RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A company pays 12.5% dividend to its investors. If an investor buys Rs.40 shares and gets 25% on investment, at what price did the investor buy the shares?
A.20
B.66
C.18
D.19
Answer: A.20
Explanation: Explanation:
Dividend on 1 share = (12.5 * 40)/100 = Rs.5
Rs.25 is income on an investment of Rs.100
Rs.5 is income on an investment of Rs. (5 * 100)/25 = Rs.20
ANSWER: A
Question: The simple interest on a sum of money is 4/9 of the principal. Find the rate percentage and time, if both are numerically equal.
A.6 1/3 % and 6 2/3 years
B.6 2/3 % and 6 1/3 years
C.6 2/3 % and 6 2/3 years
D.6 1/3 % and 6 1/3 years
Answer: C.6 2/3 % and 6 2/3 years
Explanation: Let sum = Rs. x. Then, S.l. = Rs. 4x/9
Let rate = R% and time = R years.
Then, (x*R*R)/100=4x/9 or R^2 =400/9 or R = 20/3 = 6 2/3.
Rate = 6 2/3 % and
Time = 6 2/3 years = 6 years 8 months
Answer is C
Question: A sum of 25 was paid for a work which A can do in 32 days, B in 20 days, B and C in 12 days and D in 24 days.How much did C receive if all the four work together ?
A.14⁄3
B.16⁄3
C.15⁄3
D.17⁄3
Answer: B.16⁄3
Explanation: A's one day's work = 1⁄32
B's one day's work = 1⁄20
(B + C)'s one day's work = 1⁄12
∴ C's one day's work = 1⁄12 - 1⁄20 = 1⁄30
D's one day's work = 1⁄24
∴ (A + B + C + D)'s one day's work
1/32+1/20+1/30+1/24=75+120+80+100/2400
= 375⁄2400 = 15⁄96 = 5⁄32
∴ Out of 5⁄32 of work done
1⁄30 of the work is done by C.
⇒ Out of 25 paid for the work, C will receive
1/30 /5/32×25, i.e, 1⁄30 × 32⁄5 × 25, i.e, 16⁄3
Answer B
Question: A man can row at 6 kmph in still water. If the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back, how far is the place?
A.5.33 km
B.6.33 km
C.5.63 km
D.7.33 km
Answer: A.5.33 km
Explanation: Speed in still water = 6 kmph
Speed of the current = 2 kmph
Speed downstream = (6+2) = 8 kmph
Speed upstream = (6-2) = 4 kmph
Let the required distance be x km
Total time taken = 2 hour
x/8 +x/4 =2
x+2x/8 =2
3x/8=2
3x=16
x=5.33 km
ANSWER:A
Question: In a soccer bet,we play 4 teams.first team odd 1.30,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?
A.219.5
B.226.49
C.235.01
D.266.74
Answer: B.226.49
Explanation: in the case we won the bet,we have:
1.30* 5.23* 3.25* 2.0*5.00=219.50
we will win 226.49
so correct answer is B
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 70. He was allowed to drop his lowest score. After doing so, his average test score improved to 75. What is the lowest test score that was dropped?
A.20
B.25
C.55
D.65
Answer: C.55
Explanation: The arithmetic mean of 4 equally weighted tests was 70. So what we can assume is that we have 4 test scores, each 70.
He dropped his lowest score and the avg went to 75. This means that the lowest score was not 70 and other three scores had given the lowest score 5 each to make it up to 70 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 70.
So the lowest score = 70 - 15 = 55
Answer (C)
Question: 103,100,97,..,91,88,85
Insert the missing number
A.88
B.78
C.94
D.98
Answer: C.94
Explanation: Missing number : 94
Answer : C
Question: The area of a triangle is with base 4m and height 5m?
A.88 m2
B.10 m2
C.66 m2
D.77 m2
Answer: B.10 m2
Explanation: 1/2 * 4 * 5 = 10 m2
Answer: B
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A.Rs. 375
B.Rs. 400
C.Rs. 600
D.Rs. 800
Answer: B.Rs. 400
Explanation: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1
C's share (for 3 days) = Rs.	(3 * 1/24 * 3200) =Rs.400
Answer = B
Question: If the height of an equilateral triangle GBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔGBC is how many times as long as a leg of the right triangle DEF?
