RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 30 other employees of Company K, how many employees does Company K have?
A. 160
B. 120
C. 190
D. 200
Answer: B. 120
Explanation: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 30
so 25% of x = 30
x = 120
Therefore there a total of 120 employees in the company K
Correct answer - B
Question: In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score ?
A.62
B.45
C.28
D.20
Answer: D.20
Explanation: Explanation:
Total runs scored = (36 x 5) = 180.
Let the runs scored by E be x.
Then, runs scored by D = x + 5; runs scored by A = x + 8;
runs scored by B = x + x + 5 = 2x + 5;
runs scored by C = (107 - B) = 107 - (2x + 5) = 102 - 2x.
So, total runs = (x + 8) + (2x + 5) + (102 - 2x) + (x + 5) + x = 3x + 120.
Therefore 3x + 120 =180 3X = 60 x = 20.
Answer: Option D
Question: Of the three-digit integers greater than 660, how many have two digits that are equal to each other and the remaining digit different from the other two?
A.47
B.60
C.92
D.95
Answer: D.95
Explanation: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. all three digits are alike;
C. two digits are alike and third digit is different.
We need to calculate C. C = Total - A - B
Total numbers from 660 to 999 = 339 (3-digit numbers greater than 660);
A. all digits are distinct = 3*8+3*9*8 = 240. If first digit is 6 then second digit can take only 3 values (7, 8, or 9) and third digit can take 8 values. If first digit is 7, 8, or 9 (3 values) then second and third digits can take 9 and 8 values respectively;
B. all three digits are alike = 4 (666, 777, 888, 999).
So, 339-240-4=95.
Answer: D
Question: If n = 30! + 29, then n is divisible by which of the following?
I. 25
II. 27
III. 29
A.I only
B.II only
C.III only
D.I and II
Answer: C.III only
Explanation: 29 divides 30! so 29 also divides 30! + 29.
25 and 27 divide 30! so they do not divide 30! + 29.
The answer is C.
Question: A man can row with a speed of 12 kmph in still water. If the stream flows at 7 kmph, then the speed in downstream is?
A.27
B.19
C.20
D.28
Answer: B.19
Explanation: M = 12
S = 7
DS = 12 + 7 = 19
Answer: B
Question: The distance between two planets is 3.08 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
A. 9.3 × 10^5
B. 9.9 × 10^6
C. 9.4 × 10^5
D. 9.9 × 10^7
Answer: C. 9.4 × 10^5
Explanation: 3.08*10^6 light years = 3.08*10^6/3.26 parsecs.
3.08/3.26 is a little bit less than 1, something like 0.9, thus 3.08*10^6/3.26 = ~0.94*10^6 = 9.4*10^5.
Answer: C.
Question: A student traveled 10 percent of the distance of the trip alone, continued another 30 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip?
A.75
B.100
C.125
D.150
Answer: A.75
Explanation: Let x be the total length of the trip.
0.1x + 30 miles + 0.5x = x
30 miles = 0.4x
x = 75 miles
The answer is A.
Question: Walking at 5/6th of its usual speed a cab is 15mnts late. Find its usual time to cover the journey?
A.25m
B.45m
C.32m
D.75m
Answer: D.75m
Explanation: New speed = 5/6th of usual speed
New time = 6/5th of usual time
6/5 UT - UT = 15m
UT/5 = 15m
UT = 75m
Answer is D
Question: A person takes 5hrs 45 min in walking to a place and ridingback. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is?
A.7 hours
B.7 hours 30 min
C.7 hours 35 min
D.7 hours 45 min
Answer: D.7 hours 45 min
Explanation: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
In fact, you can do all these calculations mentally and save a lot of time
which will be a real benefit for you.
D
Question: A runs 1 ¾ times as fast as B. if A gives B a start of 84 m, bow far must winning post be so that A and B might reach it at the same time?
A.85 m
B.98 m
C.196 m
D.123 m
Answer: C.196 m
Explanation: Ratio of the rates of A and B = 7/4 : 1 = 7 : 4.
So, in a race of 7 m, A gains 3m over B.
:. 3 m are gained by A in a race of 7 m.
:. 84 m are gained by A in a race of (7/3 x 84) m = 196 m.
:. Winning post must be 196 m away from the starting point.
ANSWER C 196 m
Question: I. q-14, q, q, q, q+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c
The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?
A.I, II, III
B.I, III, II
C.II, III, I
D.III, I, II
Answer: A.I, II, III
Explanation: S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of q or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end.
A.
Question: 10,995,1839,91635, 279570 which number is wrong in series
A.10
B.27950
C.995
D.1839
Answer: D.1839
Explanation: 1839...........
all are multiples of 5 expect 1839
ANSWER:D
Question: Find the smallest number of five digits exactly divisible by 32,40,56 and 64.
