RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What is the diffference between the place value and face value of 3 in the numeral 1375?
A.259
B.270
C.297
D.298
Answer: C.297
Explanation: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
C
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 40 percent alcohol?
A. 7/2
B. 5
C. 100/3
D. 8
Answer: C. 100/3
Explanation: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 40% of (100+x)
OR
20+x=(100+x)2/5
100+5x=200+2x
3x=100
x=100/3
Ans:C
Question: The average (arithmetic mean) of the integers from 200 to 800, inclusive, is how much greater than the average of the integers from 50 to 300, inclusive?
A. 450
B. 375
C. 400
D. 425
Answer: D. 425
Explanation: For an AP the mean or average of series is average of first and last term.
So, average of numbers between 200 to 800, inclusive = (200+800)/2 = 500
average of numbers between 50 to 300, inclusive = (50+300)/2 = 175
difference = 500 - 175 = 425
Answer is D
Question: 0.03 x 0.0172 is equal to:
A.6.48 x 10(power -4)
B.6.84 x 10(power -4)
C.5.16 x 10(power -4)
D.5.48 x 10(power -4)
Answer: C.5.16 x 10(power -4)
Explanation: 3 x 172 = 516. Sum of decimal places = 6.
So, 0.03 x 0.0172 = 0.000516 = 5.16 x 10(power -4)
Answer is C
Question: In what time a sum of money double itself at 3% per annum simple interest?
A.33 1/8%
B.33 1/3%
C.83 1/3%
D.33 4/3%
Answer: B.33 1/3%
Explanation: P = (P*3*R)/100
R = 33 1/3%
Answer:B
Question: Line A has the equation 3x + y = 7. Which of the following lines is perpendicular to Line A?
A.y = 3x + 4
B.y = –3x – 6
C.y = (1/3)x – 1
D.y = (–1/3)x + 2
Answer: C.y = (1/3)x – 1
Explanation: What’s tricky about this problem: we have to begin by solving the given equation for y, so that we know its slope.
The slope of the original line is m = –3, and the negative reciprocal of that is +1/3, so the perpendicular line must have a slope of +1/3. Among the answer choices, the only line with a slope of +1/3 is (C).
Answer C
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
A.266 Sec
B.190 Sec
C.776 Sec
D.166 Sec
Answer: B.190 Sec
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer: B
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
A.27 7/6 m
B.27 7/4 m
C.27 7/2 m
D.27 7/9 m
Answer: D.27 7/9 m
Explanation: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.Answer:D
Question: Last year a certain bond yielded 6 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $7,500, what is the bonds face value?
A.$5,000
B.$6,750
C.$7,425
D.$7,500
Answer: A.$5,000
Explanation: Interest = 0.06*face value = 0.04*7,500 --> face value = 0.04*7,500/0.06 = 5,000.
Answer: A.
Question: Williams, a painter, has 9 jars of paint: 4 are orange, 2 are yellow, and the rest are brown. Williams will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no orange paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of orange paint 4) J2, if the paint contains exactly 1 jar of orange paint What is the probability that the new colour will be a shade of J (J1 or J2)?
A.74/42
B.37/84
C.21/42
D.37/42
Answer: D.37/42
Explanation: the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2
For C1-3C2(Brown)*2C1(Yellow)=3*2=6
For C2-3C3(all brown)=1
Total=9C3=84
1-7/84=77/84= 37/42
Answer : D
Question: An escalator moves towards the top level at the rate of 12 ft.sec and its length is 210 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length.
A.15 sec
B.10 sec
C.12 sec
D.8 sec
Answer: A.15 sec
Explanation: Time taken to cover the entire length = tot.dist/resultant speed
= 210/ (12+2)
= 15 sec
ANSWER:A
Question: 3 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
A.2
B.3
C.4
D.6
Answer: A.2
Explanation: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 3
hence ans = 2 factorial = 2
hence A
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 56?
A.s.3944
B.s.3948
C.s.3942
D.s.3808
Answer: D.s.3808
Explanation: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 56
= Rs.3808.