A.(√2)/(√3)
B.(√3)/(√2)
C.√2
D.(2√2)/(√3)
Answer: D.(2√2)/(√3)
Explanation: Side of the equilateral triangle GBC = 2m ----> height = m * sqtr(2)
Hipotenuse of the right triangle GBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)
Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D
Question: An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 7. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
A.Rs 1200
B.Rs 1500
C.Rs 1600
D.Rs 1900
Answer: A.Rs 1200
Explanation: Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 7x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2100.
Hence, (R - p) = (2100 - 900) = 1200
Answer : A
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
A.19878
B.12798
C.26908
D.11750
Answer: D.11750
Explanation: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
A.1/2
B.1/5
C.1/3
D.1/7
Answer: C.1/3
Explanation: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
C
Question: If books bought at prices ranging from Rs. 125 to Rs. 350 are sold at prices ranging from Rs. 170 to Rs 420, what is the greatest possible profit that might be made in selling 12 books ?
A.Rs. 3500
B.Rs. 3540
C.Rs. 3520
D.Rs. 3200
Answer: B.Rs. 3540
Explanation: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 12 books = 125*12 = Rs. 1,500
Maximum selling price of 12 books = 420 *12 = Rs. 5,040
So, maximum profit = 5040 - 1500 = Rs. 3,540
ANSWER : OPTION B
Question: What is the remainder when 12346 is divided by 9?
A.7
B.6
C.5
D.4
Answer: A.7
Explanation: If the sum of the digits of a number is divisible by 9, the number will be divisible by 9.
1+2+3+4+6 = 16
The nearest multiple of 9 is 9.
16-9= 7.
ANSWER:A
Question: A’s speed is 30/17 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
A.1/17
B.13/30
C.17/30
D.11/30
Answer: B.13/30
Explanation: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 30 meters, B covers 17 meters in that time. So if the race is 30 meters long, when A reaches the finish line, B would be 13 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 13 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 30 meters) would be the same as the time required by B (to cover 17 meters) to reach the finish line.
So B should get a head start of 13/30th of the race.
Answer (B)
Question: Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is:
A.Rs 200
B.Rs 300
C.Rs 400
D.Rs 500
Answer: C.Rs 400
Explanation: Let C = x.
Then B = x/2
and A = x/4
A:B:C = 1:2:4.
C's share Rs.[(4/7)x700) = 400
answer :C
Question: In a garden, there are four blue flowers, three red flowers, four green flowers, and four pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?
A.11/10
B.1/55
C.31/10
D.3/55
Answer: D.3/55
Explanation: P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)
= P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)
= 1x3/11x2/10
= 3/55
Answer: D
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
A.9
B.7
C.8
D.6
Answer: C.8
Explanation: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Question: How many different positive integers are factors of 64 ?
A. 10
B. 12
C. 14
D. 16
Answer: D. 16
Explanation: 8×8=4^2 × 2^2
So total factors = (3+1)(3+1) = 16
Answer: D
Question: If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
A.1/16
B.3/16
C.1/8
D.3/8
Answer: B.3/16
Explanation: A) 3 heads..
all three heads can be taken as one, so total are 4- 3H,T,T,T...
3H can take any of four places= 4 ways..
B) 4 Heads..
again 3H are one but it cannot have fourth one next to it..
(i)so if we have 3H in edges.. 3H,T,_,_
the last two can be H,T or T,H--- so 2 ways..
similarily if 3H in the rightmost position-- _,_,T,3H---- 2 ways..
(ii) if we have 3H in middle... T,3H,T,H and H,T,3H,T--- 2ways..
TOTAL=2+2+2=6 ways..
C) 5 heads..
Again 3H in edges-- 3H,T,H,H or H,H,T,3H--2 ways.
we cannot have 3H in middle, as it will surely have a H adjacent to it, resulting in 4 H in a row..