A.11020
B.11030
C.11040
D.11060
Answer: C.11040
Explanation: Smallest number of five digits is 10000.
Required number must be divisible by L.C.M. of 32,40,56,64 i.e 2240,
On dividing 10000 by 2240,we get 1200 as remainder.
Therefore, Required number = 10000 +( 2240 â€“ 1200 ) = 11040.
Answer is C.
Question: Let x be a positive integer, what is the remainder when 5^(3x+1)+5 is divided by 5?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: For: (5^(3x+1)+5)/3
Let n = 3x + 1
5^n
5^1 = 5
5^2 = 25
5^3 = 125, ... last digit is always 5.
Rule: x^(m+n) = (x^m)(x^n)
(5^(3x))(5^1)
Rule: x^(mn) = (x^m)^n
((5^3)^x)(5) => Now, (5)(125^x) + 5 = (5)(5) + 5 => Finally, 30/5 divides evenly with 0 remainder.
Answer: A
Question: (x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. 3
II. -4
III. 2
IV. 5
A.I and II only
B.I and III only
C.II and III only
D.II and IV only
Answer: D.II and IV only
Explanation: (x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only -4 and 2 and 3 satisfy both inequalities.
Answer: D.
Question: Anintegratedteam consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 7 members and the design team has 3 members, how manyintegratedteam formations are possible?
A. 36
B. 54
C. 63
D. 90
Answer: C. 63
Explanation: 2 out of 7 times 2 out of 3 => 7*6/2*1 * 3*2/2*1 = 63
C
Question: A box contains seven bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
A.2045/2401
B.2121/2401
C.2145/2401
D.2345/2401
Answer: C.2145/2401
Explanation: Required probability
= 1 - 256/2401
= 2145/2401
Answer: C
Question: On the shelf, there are four books of poetry, four novels, and five reference works. Suppose we picked two books at random. What is the probability that we pick one novel and one reference work?
A.4/25
B.6/31
C.8/35
D.10/39
Answer: D.10/39
Explanation: We could pick one novel and then one reference work, or, we could choose one reference work and then one novel.
P(one novel and one reference work) = 4/13*5/12 + 5/13*4/12 = 10/39
The answer is D.
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 48. What is a possible value for the mean of the distribution?
A.46
B.47
C.48
D.55
Answer: D.55
Explanation: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 48:
{Mean} - 3*{SD} > 48;
{Mean} - 6 > 48;
{Mean} > 54.
Answer: D.
Question: Magnabulk Corp sells boxes holding n magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
A.100bn/m
B.100m/(bn)
C.bn/(100m)
D.m/(bn)
Answer: B.100m/(bn)
Explanation: crate has = bn magnates
C crate cost = m dollars = 100 m cents
each magnate cost for each crate = 100 m / bn
Ans; B
Question: What is the length of a bridge (in meters), which a train 148 meters long and travelling at 45 km/h can cross in 30 seconds?
A.211
B.219
C.227
D.235
Answer: C.227
Explanation: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 30 seconds, the train can travel 25/2 * 30 = 375 meters
375 = length of train + length of bridge
length of bridge = 375 - 148 = 227 meters
The answer is C.
Question: How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph?
A.26
B.72
C.28
D.82
Answer: C.28
Explanation: Explanation:
D = 100 + 180 = 280
S = 36 * 5/18 = 10 mps
T = 280/10 = 28 sec
Answer: Option C
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 9 years ago was 20 years. The present age of the husband is:
A.20 years
B.30 years
C.60 years
D.32 years
Answer: D.32 years
Explanation: D
32 years
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 9 x 2) years = 58 years.
Husband's present age = (90 - 58) years = 32 years.
Question: Find the average of x and y if the average (arithmetic mean) of x, y, and 30 is 10 greater than the average of x, y, 20, and 30.
A.50
B.75
C.100
D.125
Answer: B.75
Explanation: consider 30 is 10 greater than 20: 30 = 20+10
similarly
(x+y+30)/3 = (x+y+20+30)/4 + 10
get a like denominator on the right side
(x+y+30)/3 = (x+y+50)/4 + 40/4
(x+y+30)/3 = (x+y+50+40)/4
(x+y+30)/3 = (x+y+90)/4
cross multiply
4(x+y+30) = 3(x+y+90)
4x+4y+120 = 3x+3y+270
collect like terms
4x-3x + 4y-3y = 270 - 120
x + y = 150
thus (x+y)/2 = 150/2
(x+y)/2 = 75
the average of x and y is 75
B
Question: Insert the missing number
6, 7, 9, 13, 21, ...