Answer: D
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 80, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.
A.K+35
B.(80+K)/2
C.2K+35
D.(70-K)/2
Answer: B.(80+K)/2
Explanation: Say Sue was hired when she was already 80 years old (k=80), then she could retire right away, at the age of 80. Now, plug k=80 in the answer choices and see which yields 80. Only C fits.
Answer: B.
Question: A large delicatessen purchased p pounds of cheese for c dollars per pound. If W pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost)
A.(p − d)(s − c)
B.s(p − d) − pc
C.s(p-W) - cp
D.d(s − c) − pc
Answer: C.s(p-W) - cp
Explanation: Total cost price = c*p ............... (1)
Wastage = W pounds
Quantity sold = p-W
Selling price per pound = s
Total selling price = s(p-W) ........... (2)
Profit = (2) - (1)
= s(p-W) - cp
C
Question: A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $800 or tripled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $60,000 in property taxes, but did not pay until October 15th?
A.$1,400
B.$2,600
C.$3,400
D.$21,400
Answer: B.$2,600
Explanation: Original amount = 60,000
Fine for July = 60,000 * 1% = 600
Fine for August = lesser of the 2 , 600+800= 1400 or 600*3=1800 . Pick 1400
Fine for September = 1400+600=2000 or 1400*3 = 4200. Pick 2000
Fine for October = 2000+600=2600 or 2000*3 = 6000. Pick 2600.
The wording of the question should be have been clearer as total fines should be = 2600+2000+1400+600 = 6600 and NOT 2600.
2600 is the fine ONLY for the month of October!
B
Question: A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
A.189/13 days
B.188/13 days
C.180/13 days
D.180/17 days
Answer: C.180/13 days
Explanation: One day work of A and B = 1/12
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/12 + 1/30 + 1/36
2(A + B + C) = 13/90
(A + B + C) = 13/180
Number of days required = 180/13 days.
Answer:C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
A.11
B.27
C.36
D.99
Answer: C.36
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: C
Question: If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 (512)
A.3.876
B.2.967
C.2.87
D.3.912
Answer: A.3.876
Explanation: log5 (512)
=	log (512)/log 5
=	log 2^9/log (10/2)
=	9 log 2/(log 10 - log 2)
=	(9 x 0.3010)/(1 - 0.3010)
=	2.709/0.699
=	2709/699
= 3.876
Answer is A.
Question: A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
A.1 kmph
B.6 kmph
C.5 kmph
D.8 kmph
Answer: B.6 kmph
Explanation: Speed downstream = d/t = 75/(2 1/2) = 30 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (30 - 18)/2 = 6 kmph
Answer:B
Question: Find the L.C.M of 72,108,2100
A.37800
B.45836
C.52416
D.25874
Answer: A.37800
Explanation: 72=2^3*3^2 108=3^3*2^2 2100=2^2*5^2*3*7
L.C.M=2^3*3^2*5^2*7=37800
Answer=(A)
Question: 1.5, 2.3, 3.1, 3.9, ..?
A.0.6
B.0.8
C.0.4
D.0.24
Answer: B.0.8
Explanation: 1.5+0.8=2.3
2.3+0.8=3.1
3.1+0.8=3.9
3.9+0.8=4.7
ANSWER:B
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
A.2
B.4
C.5
D.6
Answer: A.2
Explanation: Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
Answer: A
Question: Pipes A and B can fill a tank in 11 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
A.1 13/17 hours
B.2 8/11 hours
C.3 9/17 hours
D.5 17/23 hours
Answer: D.5 17/23 hours
Explanation: Solution
Net part filled in 1 hour	= (1/11 + 1/6 -1/12)
= 23/132.
Therefore, the tank will be full in 132/23 hrs.	â€¹=â€º 5 17/23 hrs.
Answer D
Question: Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 9 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
A.12
B.24
C.48
D.60
Answer: C.48
Explanation: the difference of the speed is 4m per second so in one minute Sacha will be 240 m ahead of Bruno..