D) 6 Heads--
NO possiblity..
TOTAL ways to have exactly 3H in a row=4+6+2=12 ways..
total combinations of 6 tosses= 2^6..
Probability= 12/2^6= 3/16
Answer: B.
Question: There is a building of 100 floors
-If an egg drops from the Nth floor or above it will break.
-If it’s dropped from any floor below, it will not break.
You’re given 2 eggs.
Find N
How many drops you need to make?
A.14
B.22
C.18
D.25 sec
Answer: A.14
Explanation: A
14
This follows the below logic.
Say, the egg breaks at floor n we try to find out by going (N-1) till the first floor by doing linear search.
Say for example, I throw the egg from 10th floor, and it breaks, I wíll go to floor 1 to 9 to find out the floor..
Then I would try the same logic for every 10 floors thereby setting a worst case scenario of 19 chances.. I.e. 10,20,30,40,50,60,70,80,90,100,91,92,93,94,95,96,97,98,99
To find optimum solution, let’s try this:
If for every n, egg doesnt break, instead of going to next n, go to N-1, this would save us one drop as we are doing a linear search with second egg when egg1 breaks…
So the series would look something like this..
N + (N-1) + (N-2) + (N-3) +…+ 1
Now this is a series which is equal to N(N+1)/2
Now since it is given that the egg may or may not break from 100th floor..
We can write it as..
N(N+1)/2>=100
And n=14(approx)
So we should start from 14 then move up N-1 to 13 floor I.e. 27,39…
So the floors from where the drop needs to be done are: 14,27,39,50,60,69,77,84,90,95,99,100
So the answer is 14
Question: A pipe is 30 m long and is 45% longer than another pipe. Find the length of the other pipe
A.20.68
B.20
C.20.12
D.20.5
Answer: A.20.68
Explanation: Explanation:
Let length of other pipe be X
According to question,
30 = 45/100 X + X
30 = 0.45X + X
30 = 1.45 X
X= 30/1.45
X = 20.68m
Thus the length of the other pipe is 20.68 metres.
ANSWER A
Question: If 3y + 7 = x^2 + P = 7x + 5, what is the value of P ?
A.8(1/4)
B.8(1/2)
C.8(1/3)
D.8(1/5)
Answer: A.8(1/4)
Explanation: Explanation:
3x + 7 = 7x + 5 => 7x - 3x = 2 => 4x = 2 => x = 1/2.
Now, 3x + 7 = x^2 + p => 3/2 + 7 = 1/4 + p => p = 8 * 1/4.
Answer: A
Question: If b is an integer, what is the greatest possible value for b that would still make the following statement true: 11*10^b < 1/10 ?
A. –4
B. –3
C. –2
D. –1
Answer: B. –3
Explanation: Just putting values, the LHS becomes
b=0 --> 11
b=-1 --> 11/10
b=-2 --> 11/100
b=-3 --> 11/1000
Anything lower will be smaller than 11/1000. b=-2, equality does not hold but it does for b=-3.
Answer is B.
Question: Ram singh goes to his office in the city, every day from his suburban house. His driver Mangaram drops him at the railway station in the morning and picks him up in the evening. Every evening Ram singh reaches the station at 5 o'clock. Mangaram also reaches at the same time. one day Ramsingh started early from his office and came to the station at 4 o'clock. Not wanting to wait for the car he starts walking home. Mangaram starts at normal time, picks him up on the way and takes him back house, half an hour early. How much time did Ram singh walk.
A.1/4 hours
B.2/4 hours
C.3/4 hours
D.5/4 hours
Answer: C.3/4 hours
Explanation: Let the time required for walk is t hours then Ram Singh will reach at the car in time (4+t), due to this walking of Ram Singh time saving = [5-(4+t)]*2 , here 2 is due to forward motion upto railway station and backward from railway station to the point where the car met to Ram Singh. It is given that time saving = 1/2 hour
so 2[1-t] = 1/2 on solving we get t = 3/4 hours
ANSWER:C
Question: By selling an article for 3200, a dealer suffers a loss equal to 1/5 of his investment. Find the cost price. At what price should he had sold it to make a gain of 10% ?
