RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If 2*f(x) - f(1/x) = x2x2 , then f(x) is?
A.f(x) = 3{2*x2x2 + (1x)2(1x)9 }
B.f(x) = 3{2*x2x2 + (1x)2(1x)2 }
C.f(x) = 3{2*x2x2 + (1x)2(1x)3 }
D.f(x) = 3{2*x2x2 + (1x)2(1x)4 }
Answer: B.f(x) = 3{2*x2x2 + (1x)2(1x)2 }
Explanation: 2*f(x) - f(1/x) = x2x2 ..............(1)
Take x = (1/x),
2*(1/x) - f(x) = (1x)2(1x)2 ...............(2)
Add: 2 (equation 1) + equation 2
3*f(x) = 2*x2x2+ (1x)2(1x)2
f(x) = {2*x2x2 + (1x)2(1x)2}/3
Answer:B
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?
A.23 years
B.22 years
C.67 years
D.16 years
Answer: A.23 years
Explanation: Explanation:
Ayush's present age = 10 years.
His mother's present age = (10 + 20) years = 30 years.
Ayush's father's present age = (30 + 5) years = 35 years.
Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
Answer: A) 23 years
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
A.20 kmph
B.24 kmph
C.50 kmph
D.35 kmph
Answer: B.24 kmph
Explanation: Explanation:
Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.
ANSWER IS B
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
A.12.5%
B.13%
C.13.15%
D.14%
Answer: A.12.5%
Explanation: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
A)
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
A.81 : 121
B.81 : 127
C.81 : 191
D.81 : 161
Answer: A.81 : 121
Explanation: Explanation:
Ratio of the sides = ³√729 : ³√1331 = 9 : 11
Ratio of surface areas = 92 : 112 = 81 : 121
Answer: Option A
Question: In a certain warehouse, 30 percent of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80 percent of the packages weigh at least 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds?
A.8
B.64
C.24
D.102
Answer: C.24
Explanation: If 80% of the packages weigh at least 25 pounds
This means that 20% of the packages weigh LESS THAN 25 pounds
Let T = TOTAL number of packages
So, 20% of T = # of packages that weigh LESS THAN 25 pounds
48 packages weigh LESS THAN 25 pounds
GREAT. So, 20% of T = 48
Rewrite to get: 0.2T = 48
Solve:T = 240
30% of the packages weigh less than 75 pounds
So, 30% ofT= number of packages that weigh less than 75 pounds
30% of240=72, so72packages weigh less than 75 pounds
OF THOSE72packages that weigh less than 75 pounds,48packages weigh less than 25 pounds.
So, the number of packages that weight BETWEEN 25 and 75 pounds =72-48= 24 = C
Question: A man can hit a target once in 9 shots. If he fires 4 shots in succession, how many ways that he will hit his target?
A.71/2
B.81/13
C.81/3
D.5/8
Answer: D.5/8
Explanation: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 - 1/9 = 8/9
Therefore, the probability that he will not hit the target in any of the four shots = 8/9^4 = 5/8
D
Question: A merchant purchased a jacket for $30 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
A.$2
B.$3
C.$4
D.$12
Answer: A.$2
Explanation: Let selling price = x
So, x = 30 + 25x/100
Calculating above, x = 40
Selling price = 40
20% Discount on Selling price = 32
So, profit = 32-30 = 2 Answer = A
Question: If 20 men can build a water fountain 56 metres long in 14 days, what length of a similar water fountain can be built by 35 men in 3 days?
A.21 m
B.24 m
C.27 m
D.29 m
Answer: A.21 m
Explanation: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 14: 3 : : 56 : x
Therefore (20 x 14 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/280=49
Hence, the required length is 21 m.
Answer : A
Question: A person travels equal distances with speeds of 8 km/hr, 9 km/hr and 10 km/hr and takes a total time of 47 minutes. The total distance is?
A.6 km
B.3 km
C.7 km
D.5 km
Answer: C.7 km
Explanation: Let the total distance be 3x km.
Then, x/8 + x/9 + x/10 = 47/60
x/3 = 47/60 => x = 2.33.
Total distance = 3 * 2.33 = 6.99 km.