Bruno will cover this in 240/5=48 secs..
C
Question: a man brought some watermelons to town and sold them. he sold 1/2 more than 1/2 of what he brought and he was left with one melon. how many melons did he bring to town?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: He sold 1/2 more than 1/2 of what he brought
thus he sold (1/2)+(x/2) and he was left with 1 water melon
so equation will be (1/2)+(x/2)+1 = x
or x/2 = 3/2 so x = 3
ANSWER:C
Question: At what rate percent on simple interest will a sum of money double itself in 20 years?
A.5%
B.3 1/9%
C.3 9/3%
D.3 2/3%
Answer: A.5%
Explanation: P = (P*20*R)/100
R = 5%
Answer: A
Question: 287 x 287 + 269 x 269 - 2 x 287 x 269 = ?
A.534
B.446
C.354
D.324
Answer: D.324
Explanation: =a^2+b^2-2ab
where a=287 and b=269
=(a-b)^2 = (287-269)^2
=(18)^2
=324
Answer is D
Question: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 240 pounds of the seed mixture?
A.6
B.12
C.20
D.24
Answer: A.6
Explanation: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 240 pounds of the seed mixture?
Amount of timothy needed for one acre is 2 pounds.
So the amount of grass seed needed for one acre is
= 2 (100/5) = 40 pounds
So the no.of acres that can be planted with 240 pounds is
= 240/40 = 6
The answer is A.
Question: A,B,C can complete a piece of work in 18,6,12 days. Working together, they complete the same work in how many days?
A.2
B.4/5
C.7/9
D.36/11
Answer: D.36/11
Explanation: A+B+C 1day work = 1/18 + 1/6 + 1/12 = 11/36
A,B,C together will complete the job in 36/11 days
Answer is D
Question: The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member?
A.23
B.27
C.40
D.28
Answer: C.40
Explanation: Explanation:
Let the average of all 10 members 4 years ago was x. After 4 years, 10 members age increases by 10 × 4 = 40. But there is no change in the average as a person is replaced by an younger one. Which means, the younger one age is 40 years less than the old one.
Answer: C
Question: In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 3 and a y-intercept of -3. If the two lines intersect at the point (a,b), what is the sum a+b?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: The equation of Line A is y = -x + 1
The equation of Line B is y = 3x - 3
3x - 3 = -x + 1
x = 1
y = 0
The point of intersection is (1,0) and then a+b = 1.
The answer is B.
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 40 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009?
A.80
B.126
C.95
D.100
Answer: B.126
Explanation: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 40% = 90*1.2 = 126
Thus ratio = 126/100 = 1.26 (in % terms = 126%). Thus B is the correct answer.
Question: Analyze the number square carefully and find out what number fits in place of question mark.
1	2	3
4	5 6
7	8	?
A.7
B.6
C.5
D.4
Answer: A.7
Explanation: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(7 / 8) * 8 = (7 / 1) = 7
A
Question: A river boat leaves Silver Town and travels upstream to Gold Town at an average speed of 3 kilometers per hour. It returns by the same route at an average speed of 7 kilometers per hour. What is the average speed for the round-trip in kilometers per hour?
A.4.2
B.7.1
C.7.2
D.7.5
Answer: A.4.2
Explanation: Pick a number which is LCM of 7 and 3 = 21.
Upstream time = 21/3 =7 hrs
Downstream time = 21/7 = 3 hrs
Total time = 10 hrs
Total distance = 42
Average Speed = 42/10 = 4.2 km/hr
Question: A began business with 12000 and is joined afterwards by B with 48000. When did B join, if the profits at the end of the year are divided equally?
A.8 months
B.3 months
C.10 months
D.7 months
Answer: B.3 months
Explanation: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12000 : (12 – x) × 48000
or 12 : 4(12 – x)
Since profit is equally divided so
12 = 4(12 – x) or x = 3. Thus B joined after 8 months.