A.Rs. 3600, Rs. 3960
B.Rs. 4000, Rs. 4400
C.Rs. 4800, Rs. 5280
D.Rs. 4200, Rs. 5080
Answer: B.Rs. 4000, Rs. 4400
Explanation: Let his CP was X.
Loss = X/5
Selling price = CP - loss
3200 = X - (X/5)
X = 4000.
CP = Rs. 4000.
To get 10% gain,
SP = 4000 + 10% of 4000 = 4000 + 400 = Rs. 4400.
ANSWER : B
Question: How many words can be formed by using all the letters of the word “DAUGHTR” so that vowels always come together & vowels are never
together?
A.4320
B.760
C.720
D.4000
Answer: A.4320
Explanation: Given word contains 8 different letters
When the vowels AUE are always together we may suppose
them to form an entity ,treated as one letter
then the letter to be arranged are DAHTR(AUE)
these 6 letters can be arranged in 6p6 = 6!
= 720 ways
The vowels in the group (AUE) may be arranged in 3! = 6 ways
Required number of words = 760 * 6 =4320
ANSWER A 4320
Question: A and B start from house at 10am. They travel on the MG road at 20kmph and 40 kmph. there is a Junction T on their path. A turns left at T junction at 12:00 noon, B reaches T earlier, and turns right. Both of them continue to travel till 2pm. What is the distance between A and B at 2 pm
A.160km
B.170km
C.180km
D.190km
Answer: A.160km
Explanation: at 12 A will travel=20*2=40km
B will travel this 40 km in 40/40=1 hr i.e. by 11am.
after T junction for A- distance travelled =2*20=40 km
for b distance travelled =40*3=120
so distance between A & B is=120+40=160km
ANSWER:A
Question: The average (arithmetic mean) of five numbers is 5. If 2 is subtracted from each of three of the numbers, what is the new average?
A.3.8
B.8.9
C.4.5
D.7.5
Answer: A.3.8
Explanation: Sum of 5 numbers = 5*5 =25
If 2 is subtracted from each of three of the numbers , we subtract 2*3=6 from the total sum
Sum of 5 number after subtracting 2 from each of three of the numbers =25-6=19
New average = 19/5=3.8
Answer A
Question: The Average of 100, 200, 300, 400, ... , 1000 is 550. If each number is divided by 5, then the new average will be equal to
A.450
B.45
C.55
D.None of these
Answer: D.None of these
Explanation: Answer
Actual average
=( 100 + 220 + 300 + ... + 1000 ) / 10
=550
New Average = 550 / 5
=110
Correct Option: D
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
A.8 kmph
B.10 kmph
C.12 kmph
D.16 kmph
Answer: C.12 kmph
Explanation: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Question: Three runners R, B and C run a race, with runner R finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?
A.36m
B.48m
C.60m
D.72m
Answer: B.48m
Explanation: Let distance of race be x mtrs. Then when R finishes x m , B has run (x- 12)mtrs and C has run x-18 mtrs. so at this point B is 6 m ahead of C. Now to finish race b needs to run another 12 m, so he runs another 12 m. when B finishes race he is 8 m ahead of C. so last 12 m B has run, C has run 10 m.
as speeds are constant, we have equation,
x-12/ x-18 = 12/10 > x = 48.
Answer B
Question: Jake remembers only the last four letters of his five-letter Klingon name. If he is sure that the first letter is neither "N" nor "Z", and assuming that there are only 10 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
A.A)8/100
B.B)1/8
C.C)1/9
D.D)4/5
Answer: B.B)1/8
Explanation: Total letters 10, out of which the first letter is anything of 10 but N or X...
So there are 8 possible letters for first place..
And only one of them is correct..
So 1/8..
Answer: B
Question: Five years ago, John’s age was half of the age he will be in 2 years. How old is he now?
