square can't be 2 or 3 or 7 or 8
Hence Option B, C D and E can be ruled out
Answer: option A
Question: The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
A.A)40
B.B)828
C.C)729
D.D)34
Answer: A.A)40
Explanation: Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 32/2 = 40 cm2
Answer: Option A
Question: A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails?
A.1/8
B.1/4
C.3/8
D.1/2
Answer: C.3/8
Explanation: We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.
Using the binary formula and defining a head as a success,
P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2
t= 6/16
= 3/8
The answer is therefore (C)
Question: A trader mixes 25 kg of rice at Rs. 40 per kg with 25 kg of rice of other variety at Rs. 20 per kg and sells the mixture at Rs. 40 per kg. His profit percent is:
A.No profit, no loss
B.33.33%
C.8%
D.10%
Answer: B.33.33%
Explanation: C.P. of 56 kg rice = Rs. (25 x 40 + 25 x 20) = Rs. (1000 + 500) = Rs. 1500.
S.P. of 56 kg rice = Rs. (50x 40) = Rs. 2000
Gain =500/1500x100% = 33.33%
Answer: Option B
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
A.24
B.26
C.42
D.46
Answer: A.24
Explanation: Explanation:
Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) = 144
2x2 + 26x - 140 = 0
(x - 2)(11x + 35) = 0
x = 2
Hence, required number = 11x + 2 = 24.
ANSWER IS A
Question: According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 12 - ounce cans of the concentrate are required to prepare 272 6-ounce servings of orange juice?
A.25
B.34
C.50
D.67
Answer: B.34
Explanation: Orange juice concentrate: water::1:3
total quantity of orange juice = 272*6 = 1632 oz
so Orange juice concentrate: water :: 408 oz:1224 oz
no. of 12 oz can = 408 oz/12 oz = 34
Answer B, 34 cans
Question: A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 3 days, B can complete the job in 4 days and C can complete the job in 6 days. How many days the company will it take to complete the job if all the machines are used simultaneously?
A.4 days
B.4/3 days
C.3 days
D.12days
Answer: B.4/3 days
Explanation: Let the total number of cans to be prepared be 12.
The number of cans prepared by A in 1 day = 4.
The number of cans prepared by B in 1 day = 3.
The number of cans prepared by C in 1 day = 2.
Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 9.
Therefore, the number of days taken to complete the whole work = 12/9 = 4/3 days.
ANSWER:B
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 9 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
A.23 years
B.24 years
C.25 years
D.26 years
Answer: D.26 years
Explanation: EXPLANATION
Let the average age of the whole team by x years.
11x â€“ (26 + 38) = 9(x -1)
11x â€“ 9x = 52
2x = 52
x = 26.
So, average age of the team is 26 years.
Answer D
Question: A man purchases 2 pens for $ 56. He sells one at 20% profit and the other at a loss of 15%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
A.$ 24 and $ 32
B.$32 and $ 24
C.$56and $32
D.$56 and $24
Answer: A.$ 24 and $ 32
Explanation: x + y = 56--- (1)
1.20x + 0.85y = 56 --- (2)
(2) - (1) --> 0.20x - 0.15y = 0
20x = 15y
x/y = 3/4= (3*8)/(4*8) = 24/32
Answer:A
Question: A rectangular block 12cm by 20cm by 36cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
A.135
B.10
C.15
D.40
Answer: A.135
Explanation: Volume of the block = 12*20*36 = 8640 cm^3
Side of the largest cube = H.C.F of 12,20,36 = 4cm
Volume of the cube = 4*4*4= 64 cm^3
Number of cubes = 8640/64 = 135
Answer is A
Question: Ron scored 344 marks out of 400 marks and his elder brother Ben scored 582 marks out of 600 marks. Who scored percentage is better?
A.97
B.21
C.28
D.26
Answer: A.97
Explanation: Percentage of marks scored by Ron = (344/400 × 100) %
= (34400/400) %
= (344/4) %
= 86 %
Percentage of marks scored by Ben = (582/600 × 100) %
= (58200/600) %
= (582/6) %
= 97 %
Hence, the percentage marks scored by Ben is better.
Answer:A
Question: It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?
A.3 hours and 45 minutes.
B.2 hours and 32 minutes.
C.4 hours and 54 minutes.
D.6 hours and 26 minutes.
Answer: A.3 hours and 45 minutes.
