RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is :
A.90
B.92
C.91
D.None of these
Answer: A.90
Explanation: Explanation :
From a certain station, there will be a ticket for each of the other 9 stations.
Since, there are 10 stations on the railway line, the number of different journey tickets will be 10×9 i.e 90.
Answer : A
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction C of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
A.1/(3x)
B.3x/(x-3)
C.(x – 3)/(3x)
D.x/(x-3)
Answer: C.(x – 3)/(3x)
Explanation: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete C=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Question: A bag contains 4red, 6blue and 3green balls. If 3 balls are picked at random, what is the probability that both are BLUE?
A.11/144
B.12/455
C.10/143
D.11/125
Answer: C.10/143
Explanation: P(Both are red),
=6C3/13C3
=10/143
C
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
A.20070
B.20000
C.20029
D.29087
Answer: B.20000
Explanation: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: B
Question: From the given equation find the value of x: x² − 3x + 2
A.3
B.2
C.5
D.6
Answer: C.5
Explanation: (x − 1)(x − 2)
x = 1 or 2.
C
Question: It takes nine minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video, rounded to the nearest hundredth?
A.13.58
B.13.87
C.14.24
D.14.59
Answer: D.14.59
Explanation: The laptop can load the video at a rate of 1/15 of the video per second.
The phone can load the video at a rate of 1/(60*9) = 1/540 of the video per second.
The combined rate is 1/15 + 1/540 = 37/540 of the video per second.
The time required to load the video is 540/37 = 14.59 seconds.
The answer is D.
Question: Four people are on an elevator that stops at exactly 4 floors. What is the probability that exactly one person will push the button for each floor?
A.4!/4^4
B.4^4/4!
C.4/4!
D.4/4^4
Answer: A.4!/4^4
Explanation: Each person out of 4 has 4 options, hence total # of outcomes is 4^4;
Favorable outcomes will be 4!, which is # of ways to assign 4 different buttons to 4 people
So basically # of arrangements of 4 distinct objects: 4!.
P=favorable/total=4!/4^4
Answer: A.
Question: A boy has twelve trousers and 17 shirts. In how many different ways can he select a trouser and a shirt?
A.299
B.278
C.204
D.108
Answer: C.204
Explanation: The boy can select one trouser in twelve ways.
The boy can select one shirt in 17 ways.
The number of ways in which he can select one trouser and one shirt is 12 * 17
= 204 ways.
Answer: C
Question: A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?
A.2
B.5
C.6
D.8
Answer: B.5
Explanation: Explanation:
\inline \fn_jvn [(100\times 35)+(200\times 5)] men can finish the work in 1 day
\inline \fn_jvn \therefore 4500 men can finish the work in 1 day. 100 men can finish it in \inline \fn_jvn \frac{4500}{100} = 45 days.
This is 5 days behind Schedule
Answer: B) 5
Question: Find the simple interest on $6000 at 15% per annum for 9 months?
A.$492
B.$512
C.$675
D.$745
Answer: C.$675
Explanation: P = $6000
R = 15%
T = 9/12 YEARS = 3/4 YEARS
S.I. = P*R*T/100 = 6000*15*3/400 = $675
Answer is C
Question: If 2x + y = 7 and x + 2y = 5, then xy/3 =
A. 1
B. 4/3
C. 17/5
D. 18/5
Answer: A. 1
Explanation: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
xy/3= 3*1/3
=1
A
Question: The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 12, which of the following represents the maximum possible value of the largest integer?
A.4
B.16
C.12
D.8
Answer: B.16
Explanation: Let the distinct number be A,B,C, and D
Its given A > B > C > D
also A + B + C + D =40 and A + B = 12 means C + D = 28
Since the question ask for the largest possible number we should choose the least value for A and B,C. So D should be 16. If D=16 then C = 12 > A,B <12
Answer : B
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B?
A.7
B.9
C.8
D.11
Answer: C.8
Explanation: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 22
⇒ 5x = 20
⇒ x = 4.
Hence, B's age = 2x = 8 years.
Answer: C
Question: Village X has a population of 72000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?
A.15
B.19
C.11
D.18
Answer: A.15
Explanation: Let the population of two villages be equal after p years
Then, 72000-1200p=42000+800p
2000p=30000
p=15
Answer is A.
Question: There are some 2 wheelers and 4 wheelers parked total number of wheels present is 240 then how many 4 wheelers were there
A.20
B.30
C.40
D.50
Answer: C.40
Explanation: 2x+4x=240;
x=40;
then two whl=2*40=80
4 whl =4*40=160;
ans: 160/4= i-e 40
ANSWER:C
Question: Express 50 mps in kmph?
A.172
B.160
C.150
D.180
Answer: D.180
Explanation: 25 * 18/5 = 180 kmph
Answer:D
Question: (112 x 54) = ?