Answer:C
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
A.18 2/71%
B.18 2/11%
C.18 9/11%
D.18 2/41%
Answer: B.18 2/11%
Explanation: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Question: A man put diesel at Rs.7.50, Rs. 8 and Rs. 8.50 per ltr for three successive years. What approximately is the average cost per ltr of diesel if he spends Rs. 4000 each year?
A.Rs. 7.98
B.Rs. 8.45
C.Rs. 8.98
D.Rs. 9.23
Answer: A.Rs. 7.98
Explanation: Total quantity of diesel
consumed in 3 years
= 4000	+	4000	+	4000 litres
7.50	8	8.50
= 4000 2	+	1	+	2	ltr
15	8	17
= 76700	ltr
51
Total amount spent = Rs. (3 x 4000) = Rs. 12000.
Average cost = Rs. 12000 x 51 = Rs.	6120 = Rs. 7.98
76700	767
A
Question: The perimeter of a rectangle is 44. The length is 5 less than double the width.
Find the dimensions
A.6 by 10
B.7 by 11
C.8 by 12
D.9 by 13
Answer: D.9 by 13
Explanation: Length x Wewillmake the length x
Width 2x−5 Width is five less than two times the length
P =2L+2W The formula for perimeter of a rectangle
(44)=2(x)+2(2x−5) Replace P , L, andW with labeled values
44=2x+4x−10 Distribute through parenthesis
44=6x−10 Combine like terms 2x+4x
+10 +10 Add 10 to both sides
54=6x The variable ismultiplied by 6
6 6 Divide both sides by 6
9=x Our solution for x
Length 9 Replace xwith 9 in the origional list of sides
Width 2(9)−5=13 The dimensions of the rectangle are 9 by 13.
correct answer D
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer a?
A.(2a-1)/(a^2- a)
B.a/2
C.a^3 (a-1)
D.2a-1
Answer: A.(2a-1)/(a^2- a)
Explanation: Let two consecutive positive integers be a and a-1 (Greater integer is a)
So,
(1/a) + [1/(a-1)]
= (2a-1)/a(a-1)
=(2a-1)/(a^2- a)
Answer : A
Question: If R is the least positive integer that is divisible by every integer from 12 to 16 inclusive, then R/13 is =
A. 40320
B. 21840
C. 1680
D. 840
Answer: C. 1680
Explanation: The integer should be divisible by: 12, 13, 14, 15 and 16, that is 3*2^2, 13, 2*7, 3*5 and 2^4. The least common multiple of these integers is the product of 13, 7, 5, 3 and 2^4. Then, R/13 is (13 * 7 * 5 * 3 * 2^4)/13 = 7*5*3*16 = 1680.
Answer: C.
Question: The angle between the minute hand and the hour hand of a clock when the time is 8:30
A.80 deg
B.40 deg
C.35 deg
D.75 deg
Answer: D.75 deg
Explanation: angle traced hr hand 17/2 hrs = 300/12 * 17/2 = 255
angle by min 30 min (360/60*30)=180
req = 255-180 = 75
ANSWER D
Question: On the xy co-ordinate plane, point C is (5,-2) and point D is (-1,3.5). The point on line segment CD that is twice as far from C as from D is:
A.(1,-1)
B.(1,1)
C.(2,0.25)
D.(3,0.5)
Answer: D.(3,0.5)
Explanation: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,0.5)
Answer: D
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 72 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
A.8715
B.0152
C.3581
D.5184
Answer: D.5184
Explanation: D
5184
n^1
72 * 72 = 5625 (sum of first 72 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Question: A certain bacteria colony doubles in size every day for 19 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
A.6.33
B.7.5
C.10
D.18
Answer: D.18
Explanation: If there is one bacteria colony, then it will reach the limit of its habitat in 20 days.
If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 18 times.
Answer: D.
Similar questions to practice:
Hope it helps.
Question: If the positive integer x is a multiple of 5/2 and the positive integer y is a multiple of 2, then xy must be a multiple of which of the following?
I. 1
II. 12
III. 5
A.II only
B.I and II only
C.I and III only
D.II and III only
Answer: C.I and III only
Explanation: x=5/2a
y=2b
xy=5ab
where a,b are integers
Hence , xy will always be divisible by 1,5 .