Explanation: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = 3 hours and 45 minutes.
correct answer A
Question: There are two groups of students in the sixth grade. There are 30 students in group A, and 50 students in group B. If, on a particular day, 20% of the students in group A forget their homework, and 12% of the students in group B forget their homework, then what percentage of the sixth graders forgot their homework?
A.13%
B.14%
C.15%
D.16%
Answer: C.15%
Explanation: Total students = 30 + 50 = 80
20% of 30 = 6
12& of 50 = 6
Total students who forget homework = 6+6 = 12
Percentage =1280∗100=15=12/80∗100=15	;Answer = C = 15%
Question: Every day, the value of a stock rises by exactly two dollars in the morning, and
then falls by exactly one dollar in the afternoon. If the stock's value at the start of the first
day is $100, on what day will the stock's value first reach $200?
A.50
B.99
C.100
D.101
Answer: B.99
Explanation: Note that each day the stock is worth $1 more than on the previous day, and that
on the first day it rises to $102 and then falls to $101. Therefore, on the nth day, the stock's
value rises to n + 101 dollars in the morning and falls to n + 100 dollars in the afternoon.
The solution is therefore the smallest n for which n+101 = 200, or n = 99. In particular,
the stock will be $200 in the middle of day 99, although not at the end of this day.
correct answer B
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 16 years at the same rate?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: P ---- 2P ---- 8 years4P ---- 16 years Answer: D
Question: Excluding stoppages, the speed of a train is 42 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
A.7.5
B.8.5
C.9.5
D.4.5
Answer: B.8.5
Explanation: T = 6/42 * 60 = 8.5
ANSWER:B
Question: The average of 9 results is 50. If the average of first 4 results is 45 and that of the last six is 48, find the 5th result?
A.15
B.20
C.35
D.18
Answer: A.15
Explanation: Sixth result = 45*5 + 48*5 - 50*9 = 15
Answer is A
Question: The average age of 25 students in a class is 12 years. 15 students whose average age is 10 years joined them. What is the present average age.
A.13
B.12.6
C.11.25
D.12
Answer: C.11.25
Explanation: Explanation :
Solution: Present average = ax + by/ a + b
= 25*12 + 15*10/25+15 years
=300 + 150/ 40 => 450/40 => 11.25.
Answer : C
Question: A certain bag contains 60 balls — 22 white, 10 green, 7 yellow, 15 red, and 6 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
A.0.09
B.0.65
C.0.54
D.0.85
Answer: B.0.65
Explanation: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 10 + 17)/60 = 39/60 = 0.65.
Answer: B.
Question: If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 20 percent, how much would she earn per week?
A. $374
B. $382
C. $385
D. $360
Answer: D. $360
Explanation: (348/116)120 =360
In this case long division does not take much time.
(348/116)=3
3*120=360(300+60)
Answer D
Question: If n is a positive integer, and n^2 has 25 factors, which of the following must be true.
1. n has 12 factors.
2. n > 50
3.√n is an integer.
A.1 and 2
B.2 only
C.3 only
D.2 and 3
Answer: C.3 only
Explanation: 25=1×25=5×5
So prime factorization of n^2 could be p^24 or p^4q^4 with p,q are distinct prime numbers.
Hence, n could be p^12 or p^2q^2
(1) If n=p12 then n has 12+1=13 different factors, so (1) is not true.
(2) If n=p^2q^2 , for example n=2^2×3^2=36<50n=22×32=36<50, so (2) is not true.
(3)
If n=p^12 ⟹√n=p^6 is an integer.
If n=p^2q^2 ⟹√n=pq is an integer.
So (3) is true.
Answer: C.
Question: Which number should replace both the asterisks in (* /21) x (*/84) = 1 ?
A.21
B.42
C.63
D.72
Answer: B.42
Explanation: Let (y/21) x (y/84) = 1
y^2 = 21 x 84 = 21 x 21 x 4
y = (21 x 2) = 42
The answer is B.
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
A.34 days
B.54 days
C.32 days
D.76 days
Answer: C.32 days
Explanation: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer:C
Question: In how many ways can six members be selected from a group of ten members?
A.10C6
B.10C8
C.10C4
D.10C3
Answer: B.10C8
Explanation: Six members can be selected from ten members in
10C6
= 10C4 ways.
Answer: B
Question: The value of 3.6x0.48x2.50 / 0.12x0.09x0.5 is
A.80
B.800
C.8000
D.80000
Answer: B.800
Explanation: Solution
Therefore	=3.6x0.48x2.50/0.12x0.09x0.5
= 36x48x250/12x9x5
= 800
Answer B