A.60000
B.70000
C.80000
D.88000
Answer: B.70000
Explanation: (112 x 54) = 112 x 10 4	=	112 x 104	=	1120000	= 70000
2	24	16
B)
Question: If PENCIL is coded as 45 and TRASH is coded as 36, then MEMORY is coded as
A.33
B.59
C.60
D.72
Answer: D.72
Explanation: PENCIL= 16+5+14+3+9+12=59 i.e 5*9=45
TRASH= 20+18+1+19+8=66 i.e 6*6=36
MEMORY 13+5+13+15+18+25=89 8*9=72
ANSWER:D
Question: 3889 + 14.952 - ? = 3854.002
A.47.95
B.49.95
C.45.97
D.47.59
Answer: B.49.95
Explanation: Let 3889 + 14.952 - x = 3854.002.
Then x = (3889 + 14.952) - 3854.002
= 3903.952 - 3854.002
= 49.95.
Answer is B
Question: In May, the grounds keeper at Spring Lake Golf Club built a circular green with an area of 36π square feet. In August, he doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
A.100PI
B.144PI
C.70
D.80
Answer: B.144PI
Explanation: AREA OF CIRCLE 36PI SQ FEET =PI R^2 THEREFORE R =6
NOW GREEN RADI DOUBLED I.E R =12 AREA =144 PI
B
Question: In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race ?
A.20 min
B.15 min
C.10 min
D.5 min
Answer: C.10 min
Explanation: After 5 minutes (before meeting), the top runner covers 2 rounds i.e., 400 m and the last runner covers 1 round
i.e., 200 m.
∴ Top runner covers 800 m race in 10 minutes.
Answer C
Question: A man sells a horse for Rs.1000 and loses something, if he had sold it for Rs.1090, his gain would have been double the former loss. Find the cost price of the horse?
A.1080
B.1040
C.1070
D.1030
Answer: D.1030
Explanation: CP = SP + 1CP = SP - g
1000 + x = 1090 - 2x
3x = 90 => x = 30
CP = 1000 + 30 = 1030
Answer: D
Question: The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
A.kmph
B.kmph
C.kmph
D.kmph
Answer: B.kmph
Explanation: Speed downstream = 50 + 20 =70 kmph
Speed upstream = 50 - 20 = 30 kmph
Answer:B
Question: In an election, candidate Smith won 52% of the total vote in Counties A and Q. He won 61% of the vote in County A. If the ratio of people who voted in County Q to County B is 3:1, what percent of the vote did candidate Smith win in County Q ?
A.A.25%
B.B.27%
C.C.34%
D.D.43%
Answer: A.A.25%
Explanation: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County Q
hence answer is A.
Question: Find the face value of 8 in 8213456
A.8000
B.80
C.8
D.800
Answer: C.8
Explanation: Face value is the value of digit itself
face value of 8 = 8
Answer : C
Question: The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
A.A)19009
B.B)19074
C.C)19008
D.D)19000
Answer: D.D)19000
Explanation: Explanation:
Money paid in cash = Rs. 1000
Balance payment = (20000 - 1000) = Rs. 19000
Answer: Option D
Question: What is the remainder when the infinite sum (1!)² + (2!)² + (3!)² + ··· is divided by 1152?
A.12
B.41
C.152
D.802
Answer: B.41
Explanation: Explanation :
We have to find out the remainder when (1!)² + (2!)² + (3!)² + ··· is divided by 1152
1152 = 27 * 32
=> (6!)2 is divisble by 1152
=> All (n!)2 are divisible by 1152 as long as n > 5
So, our problem is now reduced to
Rem [((1!)² + (2!)² + (3!)² + (4!)² + (5!)²)/1152]
= Rem[(1 + 4 + 36 +576 + 14400) / 1152]
= Rem [15017/1152]
= 41
Answer : B
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 7% of bananas were rotten. Find the percentage of fruits in good condition?
A.92.5%
B.88.2%
C.85.2%
D.96.8%
Answer: B.88.2%
Explanation: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 7% of 400
= 28
Therefore, total number of rotten fruits = 90 + 28= 118
Therefore Number of fruits in good condition = 1000 - 118 = 882
Therefore Percentage of fruits in good condition = (882/1000 × 100)%
= (88200/1000)%
= 88.2%
Answer:B
Question: If a class of 10 students has four men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
A.5!4!
B.5!5!
C.4!3!
D.10!
Answer: C.4!3!
Explanation: for no two men to sit together, either all are in even or odd position
fix one at any one position then rest three can be fixed in 3! ways...
also rest four position of women can be fixed in 4!..
total ways 4!3!