A.25
B.29
C.37
D.32
Answer: C.37
Explanation: Difference between two numbers in the series is multiplied by 2 to get the next number
6,7 ...Difference is 1
7,9 Difference is 2
9,13 difference is 4
13,21 Difference is 8
21, 37 Difference is 16
ANSWER:C
Question: M = {9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5}
The mean and standard deviation of the 8 numbers in M are 10.0 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
A.70%
B.75%
C.80%
D.85%
Answer: B.75%
Explanation: If mean of the 8 numbers in M is 10.0 & standard deviation 0.3,
the number that lie within the 1st standard deviation (M - SD to M + SD)
range from 9.7 to 10.3 (both inclusive)
The numbers in this set in that range are 6/8 or 75%
Ans : (Option B)
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
A.Rs.8000, Rs.17000
B.Rs.9000, Rs.16000
C.Rs.18000, Rs.7000
D.Rs.10000, Rs.15000
Answer: D.Rs.10000, Rs.15000
Explanation: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000
ANSWER:D
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 2000. The difference between the profit shares of A and C is?
A.621
B.276
C.236
D.800
Answer: D.800
Explanation: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 2000
=> 5 parts out of 15 parts is Rs. 2000
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (2000) = Rs. 800
Answer: D
Question: What is the length of the longest pole which can be kept in a room 9 m long, 4 m broad and 3 m high?
A.10.29
B.9
C.11
D.13
Answer: A.10.29
Explanation: Explanation:
d2 = 92 + 42 + 32 = 10.29
A)
Question: A retailer sells 7 shirts. The first 2 he sells for $38 and $42. If the retailer wishes to sell the 7 shirts for an overall average price of over $50, what must be the minimum average price of the remaining 5 shirts?
A.$54.00
B.$57.00
C.$58.00
D.$60.50
Answer: A.$54.00
Explanation: First 2 shirts are sold for $38 and $42=$80.
To get average price of $50,total sale should be 7*$50=$350
So remaining 5 shirts to be sold for $350-$80=$270
Answer should be 270/5=$54.00 that is A
Question: What is the product of all the prime factors of 15?
A.12
B.3
C.4
D.15
Answer: D.15
Explanation: factors : 3,5
3*5 =15
Answer : D
Question: Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 1 and the 2 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
A. 72
B. 66
C. 76
D. 78
Answer: A. 72
Explanation: Number of arrangements using 5 distinct digits = 5!
Number of arrangements in which 1 and 2 are adjacent - consider 1 and 2 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 1 and 2 can be arranged as 12 or 21.
Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72
Answer : A
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $400, what were her original savings?
A.$1500
B.$1600
C.$1700
D.$1800
Answer: B.$1600
Explanation: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $400. So 1 / 4 of her savings is $400. So her original savings are 4 times $400 = $1600
correct answer B
Question: At what time between 3 and 4 o'clock the hands are in opposite direction?
A.49 1/11 min past 3
B.16 min past 3
C.2 min past 4
D.3 2/11 min past 3
Answer: A.49 1/11 min past 3
Explanation: at 3'0 clock the minutes hand will be 15 min away from hours hand
both hands are opposite when they are 30 minutes away from each other
so,min hand has to gain 45 mins
to gain 1 min minute hand 12/11minutes=45*12/11=49 1/11
ans:49 1/11
ANSWER:A
Question: If the average of ten numbers is 40, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 10
III. 40
A.I
B.II
C.all three options
D.III
Answer: C.all three options
Explanation: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.
IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.
C
Question: If all the sides of a right triangle increase in length by 30%, then by what percentage does the area of the triangle increase?
A.69%
B.81%
C.85%
D.96%
Answer: A.69%
Explanation: Let B be the base and H be the height of the original triangle.
The original area is (1/2)BH.
The area of the expanded triangle is (1/2)(1.3B)(1.3H) = (1.3)(1.3)(1/2)BH = 1.69(1/2)BH
The answer is A.
Question: In a contest, a bowl contains 12 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
A.1/11
B.1/12
C.1/6
D.11/120
Answer: C.1/6
Explanation: P(not winning) = 11/12*10/11 = 5/6
P(winning) = 1 - 5/6 = 1/6
The answer is C.
Question: One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader?
A.120 %
B.140 %
C.162/3 %
D.20 %
Answer: D.20 %
Explanation: Sol.
CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain.
