RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If b = 4p, where p is a prime number greater than 2, how many different positive even divisors does b have, including b ?
A. Two
B. Three
C. Four
D. Six
Answer: C. Four
Explanation: b=4p
since b = 4p thenevendivisors are:
4p/4p= 1
4p/2p= 2
4p/4= p
4p/2= 2p
so the answer is (C)
Question: In a class there are 10 boys and 15 girls. In how many ways can a boy and a girl be selected?
A.150
B.500
C.600
D.530
Answer: A.150
Explanation: Explanation:
We can select one boy from 10 boys in 10 ways.
We select one girl from 15 girls in 15 ways
We select a boy and girl in 10 * 15 ways i.e., = 150 ways.
Answer: Option A
Question: Average of 10 numbers is zero. At most how many numbers may be greater than zero
A.0
B.1
C.5
D.9
Answer: D.9
Explanation: Option D
Question: The area of a square is equal to five times the area of a rectangle of dimensions 32 cm *10 cm. What is the perimeter of the square?
A.289 cm
B.160 cm
C.829 cm
D.288 cm
Answer: B.160 cm
Explanation: Area of the square = s * s
= 5(32 * 10)= 1600
=> s =40
= 40 cm
Perimeter of the square
= 4 * 40
= 160 cm.
Answer: B
Question: The average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 58 kg is replaced by a new man. What is the weight of the new man?
A. 80 kg
B. 73 kg
C. 70 kg
D. 75 kg
Answer: B. 73 kg
Explanation: Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 58+10x1.5
58+15=73 Kg
Ans: 'B'
Question: A cycle is bought for Rs.900 and sold for Rs.1160, find the gain percent?
A.11
B.29
C.99
D.77
Answer: B.29
Explanation: 900 ---- 260
100 ---- ? => 29%
Answer: B
Question: Two trains 100 meters and 120 meters long are running in the same direction with speeds of 72 km/hr, 54 km/hr In how much time will the first train cross the second
A.36 sec
B.40 sec
C.44 sec
D.46 sec
Answer: C.44 sec
Explanation: Explanation:
Relative speed of the trains = (72 - 54) km/hr = 18 km/hr
= (18 × 5/18) m/sec = 5 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.
Answer: Option C
Question: Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?
A.1 hour 10 minutes
B.1 hour 82 minutes
C.2 hour 12 minutes
D.1 hour 12 minutes
Answer: D.1 hour 12 minutes
Explanation: New speed = 6/7 of usual speed
Speed and time are inversely proportional.
Hence new time = 7/6 of usual time
Hence, 7/6 of usual time - usual time = 12 minutes
=> 1/6 of usual time = 12 minutes
=> usual time = 12 x 6 = 72 minutes = 1 hour 12 minutes
Answer :D
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.76 kmph
B.10 kmph
C.29 kmph
D.25 kmph
Answer: B.10 kmph
Explanation: Speed of the boat in still water
= (60+80)/2 = 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:B
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
A.1/7
B.1/6
C.2/3
D.2/5
Answer: B.1/6
Explanation: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
B)
Question: A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.1
B.4.2
C.5.3
D.1.5
Answer: A.1
Explanation: M = 3
S = x
DS = 3 + x
US = 3 - x
3 + x = (3 - x)2
3 + x = 6 -2x
3x = 3
x = 1
Answer:A
Question: How many positive integers less than 130 are there such that they are multiples of 13 or multiples of 12 but not both?
A.16
B.18
C.20
D.24
Answer: C.20
Explanation: for 13: 13...130=13*10
for 12: 12...130 =12*10
but there is one integer 13*12. so
N=(10)+(10)=20
C
Question: Find the lowest common multiple of 24, 30 and 40.
A.360
B.420
C.120
D.320
Answer: C.120
Explanation: LCM=2*2*2*3*5=120.
Answer is C
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is
A.54.48
B.54.68
C.54.6
D.54.58
Answer: B.54.68
Explanation: Explanation:
(55×50)+(60×55)+(45×60)/55+60+45
8750/160=54.68
Answer: Option B
Question: Find the LCM of 23,46,827
A.227
B.83
C.23
D.827
Answer: B.83
Explanation: Explanation:
Whenever we have to solve this sort of question, remember the formula.