Answer B
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
A.87
B.16
C.10
D.76
Answer: D.76
Explanation: Average after 11 innings = 36
Required number of runs
= (36 * 11) - (32 * 10) = 396 - 320
= 76.
Answer: D
Question: (422 + 404)2 − (4 × 422 × 404) = ?
A.None of these
B.342
C.324
D.312
Answer: C.324
Explanation: Explanation :
Given Equation is in the form (a + b)2 − 4ab where a = 422 and b = 404
Hence answer = (a + b)2 − 4ab = (a − b)2 =(422 − 404)2 = 182 = 324, Answer : Option C
Question: A chair is bought for Rs.600/- and sold at a loss of 40% find its selling price
A.s.360/-
B.s.550/-
C.s.560/-
D.s.590/-
Answer: A.s.360/-
Explanation: 100 % ------> 600 (100 * 6 = 600)
60 % ------> 540 (60 * 6 = 360)
Selling price = Rs.360/-
A)
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 m?
A.120 sec
B.99 sec
C.89 sec
D.80 sec
Answer: C.89 sec
Explanation: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+650)/10 = 89 seconds
Answer: Option C
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
A.7 kmph
B.9 kmph
C.4 kmph
D.8 kmph
Answer: D.8 kmph
Explanation: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer:D
Question: There are 4 couples. If they will sit 8 chairs in a row such that each couple sits side by side, how many possible cases are there?
A.120
B.384
C.1,200
D.2,460
Answer: B.384
Explanation: Tie the couples. Then we have 4 persons that have to be arranged in 4 places. 4! ways.
Now the couples can change position with each other. 2! ways.
4! * (2!)^4 = 24 *16 = 384
Answer is B.
5! * 2! = 240 ways.
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A.1/2
B.2/5
C.8/15
D.9/20
Answer: D.9/20
Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) =	n(E)/n(S)	=	9/20	.
Answer :D
Question: A boy has to cover a total distance of 300 kms. in 6 hours. He travels at the rate of 60 kmph. for first 90 minutes and next 100 kms. at the rate of 50 kmph. At what average speed must he travel now in order to complete the journey in 6 hours?
A.24 kmph
B.84 kmph
C.48 kmph
D.44 kmph
Answer: D.44 kmph
Explanation: Explanation:
The boy travels 60 kmph for 90 min, this means he travels 90 km.
Next 100 km at the rate of 50 kmph, this means he travels 100 km.
Total distance traveled till now = 100 + 90 = 190 km
Time spent = 1.5 + 2 = 3.5 hr
Required speed = Remaining distance/ Time
= (300 – 190) /(6 – 3.5)
= 110/ 2.5 = 44 kmph\
ANSWER: D
Question: How many seconds will a 600 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.700
B.288
C.500
D.277
Answer: A.700
Explanation: Let length of tunnel is x meter
Distance = 600+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
600+x = (65/3) * 60
600+x = 20 * 65 = 1300
x = 1300 - 600 = 700 meters
Answer: A
Question: How many bricks, each measuring 25 cm x 11 cm x 6 cm, will be needed to build a wall of 8 m x 1 m x 5 cm?
A.5600
B.6000
C.242
D.7200
Answer: C.242
Explanation: Number of bricks =Volume of the wall/Volume of 1 brick =	(800 x 100 x 5)/(25 x 11 x 6) = 242.
Answer: Option C
Question: A certain sum of money doubles itself in 7 years in how much many years will it trible itself at the same rate?
A.20 years
B.14 years
C.88 years
D.44 years
Answer: B.14 years
Explanation: 100 ---- 100 --- 7
100 --- 7
--------------------
300 ---- 14 years
Answer: B
Question: How much time will it take for an amount of 450 to yield 81 as interest at 4.5% per annum of simple interest?
A.3.5 years
B.4 years
C.4.5 years
D.5 years
Answer: B.4 years
Explanation: Explanation: Time = (100 x 81)/(450 x 4.5) years = 4 years.