A.14years
B.12years
C.16years
D.17years
Answer: B.12years
Explanation: Let John=j,j-5=(j+2)/2,then j=12years
ANSWER:B
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 110 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A.110 * sqrt 2
B.110 * sqrt (2^7)
C.110 * sqrt (2^12)
D.110 * the twelfth root of (2^7)
Answer: A.110 * sqrt 2
Explanation: Let the constant be k.
F1 = 110
F2 = 110k
F3 = 110 k * k = 110 * k^2
F13= 110 * k^12
we know F13 = 2 *F1 = 2 * 110 = 220
220/110 = k^12
k = twelfth root of 2
for F7...
F7 = 110 * k^6 ( as we wrote for F2 and F3)
F7 = 110 * (twelfth root of 2) ^ 6
F7 = 110 * sqrt (2)
The answer is A.
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case.
A.627
B.528 soldiers
C.626
D.657
Answer: B.528 soldiers
Explanation: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k
As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)
x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.
Answer:B
Question: The operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.
I. z T z/z-1=1
II.x T (-z)=0
III. 2/z T 2/z=z
A.a.) I
B.b.) I and II only
C.c) I and III only
D.d) II and III only
Answer: C.c) I and III only
Explanation: Statement I is TRUE
Statement II is not TRUE
Statement III is TRUE
Answer : C
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 262 runs?
A.6.25
B.6.22
C.6.29
D.5.75
Answer: D.5.75
Explanation: Required run rate
= [262 - (3.2 * 10)]/40
= 230/40
= 5.75
Answer: D
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
A.19%
B.72%
C.12%
D.16%
Answer: C.12%
Explanation: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Question: The total of the ages of Amar, Akbar and Anthony is 62 years. What was the total of their ages three years ago ?
A.51 years
B.55 years
C.74 years
D.53 years
Answer: D.53 years
Explanation: Explanation:
Required sum = (62 - 3 x 3) years = (62 - 9) years = 53 years.
Answer: Option D
Question: A and B can do a work in 4days, B and C in 5days, C and A in 7days. If A,B and C work together , they will complete the work in?
A.3days
B.5days
C.7days
D.1days
Answer: A.3days
Explanation: A+B 1day work = 1/4
B+C 1day work = 1/5
C+A 1day work = 1/7
Adding we get 2(A+B+C) = 1/4 + 1/5 + 1/7 = 83/140
A+B+C 1 day work = 83/280
A,B,C can finish the work in 280/83 days = 3days approximately
Answer is A
Question: What is the greatest possible straight line distance, in inches, between any two points on a rectangular box that is 5 inches wide, 3 inches long, and 4 inches high?
A.2√5
B.5
C.5√2
D.10
Answer: C.5√2
Explanation: The maximum possible distance in a cuboid is the diagonal.
Diagonal length = sqrt(length^2 + breadth^2 + height^2) = sqrt(50)
= 5√2
(Option C)
Question: Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 30 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?
A.4
B.5
C.6
D.12
Answer: D.12
Explanation: The part of job that Suresh completes in 9 hours
= 9â„15 = 3â„5
Remaining job = 1 - 3â„5 = 2â„5
Remaining job can be done by Ashutosh in 2â„5 Ã— 30 = 12 hours
Answer D
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point T at the same time, how long, in hours, after the trains depart will they again meet at Point T?
A.3
B.6
C.9
D.18
Answer: B.6
Explanation: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train A be X, thus that covered by the train B will be 12*3.14-X
dA = X dB = 12*3.14 - X
Times taken by A and B are
tA= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of A and B: totalSpeed T= 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tA =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5=B
Question: Yesterday's closing prices of 1,760 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
A. 960
B. 726
C. 1,100
D. 1,320
Answer: A. 960
Explanation: Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 1760 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1)(2) to get H = 960.
A is my answer.
Question: If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true?
i. s=u
ii. u is not equal to v
iii. s > v
A.None
B.I only
C.II only
D.III only
Answer: D.III only
Explanation: Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.
Answer: D
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 4, then v=
A.6
B.9
C.12
D.15
Answer: B.9
Explanation: (v*)* = (v - v/3) - (v - v/3) / 3
4 = 2v/3 - 2v/9 = 4v/9
v = 9
The answer is B.