C
Question: A cask initially contains pure alcohol up to the brim. The cask can be emptied by removing exactly 5 liters at a time . Each time this is done, the cask must be filled back to the brim with water. The capacity of the cask is 15 liters. When the cask is completely emptied and filled back to the brim two times, what is the ratio of alcohol to water in the cask
A.4/5
B.3/5
C.4/6
D.3/6
Answer: A.4/5
Explanation: You are given that the initial quantity of the cask is 15 l. So for the changing of the liquids,
The first time you remove 5 l of pure alcohol---> 10 l of alcohol remaining and you add 5 l of water. Ratio of alcohol in the remaining mixture = 10/(10+5) = 10/15 =2/3, similarly water = 1/3.
The second time you remove 5 l of the mixture having alcohol = 5*2/3 = 10/3 --> remaining alcohol = 10-10/3 =20/3
Similarly, the amount of water removed = 5*1/3=5/3 ---> remaining water = 5-5/3=10/3 but you also add 5 l more of water --> total water now = 5+10/3 = 25/3
Finally, ratio asked = 20/3 / 25/3 = 20/25 = 4/5
A is the correct answer.
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
A.720
B.144
C.120
D.36
Answer: B.144
Explanation: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
ANSWER:B
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
A.15 : 8
B.14 : 8
C.17 : 8
D.13 : 8
Answer: A.15 : 8
Explanation: A
15 : 8
Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15 : 8
Question: A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.1.7
B.1.9
C.1.1
D.2
Answer: D.2
Explanation: M = 6
S = x
DS = 6 + x
US = 6 - x
6 + x = (6 - x)2
6 + x = 12 -2x
3x = 12-6=6
x = 2
Answer:D
Question: Convert 300 miles into km?
A.360km
B.480km
C.510km
D.320km
Answer: B.480km
Explanation: 1 mile = 1.6 km approximately
300mile = 300*1.6 = 480km
Answer is B
Question: What number continues the sequence?
25, 50, 27, 46, 31, 38, 39, ?
A.21
B.22
C.23
D.24
Answer: B.22
Explanation: B
22
There are two alternate sequences, the first increases by 2, 4, 8 etc and the second decreases by 4, 8, 16 etc.
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 4, what is the greatest number of four-digit extensions that the company can have?
A.4
B.6
C.12
D.16
Answer: C.12
Explanation: Since the phone number must be even, the unit's digit can be either 2 or 4.
When the unit's digit is 2 --> number of possibilities is 3! = 6
When the unit's digit is 4 --> number of possibilities is 3! = 6
Largest number of extensions = 6 + 6 =12
Answer:C
Question: A couple spent $198 in total while dining out and paid this amount using a credit card. The $198 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food. What was the actual price of the food before tax and tip?
A.$130
B.$140
C.$150
D.$160
Answer: C.$150
Explanation: Let the price of the meal be x.
After a 10% sales tax addition, the price is 1.1*x
After a 20% tip on this amount, the total is 1.2*1.1*x = 1.32x
1.32x = 198
x = $150
The correct answer is 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.5 kmph
B.7 kmph
C.9 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: T is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in T?
I. 9
II. 15
III. 27
A.I only
B.II only
C.I and II only
D.I and III only
Answer: C.I and II only
Explanation: Solution:
T->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
A.16
B.15
C.17
D.18
Answer: D.18
Explanation: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Question: Four bells begin to toll together respectively at the intervals of 8, 10, 12 and 16 seconds. After how many seconds will they toll together again?
A.246 seconds
B.242 seconds
C.240 seconds
D.243 seconds
Answer: C.240 seconds
Explanation: LCM of 8,10,12 and 16 is
240
LCM=240
ANSWER:C
Question: The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse.
A.17
B.18
C.19
D.20
Answer: A.17
Explanation: Let a and b be the two sides of the triangle such that a is longer than b. The statement "the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle" may be fomulated by
h = a + 2 or a = h - 2
The statement "the shorter side of the triangle is 7 centimeters less than the longer side" may be formulated .
b = a - 7 or b = (h - 2) - 7 = h - 9
We now use Pythagora's theorem to write a third equation
h 2 = a 2 + b 2
Substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only.
h 2 = (h - 2) 2 + (h - 9) 2
Simplify and rewrite the above equation in standard form.
h 2 -22 h + 85 = 0
Solve for h.
h = 5 and h = 17.
Only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle.
Answer A
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.800 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
A.3999
B.10000
C.2500
D.2772
Answer: B.10000
Explanation: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 800
B capital = 60000*1/6 = 10000.Answer: B
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
A.24
B.27
C.20
D.35
Answer: C.20
Explanation: C
20
x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Question: How many hours are there in 1200 minutes?
A.10
B.20
C.85
D.86
Answer: B.20
Explanation: We know that there are 60 minutes in 1 hour.Divide the number of minutes by the number of minutes in 1 hour. We get, divide 1200 by 601200 ÷ 60 = 20
So there are 20 hours in 1200 minutes.