Answer: Option B
Question: K and L start a business jointly. L invests Rs.16000 for 8 months and L remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B ?
A.12,812
B.12,820
C.12,800
D.12,120
Answer: C.12,800
Explanation: 16x8 : Px4 = 5:2
P = 12.8 => Rs.12,800
Answer: C
Question: A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
A.400
B.267
C.288
D.278
Answer: A.400
Explanation: 2000 ---- 50
2000 ---- 40
x ----- 50
x*50 = 2000*40
x=1600
2000
-------
400
Answer: A
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.250
B.327
C.367
D.289
Answer: A.250
Explanation: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer:A
Question: If the sum of 5 consecutive integers is 125, what is sum of the 5 consecutive integers preceding the former sequence?
A.35
B.25
C.100
D.105
Answer: C.100
Explanation: 1) least of each will have a difference of 5 and next least too will have a difference of 5 and so on...
Therefore all 5 terms will have a term LESS by 5..
Sum = 125-(5*5) = 100
2.) if sum is 125, the average = median = 125/5 = 25. The median of previous 5 will be 25-5 = 20.
And sum would be 20*5 = 100
Answer: C
Question: What is the range of all the roots of |x^2 - 4| = x ?
A.4
B.3
C.2
D.1
Answer: B.3
Explanation: we get 2 quadratic equations here ..
1) x^2-x-4=0 ....... roots 2 , -1
2) x^2+x-4=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=4 or x=1
I guess range is 4-1 =3
B
Question: (X+1) is an even number and (Y+1 )is a positive odd number. Which of the following expressions cannot be ODD?
A.(Y+1)
B.(Y+1)^2
C.(X+1) (Y+1)
D.(Y+1)^3
Answer: C.(X+1) (Y+1)
Explanation: (X+1) (Y+1) WILL BE EVEN
C
Question: In the quadrilateral PQRS d=6 cm, h1=5 cm and
h2=2.5 cm. Find the area
A.21
B.22.5
C.23
D.24
Answer: B.22.5
Explanation: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)
so 1/2*6*(5+2.5)=22.5
ANSWER:B
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
A.229
B.108
C.278
D.126
Answer: B.108
Explanation: S = 180/6 * 18/5 = 108 kmph
Answer: B
Question: Richard's company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 30 hrs and a machine of type S does the same job in 15 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
A.3
B.4
C.5
D.9
Answer: C.5
Explanation: Rate of machine R =1/30
Rate of machine S =1/15
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/30 +x/15 =1/2
3x/30=1/2
x=30/6=5
So no of machine R is 5
Answer C
Question: What is the sixth digit to the right of the decimal point, in the decimal expansion of (3/5)^6?
A. 2
B. 4
C. 6
D. 8
Answer: C. 6
Explanation: Step 1 Convert fraction to decimal with two decimal places 3/5 = 0.60 then convert to scientific number = 6*10^-1
Step 2 Multiply 6^6 by 10^-6
Step 3 6 has the sequence 6, 36, 216
Answer is C
Question: There is a five digit code consist of letters and digit. the code can have one digit from 1,2,3 and any four letters from A,b,c,d,e. first and last code must be a letter and all letters can be repeated. How many combinations can be possible?
A.625
B.3840
C.5625
D.11520
Answer: C.5625
Explanation: since repetitions are allowed so there are 5 ways to choose the letters for the first slot, and five ways to choose for last slot
that can be like:- 5 x _ x _ x _ x 5
you still have to choose 1 digit and 2 letters between. For the letters, again, repetitions are allowed so each slot can be filled in 5 ways. For digit, it can only be filled in 3 ways. However, since the digit can be in any one of the 3 middle slots, so we multiply by 3 again:
5 x 3 x 5 x 5 x 5 or
5 x 5 x 3 x 5 x 5 or
5 x 5 x 5 x 3 x 5
so 5 x 5 x 5 x 5 x 3 x 3 = 5^4 x 3^2 = 5625.
ANSWER:C