Answer D
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 10 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
A.1 : 2 : 400
B.1 : 4 : 100
C.20 : 4 : 1
D.100 : 4 : 1
Answer: A.1 : 2 : 400
Explanation: B.........M........Y
20.....0,10......Y
B.........4........1
What I did first was to turn 0.20 to 2 (by multiplying by 10), so that it is easy to find the LCM. This led me to this:
B.........M........Y
200.....1.........Y
B........20......10
Then I multiplied every row by 20 (the LCM of 1 and 40), which led me to this:
B.........M........Y
4000...20.......10
Then I got rid of the extra zero, and in the correct order this is Y:M:B=1:2:40
ANS A
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
A.2:1
B.1:8
C.8:1
D.1:1
Answer: D.1:1
Explanation: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1 : 1
Answer: D
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
A.190 sec
B.120 sec
C.130 sec
D.210 sec
Answer: A.190 sec
Explanation: A
190 sec
Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
A.28%
B.20%
C.29%
D.27%
Answer: B.20%
Explanation: 900 ---- 180
100 ---- ? => 20%
Answer:B
Question: A certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
A.81
B.82
C.84
D.86
Answer: C.84
Explanation: 1C4*2C7 = 4*21 = 84
the answer is (C)
Question: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
A.9
B.7
C.6
D.5
Answer: A.9
Explanation: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9.
Answer:A
Question: If e is an even integer and q is an odd integer, which of the following must be an odd integer?
A.e/q
B.eq
C.2e+q
D.2(e+q)
Answer: C.2e+q
Explanation: this is a must question:
A. e/q
can be a non-integer
B. eq
always even
C. 2e+q
e = even -> even+odd = odd
D. 2(e+q)
always even - e+q = odd *2 -> even
E. e/q
might be a non integer.
C
Question: Of the 90 people in a room, 2/5 are women. If 2/3 of the people are married, what is the maximum number of women in the room who could be unmarried?
A.26
B.30
C.32
D.34
Answer: B.30
Explanation: women = 2/5 * 90 = 36
married = 2/3 * 90 = 60
unmarried = 30
max(un-married women) = 30
B
Question: Matt buys a roses for his wife for rs.64.99 and then they get into a fight, so he decides to sell them for rs.74.99. Find his gain %.
A.17.92%
B.12.46%
C.2%
D.15.39%
Answer: D.15.39%
Explanation: sol. cp=rs64.99, sp=rs 74.99
gain=rs(74.99 –64.99)=rs10.00
so gain%={(10.00/64.99)*100}=15.39%
Answer is D.
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number I and the smallest possible number of students that could have taken both geometry and biology?
A.144
B.119
C.113
D.88
Answer: D.88
Explanation: OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number I of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Question: The mean of 50 observations was 36. It was found later that an observation 90 was wrongly taken as 23. The corrected new mean is?
A.37.3
B.36.1
C.36.5
D.36.9
Answer: A.37.3
Explanation: Correct sum
= (36 * 50 + 90 - 23)
= 1867.
Correct mean = 1825/50
= 37.3
Answer:A
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 140. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
A.62
B.68
C.76
D.84
Answer: D.84
Explanation: We see that h will be a maximum h=140 when t-3=0, that is when t=3.
At t=5, h = -14(5-3)^2 + 140 = -14(4) + 140 = 84
The answer is D.
Question: A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ?
A.100 m
B.80 m
C.130 m
D.150 m
Answer: B.80 m
Explanation: Explanation :
Solution: Relative speed = (10 - 8) = 2 km/hr.
Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m.
.'. Distance between the criminal and policeman = (180 - 100) m = 80 m.
Answer : B
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
A.22
B.28
C.27
D.80
Answer: D.80
Explanation: 1/2 * d (10 + 6) = 640
d = 80
Answer:D
Question: Evaluate 28% of 450 + 45% of 280
A.232
B.242
C.252
D.262
Answer: C.252
Explanation: Explanation:
= (28/100) * 450 + (45/100) * 280
= 126 + 126 = 252
Option C
Question: If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is:
A.M2
B.3M2
C.6M2
D.9M2
Answer: B.3M2
Explanation: Explanation :
We have : (a + b + c)/3 = M or (a + b + c) = 3M.
Now, (a + b + c)*(a + b + c) = (3M)^2 = 9M^2
a2 + b2 + c2 + 2 (ab + bc + ca) = 9M^2
a2 + b2 + c2 = 9M^2
Required mean = (a2 + b2 + c2)/3 = 9M^2/3 = 3M2
Answer : B
Question: Two boats are heading towards each other at constant speeds of 5 miles/hr and 25 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
A.1/12
B.5/12
C.1/6
D.1/2
Answer: D.1/2
Explanation: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 5+25=30 mph then 1/60 hours before they collide they'll be rate*time=distance --> 30*1/60=1/2 miles apart.
Answer: D.
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg. What is the weight of the new person?
A.75
B.65
C.55
D.95
Answer: C.55
Explanation: Total increase in weight = 8 × 2.5 = 20
If x is the weight of the new person, total increase in weight = x−35
=> 20 = x - 35
=> x = 20 + 35= 55
Answer is C.
Question: The number of arrangements that can be made with the letters of the word MAETHS so that the word starts with M and ends with S
A.A)2!
B.B)3!
C.C)4!
D.D)6!
Answer: C.C)4!
Explanation: M _ _ _ _ S
the remaining 4 places can be filled by 4!
C