LCM = \\begin{aligned} \\frac{HCF of Denominators}{LCM of Numerators} \\end{aligned}
So answers will be option 2,
Please also give attention to the difference in formula of HCF and LCM
Answer: Option B
Question: A man can row 3 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.2.9
B.2.8
C.2.4
D.2.8
Answer: C.2.4
Explanation: M = 3
S = 1.2
DS = 3.6
US = 1.8
x/3.6 + x/1.8 = 1
x = 1.2
D = 1.2 * 2 = 2.4
Answer:C
Question: Solution X is 20% chemical A and 80% chemical B by volume; Solution Y is 30% chemical A and 70% chemical B. If a mixture of X and Y is 22% chemical A, what percent of the mixture is Solution X?
A.20%
B.44%
C.50%
D.80 percent
Answer: D.80 percent
Explanation: 22% of chemical A in X+Y grams of solution comes from 20% chemical A in solution X and 30% chemical A in solution Y, thus:
0.22(X + Y) = 0.2X + 0.3Y --> X = 4Y --> X/(X+Y)=4/5=0.8.
Answer: D.
Question: 2 pipes P1 and P2 together can fill a tank in 6 hrs and P3 alone can fill the tank in 10 hrs if they work together what is the time taken to fill the tank?
A.7/4 hrs
B.9/4 hrs
C.13/4 hrs
D.15/4 hrs
Answer: D.15/4 hrs
Explanation: Explanation:
(P1 +P2) can fill 1/6 tank in 1 hr
P3 can fill 1/10 tank in 1 hr
(P1+P2+P3) can fill tank (1/6+1/10)= 4/15
=>3 pipes can fill the tank in 15/4 hrs
Answer: Option D
Question: Three candidates contested an election and received 561, 716 and 1111votes respectively. What percentage of the total votes did the winning candidate got?
A.46%
B.35%
C.50%
D.25%
Answer: A.46%
Explanation: Total number of votes polled = (561 + 716 + 1111) = 2388
Required percentage = 1111/2388 * 100 = 46% (approximately)
Answer: Option A
Question: The total of the ages of Jayant, Prem and Saransh is 75 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Jayant?
A.20 years
B.32 years
C.34 years
D.38 years
Answer: A.20 years
Explanation: Solution
Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,
(2x + 10)+(3x + 10)+(4x + 10)	= 75.
‹=›9x = 45
x = 5.
∴ Jayant's present age = 2x + 10 = 20 years.
Answer A
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
A.7 1/7 sec
B.7 7/2 sec
C.7 1/8 sec
D.7 1/2 sec
Answer: D.7 1/2 sec
Explanation: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 1/2 sec
Answer: D
Question: Laura has a deck of standard playing cards with 14 of the 70 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
A.1/4
B.12/42
C.5/26
D.1/5
Answer: D.1/5
Explanation: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.
If there is no replacement then how is the (P) that the 10th card is 14/70 ??
there are many cases here to be considered here if there is no replacement such as:
H- Denotes heart X-may be any diamond, spade or club.
1. HXXXXXXXXH
2. HHXXXXXXXH
3. HHHXXXXXXH
.
.
.
.
.
9. HHHHHHHHHH
10. XXXXXXXXXH
All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.
For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 14/70 = 1/5 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....
D
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is
A.288
B.278
C.245
D.397
Answer: C.245
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
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.3/4
B.1/3
C.7/19
D.8/21
Answer: B.1/3
Explanation: 7C1/21C1=7/21=1/3
ANSWER:B
Question: If |z|/w = 2, which of the following must be true?
A.z = -2w
B.z = 2w
C.z^2 = 4w^2
D.z^2 = 4w^3
Answer: C.z^2 = 4w^2
Explanation: |z|/w = 2.
|z| = 2w.
Then z = 2w or -2w and so z^2 = 4w^2.
The answer is C.