C is the answer.
Question: There are 30 people in anime club. 5 of the people voted to watch Case Closed that day. 10 people voted to watch Skip Beat. 3 people voted to watch My Hero Academia Academia. How many people did not vote if no one voted twice?
A.5
B.10
C.11
D.12
Answer: D.12
Explanation: As the categories do not overlap, you can simply subtract the number of people who voted for each anime from the total number of people in the club: 30-5-10-3=12. As such, the correct answer is D: 12.
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
A.337
B.279
C.800
D.277
Answer: C.800
Explanation: (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Answer: C
Question: Sum of three numbers 274, If the first number be twice then second and third number be one third of the first, then the second number is
A.A)70
B.B)71
C.C)75
D.D)73
Answer: C.C)75
Explanation: Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=274
<=>11x/3=274
=>x=75
Answer: Option C
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
A.7
B.4
C.3
D.2
Answer: B.4
Explanation: 1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
Answer: B
Question: If (x/y)=(11/5), find the value (x^2+y^2)/(x^2-y^2)
A.73/48
B.59/11
C.51/77
D.41/11
Answer: A.73/48
Explanation: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(11/5)^2+1] / [(11/5)^2-1]
= [(121/25)+1] / [(121/25)-1] = 73/48
Answer is A.
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 12 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
A.22 cm
B.47.14 cm
C.84.92 cm
D.94.94 cm
Answer: A.22 cm
Explanation: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 12) = 56 cm Parameter of the square = 56 cm
i.e. 4a = 56
A = 14
Diameter of the semicircle = 14 cm
Circimference of the semicircle
= 1/2(∏)(14)
= 1/2(22/7)(14) = 308/14 = 22 cm
ANSWER:A
Question: A bus covers a distance of 12 km in 5 min. If it takes 5 sec to pass a telegraph post, then the length of the bus is?
A.120m
B.180m
C.240m
D.200m
Answer: D.200m
Explanation: Speed = (12/5 * 60) km/hr = (144 * 5/18) m/sec = 40 m/sec.
Length of the bus = 40 * 5 = 200 m.
ANSWER:D
Question: One of the two buses completes a journey of 300 miles in 7 1/2 hours and the other journey of 450 miles in 10 hours. the ratio of their average speed is
A.2:3
B.4:5
C.3:4
D.8:9
Answer: D.8:9
Explanation: 300 miles completed in 7 1/2 hours means 27000 sec
450 miles completed in 10 hours means 36000 sec
speed=distance/time
1st bus speed:2nd bus speed=300/27000:450/36000=10/9:5/4=40:45=8:9
ANSWER:D
Question: What number comes next?
482, 693, 714, 826, 937, ?
A.113
B.231
C.245
D.148
Answer: D.148
Explanation: D
148
The numbers 48269371 are being repeated in the same sequence.
Question: In a shower, 6 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A.75 cu. m
B.900 cu. m
C.750 cu. m
D.9000 cu. m
Answer: B.900 cu. m
Explanation: 1 hectare = 10000 sq mtr
The volume of water that falls on 1.5 hectares of ground = 0.06*1.5*10000 = 900 cub mtr .
ANSWER:B
Question: The forth proportional to 24,8,15 is?
A.5
B.12
C.18
D.20
Answer: A.5
Explanation: Let the fourth proportional to 24,8,15 be x
then 24:8::15:x
24x = 8*15
x = 5
Answer is A
Question: Two trains of length 220 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
A.28
B.266
C.990
D.25
Answer: D.25
Explanation: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 220 + 280 = 500 m.
The time required = d/s = 500/20 = 25 sec.
Answer: D
Question: The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?
A.14 M
B.20 M
C.18 M
D.12 M
Answer: B.20 M
Explanation: LB = 460 M2
LET BREATH = B
L = B * (100 + 15)/100 = 115B/100
FROM THESE 115B/100 * B = 460
B2 = 46000/115 = 400
B = ROOT OF 400 = 20 M
ANSWER B
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 4.5), (8, 0), (0, -4.5), (-8, 0)?