ANSWER IS B
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
A.11
B.20
C.99
D.77
Answer: B.20
Explanation: 900 ---- 180
100 ---- ? => 20%
Answer: B
Question: Of the 75 cars on a car lot, 45 have air-conditioning, 35 have power steering, and 12 have both air-conditioning and power steering. How many of the cars on the lot have neither air-conditioning nor power steering?
A. 7
B. 8
C. 10
D. 15
Answer: A. 7
Explanation: Total -Neither = All Air Conditioning + All Power steering - Both
or 75 - Neither = 45 + 35 -12 = 68.
=> Neither = 7, hence A.
Answer : A
Question: When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/3 of its capacity. In terms of n, what is the capacity of the tank, in liters?
A.1/2 n
B.4/3 n
C.3/2 n
D.9/4 n
Answer: A.1/2 n
Explanation: A is the answer.
To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.
Given
- tank was already 1/3 full.
- When n ltr added, it became 7/3
So 1/3 + n = 7/3
n = 7/3 - 1/3
n = 6/3
capacity of the tank is full fraction . i.e. 1 i.e. 3/3
so the question is 3/3 is how much times n
= 3/3 = 1 = xn
so x = 3/6
and total = 3/6n=1/2n
Question: If r < y < -1, which of the following is true?
A.r/y > ry
B.y/r > r+y
C.y/r > ry
D.y/r < r+y
Answer: B.y/r > r+y
Explanation: Consider :
r= -3
y= -2
then put for every option. U'll get ans B.
Question: Find the value of 72518 x 9999 = m?
A.345434667
B.246465757
C.465767867
D.725107482
Answer: D.725107482
Explanation: 72518 x 9999 = 72518 x (10000 - 1)
= 72518 x 10000 - 72518 x 1
= 725180000 - 72518
= 725107482
D
Question: If the sides of a triangle are 26 cm, 18 cm and 10 cm, what is its area?
A.90
B.110
C.130
D.140
Answer: A.90
Explanation: The triangle with sides 26 cm, 18 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 18 * 10 = 90 cm2
Answer: Option A
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.6 kmph
C.5 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: Ramesh can finish a piece of work in 16 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?
A.8/3 days
B.9/3 days
C.16/3 days
D.11/3 days
Answer: C.16/3 days
Explanation: Ramesh can finish a piece of work in 16 days. Rohan is twice as efficient as Ramesh.
So Rohan can finish a piece of work in 8 days.
days needed to finish the same amount of work = 1/(1/8+1/16)=16/3 days
ANSWER:C
Question: A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A.10
B.8
C.6
D.4
Answer: C.6
Explanation: Explanation:
Distance = 110 m
Relative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= m/sec = m/sec
Time taken to pass the man = = 6 s
ANSWER IS C
Question: a,b and c are positive integers less than or equal to 9 and multiple of 3. If a,b and c are assembled into the three-digit number abcabc, which of the following must be a factor of abcabc?
A.6
B.4
C.7
D.5
Answer: A.6
Explanation: as a, b and c are multiple of 3, they can be written as a=3l, b=3m and c=3n. the sum of digits of abc is a+b+c = 3(l+m+n+l+m+n)=6(l+m+n).
Thus, 6 is always a factor.
Answer: A
Question: y =x^2 + bx + 128 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
A.-129
B.-132
C.32
D.64
Answer: A.-129
Explanation: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form of ax^2+bx+c=0,
The product of the roots =c/a= 128/1 = 64 and the sum of the roots =-b/a=-b/1
128 can be expressed as product of two numbers in the following ways:
1 * 128
2 * 64
4 * 32
8 * 16
The sum of the roots is maximum when the roots are 1 and 128 and the maximum sum is 1 + 128 = 129.
The least value possible for b is therefore -129.
a
Question: Last year a certain bond yielded 12 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.$6,000
B.$6,750
C.$7,425
D.$2,500
Answer: D.$2,500
Explanation: Interest = 0.12*face value = 0.04*7,500 --> face value = 0.04*7,500/0.12 = 2,500.
Answer: D.
Question: A bakery currently has 5 pies and 6 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
A.3/11
B.25/77
C.5/11
D.7/11
Answer: B.25/77
Explanation: We need the probability that the owner will select PPPCC: 5!/3!∗2!∗(5/11∗4/10∗3/9)∗(6/8∗5/7)=25/77, we are multiplying by 5!/3!∗2! since PPPCC scenario can occur in number of ways: PPPCC, PPCPC, PCPPC, CPPPC, ... Notice that the number of occurrences of PPPCC basically is the number of arrangements of 5 letters PPPCC out of which 3 P's and 2 C's are identical, so it's 5!/3!∗2!
Answer: B.
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
A.22 sec
B.16 second
C.77 sec
D.55 sec
Answer: B.16 second
Explanation: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer:B