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
A.15 kmph
B.17 kmph
C.75 kmph
D.18 kmph
Answer: A.15 kmph
Explanation: 90 * 10/60
= 15 kmph
Answer: A
Question: Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 6 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?
A.11.
B.12
C.13
D.14
Answer: B.12
Explanation: Let the Candy and Soda before the increase be C and S respectively
so Increased price of can = C(1+ 25/100) =10 -----------> C= 8
Increase price of soda : S(1+1/2) = 6 -----------> S=4
Hence total = 8+4 =12.. hence answer: B
Question: Find the odd man out
864, 420, 200, 85, 40, 16, 6
A.420
B.85
C.16
D.40
Answer: B.85
Explanation: 6x2+4=16
16x2+8=40
40x2+12=92
92x2+16=200.. and so on. 85
ANSWER:B
Question: Bob bikes to school every day at a steady rate of d miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
A.(d + y) / t
B.2(d + t) / dy
C.2dyt / (d + y)
D.2(d + y + t) / dy
Answer: C.2dyt / (d + y)
Explanation: If we choose for d (distance): 10 miles, for d 10 and for y 5.
t would be 90 minutes or 1,5 hours.
If I try this for answer choice C it fits.
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
A.12
B.10
C.11
D.9
Answer: C.11
Explanation: Explanation :
speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distance / speed= 9 / 54 hour = 1/6 hour = 60/6 min=10 min
Answer : C
Question: A train covers a distance of 12 km in 10 min. If it takes 4 sec to pass a telegraph post, then the length of the train is?
A.20
B.110
C.120
D.80
Answer: D.80
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 4= 80 m.
Answer: Option D
Question: A factory makes 134,341 jam packets which need to be placed in boxes and each box can contain at most 9 packets.How many packets will be in the last unfilled box?
A.1 packet
B.2 packets
C.3 packets
D.4 packets
Answer: B.2 packets
Explanation: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 134,341 = 16 and 9 is divisible by 9.
Hence,we need to add 2 to this number for it to be divisible by 9
Correct Option: B
Question: A person incurs a loss of 5% be selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit
A.Rs.1200
B.Rs.1230
C.Rs.1260
D.Rs.1290
Answer: C.Rs.1260
Explanation: Explanation:
Let the new S.P. be x, then.
(100 - loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)
=>(95/1140=105/x)=>x=1260
Option C
Question: If two numbers are in the ratio 4:3. If 10 is added to both of the numbers then the ratio becomes 5:4 then find the biggest number.
A.60
B.80
C.70
D.40
Answer: B.80
Explanation: 4:3
4x + 20 : 3x + 20 =5 : 4
4[4x + 20] =5[3x + 20]
16x + 80 = 15x + 100
16x -15x = 100 - 80
x = 20
Then biggest number is = 4x
4x = 80
B
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
A.1.6
B.1.5
C.1.2
D.1.9
Answer: B.1.5
Explanation: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer:B
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 50 cms?
A.187
B.476
C.119
D.208
Answer: C.119
Explanation: Area of the room =3.5 * 8.5 = 29.75
Area of the tile = 0.5 *0.5=0.25
No. of tiles = 29.75/0.25 = 119
Answer : C
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 13 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
A.345600
B.153400
C.153600
D.154000
Answer: A.345600
Explanation: Perimeter = Distance covered in 8 min. = 18000 x 8 m = 2400 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 2400 or x = 240.
Length = 720 m and Breadth = 480 m.
Area = (720 x 480) m2 = 345600 m2.
A
Question: If n = 3 x 4 x p, where p is a prime number greater than 3, how many different positive non-prime divisors does n have, excluding 1 and n?
A.Six
B.Seven
C.Eight
D.Nine
Answer: B.Seven
Explanation: N=Xa∗Yb where X and Y are prime,
then number of factors of N are given by the formula (a+1)(b+1) { Notice I have simply increased the powers of X and Y by one and then multiplied them. Also Make sure X and Y are DISTINCT primes)
So, in your question, n = 3 x 4 x p, where p is prime.