A.56
B.72
C.112
D.116
Answer: B.72
Explanation: Ares of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 8+8= 16
Length of 2nd diagonal= 4.5+4.5=9
Area= 1/2*16*9= 72
B is the answer
Question: If 40 people get the chance to pick a card from a canister that contains 5 free passes to an amusement park mixed in with 35 blank cards what is the probability that the 40th person who picks will win?
A.35/175
B.36/175
C.38/175
D.39/175
Answer: B.36/175
Explanation: 35 - lose, 5 - win
Pick 5 people to win => 40C5 = total number of outcomes.
Favorable outcome is : First pick the 40th person, then pick any other 4.
=> 1*40C4
So, probability = 40C5 / 40C4
= 40!*36!*4! / (35!*5!*40!)
= 36/(35*5)
= 36 / 175
ANSWER:B
Question: A man buys a cycle for Rs. 1200 and sells it at a loss of 10%. What is the selling price of the cycle?
A.s. 1080
B.s. 1140
C.s. 1090
D.s. 1202
Answer: A.s. 1080
Explanation: S.P. = 90% of Rs. 1200 = Rs.	90	x 1200/100 = Rs. 1080
Answer: Option A
Question: If k and w are the dimensions of a rectangle that has area 20 and if k and w are integers such that k > w, what is the total number of possible values of k?
A. Two
B. Three
C. Four
D. Five
Answer: B. Three
Explanation: kw=20=20*1=10*2=5*4--> k can take 3 values,
Answer: B
Question: A man complete a journey in 40 hours. He travels first half of the journey at the rate of 20 km/hr and second half at the rate of 30 km/hr. Find the total journey in km.
A.960 km
B.224 km
C.230 km
D.232 km
Answer: A.960 km
Explanation: 0.5x/20 + 0.5x/30 = 40
--> x/20+ x/30= 80
--> 5x = 60x80
--> x = (60x80)/5 =960 km.
Answer :A
Question: Evaluate:56- 12*3*2 =?
A.42
B.48
C.62
D.72
Answer: B.48
Explanation: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
56 - 12*3*2 = 56- 8 = 48
correct answer B
Question: Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly.
A.Rs 824.32
B.Rs 822.32
C.Rs 825
D.Rs 723
Answer: A.Rs 824.32
Explanation: Principal = Rs. 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount =
Rs [10000 * (1+(2/100))4] = Rs(10000 * (51/50) * (51/50) * (51/50) * (51/50))
= Rs. 10824.32.
:. C.I. = Rs. (10824.32 - 10000) = Rs. 824.32.
ANSWER A Rs 824.32
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 1 day, B can complete the job in 2 days and C can complete the job in 5 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.10/17 days
D.12days
Answer: C.10/17 days
Explanation: Let the total number of cans to be prepared be 10.
The number of cans prepared by A in 1 day = 10.
The number of cans prepared by B in 1 day = 5.
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 = 17.
Therefore, the number of days taken to complete the whole work = 10/17 days.
ANSWER:C
Question: The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for xequal to:
A.0.02
B.0.2
C.0.04
D.0.4
Answer: C.0.04
Explanation: EXPLANATION
Given expression = (11.98)2 + (0.02)2 + 11.98 x x.
For the given expression to be a perfect square, we must have
11.98 x x = 2 x 11.98 x 0.02 or x = 0.04
Answer C
Question: What is the least integer that is a sum of four different prime numbers each greater than 40?
A.178
B.180
C.182
D.184
Answer: D.184
Explanation: The sum of the four smallest primes greater than 40 is 41+43+47+53=184.
The answer is D.
Question: A theater box office sold an average (arithmetic mean) of 68 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 80, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?
A.2:3
B.1:4
C.5:6
D.7:11
Answer: A.2:3
Explanation: Deviation from the mean for the daytime staff = 80 - 68 = 12.
Deviation from the mean for the evening staff = 68 - 60 = 8.
Thus, the ratio of the number of daytime staff members to the number of evening staff members is 8:12 = 2:3.
The answer is A.
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length
A.12
B.12.1
C.13
D.14
Answer: B.12.1
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: Option B
Question: The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 5600 for a computer table, then what was the cost price of the computer table?
A.Rs. 4480
B.Rs. 5275
C.Rs. 6275
D.Rs. 6725
Answer: A.Rs. 4480
Explanation: CP = SP * (100/(100 + profit%))
= 5600(100/125) = Rs. 4480.
ANSWER:A
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
A.Rs.45
B.Rs.78
C.Rs.44
D.Rs.40
Answer: C.Rs.44
Explanation: Explanation:
π (152 - 132) = 176
176 * 1/4 = Rs.44
ANSWER IS C
Question: When d is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when d + y is divided by 5?
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: In my view the answer should be C
d/5 has Remainder=3 -> d = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
Question: (1.2)(power 3) - (0.9)(power 3)/ (1.2)(power 2) + 1.08+ (0.9)(power 2) is:
A.0.68
B.0.6
C.0.8
D.0.3
Answer: D.0.3
Explanation: Given expression
= (1.2) (power 3) - (0.9)(power 3) / (1.2)(power 2) + (1.2 x 0.9) + (0.9)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (1.2 - 0.9)
= 0.3
Answer is D
Question: The mean of (54,823)^2 and (54,825)^2 =
A.(54,821)^2
B.(54,821.5)^2
C.(54,820.5)^2
D.(54,824)^2 + 1
Answer: D.(54,824)^2 + 1
Explanation: 54823^2 = (54824-1)^2 = 54824^2 + 1^2 - 2*54824*1
54822^2 = (54824+1)^2 = 54824^2 +1^2 + 2*54824*1
Taking the average of above 2 , we get (54824)^2 +1
hence the answer is D
Question: Find the total no of divisors of 1728 (including 1 and 1728)
A.33
B.28
C.99
D.27
Answer: B.28
Explanation: Direct formula from our lesson on factors. Click Here.
The number of factors or divisors of a number N=ap.bq.cr...N=ap.bq.cr... = (p+1).(q+1).(r+1)... where a, b, c ... prime numbers.
1728 = 26×3326×33
So total number of divisors = (6 + 1).(3 + 1) = 28
Answer:B
Question: In a rectangular coordinate system, what is the area of a triangle whose vertices have the coordinates (4, 0), (6, 3), and (6, -3)?
A.7.5
B.7
C.6.5
D.6
Answer: D.6
Explanation: Area of the triangle = 1/2*base*height.
Here base = Distance between (6,3) and (6,-3) => 3-(-3) = 6
Height = distance between the base (6,0) and 4,0 => 2
Area = 1/2*6*2 = 6.
ANSWER:D
Question: How many numbers are divisible by 4 between 1 and 100?
A.25
B.24
C.23
D.22
Answer: B.24
Explanation: Numbers divisible by 4 till 100=(100/4)=25
But we should not consider 100 as we are asked to find the numbers between 1 and 100 which are divisible by 4.
so answer is 24 numbers.
Answer is option B
Question: The function f is defined for each positive three-digit integer n by f(n)=2x3y5zf(n)=2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
A.8
B.9
C.18
D.20
Answer: D.20
Explanation: Soln:-
m=xyz
v=pqr
m-v = 100(x-p) + 10(y-q) + (z-r)............................(1)
f(m)= 2^x*3^y*5^z
f(v)= 2^p*3^q*5^r
Given that,
f(m) = 9 f(v)
=> 2^x*3^y*5^z = 9* 2^p*3^q*5^r
=> 2^x*3^y*5^z = 3^2*2^p*3^q*5^r
=> 2^x*3^y*5^z = 2^p*3^(q+2)*5^r
=> 2^[x-p]*3^[y-q-2]*5^[z-r] = 1
=> 2^[x-p]*3^[y-q-2]*5^[z-r] = 2^0*3^0*5^0
(x-p)=0
(z-r)=0
(y-q)=2
Substituting the above values in equation (1).
m-v = 100(x-p) + 10(y-q) + (z-r)
=> 0 + 10*2 + 0
=>20
ANSWER:D
Question: How many different possible arrangements Z can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
A.360
B.720
C.900
D.1800
Answer: C.900
Explanation: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's
_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!
Therefore ans Z= 7!/ (2!2!) -6!/2! = 900
HENCE C.