I can n=31∗22∗p^1
or number of factors = (1+1) * (2+1) * (1+1) = 12.
But Notice we need to find Non prime and Other than 1 and n, so we have three prime numbers (2,3,p) , 1 and N.
Excluding these, we have 12-5 = 7 such factors.
Hence Answer is B
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
A.66 sec
B.46 sec
C.48 sec
D.65 sec
Answer: C.48 sec
Explanation: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer:C
Question: A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 10 pounds of the body weight, by what percent was the prescribed dosage lesser than the typical dosage?
A.8%
B.-37.5%
C.11%
D.12.5%
Answer: B.-37.5%
Explanation: Typical dosage per 10 pound of the body weight = 2 c.c
Typical dosage per 120 pound of the body weight = 2 *(120/10)
= 2 * 12
= 24 c.c
Dosage prescribed by doctor for 120 pound patient = 18 c.c
% prescribed dosage greater than the typical dosage = (18-24/16) *100%
=(-6/16) *100%
= -37.5%
Answer B
Question: Ganesh ,Ram and Sohan together can do a work in 16 days. If Ganesh and Ram together can do a the same work in 24 days then, how long will take Sohan to do the same work?
A.48
B.58
C.68
D.78
Answer: A.48
Explanation: Solution:
Work done by three of them together in 1 day= 1/16............(1)
Work done by Ganesh and Ram together in 1 day= 1/24.....(2)
So,work done by Sohan in one day=(1)- (2)=(1/16) - (1/24)=1/48
=>Total days taken by Sohan to complete the work alone= 48 days.
Answer A
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 40/kg. how much did a kg of coffee cost in june ?
A.40
B.60
C.80
D.100
Answer: A.40
Explanation: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (400gm) of tea and 1/2 kg (400gm) of coffee (equal quantities) = 40
1.2x(1/2) + 0.8x(1/2) = 40
=> x =40
Thus proved...option A.
Question: If two sides of a triangle are 6 and 13, respectively, which of the following could NOT be the area of this triangle?
A.40
B.6
C.17
D.29
Answer: A.40
Explanation: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 6 and 12.
We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)13 * 6 -or- (.5)6 * 13 will result in a maximum area of 39 for the triangle; therefore, the triangle could never have an area of 40.
A
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 136, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
A.24
B.33
C.55
D.77
Answer: A.24
Explanation: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 136 => .1x + 3/4x = 136 => x = 160
160 - 136 = pure gala =24.
A
Question: Simplify: 100 x 100 - 50 x 50
A.7612
B.7614
C.7500
D.7615
Answer: C.7500
Explanation: (100)^2 - (50)^2 = (100 + 50) (100 - 50) = 150 x 50 = 7500.
Answer is C.
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes and his sister’s time is currently 8 minutes 30 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
A. 3%
B. 15%
C. 8%
D. 10%
Answer: B. 15%
Explanation: Bob's time = 600 secs.
His sis' time = 510 secs.
Percent increase needed = (640-510/600) * 100 = 90/600 * 100 = 15%. Ans (B).
Question: An unbiased cubic die is thrown.What is the probabiltiy of getting a multiple of 3 or 4?
A.1/12
B.1/2
C.3/4
D.1/6
Answer: B.1/2
Explanation: S={1,2,3,4,5,6}
P(E)=n(E)/n(S)
n(s)=Total numbers in a die=6
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(mutliple of 3) = 2/6 = 1/3
Let E be the event of getting the multiple of 4
then ,E={4}
P(multiple of 4) = 1/6
P(multiple of 3 or 4) = 1/3 + 1/6 = 1/2
ans B
Question: Mahesh and suresh are ranked 31th and 32th respectively form the top in a class of 41 Students. What will be their respective ranks from the bottom ?
A.9th and 10th
B.11th and 12th
C.12th and 13th
D.10th and 11th
Answer: D.10th and 11th
Explanation: 1-----41
2-----40
3-----39
4-----38
.
.
.
.
31---11
32---10
33---9
34---8
35----7
36---6
37---5
38----4
39----3
40---2
41----1
so....from bottom mahesh suresh ranks are 11th and 10th
ANSWER:D
Question: find the smallest number in GP whose sum is 38 and product is 1728
A.5
B.6
C.7
D.8
Answer: D.8
Explanation: Let x,y,z be the numbers in geometric progression?
y^2=xz
x+y+z=38
xyz=1728
xyz = xzy = y^2y = y^3 = 1728
y = 12
y^2=xz=144
z=144/x
x+y+z = x+12+144/x = 38
x^2+12x+144=38x
x^2-26x+144=0
(x-18)(x-8)=0
x=8,18
If x =8, z = 38-8-12=18
The numbers are 8,12, 18
Their sum is 38
Their product is 1,728
The smallest number is 8
ANSWER:D
Question: If YWUSQ is 25 - 23 - 21 - 19 - 17 then MKIGF is
A.9 - 8 - 7 - 6 - 5
B.1 - 2 - 3 - 5 - 7
C.7 - 8 - 4 - 5 - 3
D.13 - 11 - 9 - 7 - 6
Answer: D.13 - 11 - 9 - 7 - 6
Explanation: In alphabet has 26 words coresponding as
A position 1
E position 5
Z position 26
similarly as given in question Y=25 ;W=23; U=21;S=19; Q=17
for M=13 ;K=11;I=9 and so on
ANSWER:D
Question: David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
A.75
B.276
C.87
D.165
Answer: A.75
Explanation: Explanation:
Average = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5 = 75.
Answer:A
Question: If it is assumed that 62 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?
A.400
B.420
C.480
D.483.8
Answer: D.483.8
Explanation: Minimum no of mail to be sent for getting 300 responses at 62%
= 300/0.62 = 483.8
Option D
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
A.79.5
B.79.0
C.79.4
D.79.2
Answer: D.79.2
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer: D
Question: A small company is planning to rent either computer A or computer B to print customer mailing lists. Both computer A and computer B must be rented on an hourly basis. The rental fee is based only on the amount of time the computer is turned on. It will cost 40 percent more per hour to rent computer A than to rent computer B. Computer B would, however, require 20 hours more than computer A to do the job. If either computer A, or computer B were rented the total cost to rent the computer would be $550.00. What would be the approximate hourly charge to rent computer B?
A.$7.85
B.$11.30
C.$13.20
D.$17.80
Answer: A.$7.85
Explanation: Pa = price of A
Pb = price of B
Ta = time for A to complete the job
Tb = time for B to complete the job
Given
Pa = 1.4 Pb
Ta+20 = Tb
Pa*Ta = Pb*Tb=550
1.4Pb * (Tb-20) = Pb*Tb
1.4 Pb Tb - Pb Tb = 1.4 Pb * 20
0.4PbTb = 28Pb
Tb = 28/0.4 = 70
Pb=550/70 ~ 7.85
A
Question: Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 6 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
A.R-4
B.R/(R+4)
C.R/(R-12)
D.8/(R-8)
Answer: C.R/(R-12)
Explanation: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.
In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*6T=R(T-1) --> 12T=RT-R -->T=R/(R-12).
Answer: C.
Question: A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
A.675
B.680
C.685
D.690
Answer: A.675
Explanation: Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec.
Length of the train = 75 * 9 = 675 m.
Answer: Option A
Question: Jane and Thomas are among the 7 people from which a committee of 3 people is to be selected. How many different possible committees of 3 people can be selected from these 7 people if at least one of either Jane or Thomas is to be selected?
A.20
B.25
C.30
D.35
Answer: B.25
Explanation: The total number of ways to choose 3 people from 7 is 7C3 = 35.
The number of committees without Jane or Thomas is 5C3 = 10.
There are 35-10 = 25 possible committees which include Jane and/or Thomas.
The answer is B.
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
A.20/9 sec
B.20/2 sec
C.20/7 sec
D.40/9 sec
Answer: C.20/7 sec
Explanation: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed
= (54 + 72)*5/18
= 7*5 = 35 mps.
The time required = d/s
= 100/35 = 20/7 sec.
Answer: C