RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
A.110.12 meters
B.111.12 meters
C.112.12 meters
D.113.12 meters
Answer: B.111.12 meters
Explanation: Explanation:
A runs 1000 meters while B runs 900 meters and C runs 800 meters.
Therefore, B runs 900 meters while C runs 800 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 800)/900 = 8000/9 = 888.88 meters
Thus, B can give C (1000 - 888.88) = 111.12 meters start
ANSWER IS B
Question: A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train ?
A.240 mts
B.270 mts
C.260 mts
D.250 mts
Answer: A.240 mts
Explanation: Explanation:
Relative speed = 120 + 80 = 200 km/hr.
= 200 x 5/18 = 500/9 m/sec.
Let the length of the other train be L mts.
Then, (L + 260)/9 = 500/9 => L = 240 mts.
ANSWER IS A
Question: A baker charges M dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?
A.2
B.4
C.6
D.8
Answer: D.8
Explanation: We're told that by selling cakes at M dollars/cake, a baker will make $320.
Reducing the price by 20% and selling 2 MORE cakes will also make her $320.
We're asked for the original number of cakes that the baker intends to sell.
$320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....
Let's TEST ANSWER D: 8 cakes
IF....
Original cakes = 8
8(M) = $320, so M = $40/cake
20% off = $8 off = 40-8 = $32/cake
+2 more cakes = 8+2 = 10 cakes
10(32) = $320
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
D
Question: You need to pick any number from '1, 3, 5, 7, 9, 11, 13 and 15' to make below equation true.
( ) + ( ) + ( ) = 30
Can you solve it ?
A.29
B.30
C.31
D.32
Answer: B.30
Explanation: Solution:
3! + 15 + 9 = 30
Explanation:
3! = 3 * 2 * 1 = 6
6 + 15 + 9 = 30
Answer B
Question: If there are thrice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?
A.3⁄20
B.11⁄60
C.9⁄40
D.1⁄10
Answer: D.1⁄10
Explanation: Consider a group of 100 men and 300 women, a total of 400 people. 30% of them, which is 120, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 60.
It means that there are 100 - 60 = 40 men who own a car, and this represents 40/400 = 1/10 of the total.
Answer D
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
A.16 2/3 days
B.13 1/3 days
C.17 1/3 days
D.16 1/2 days
Answer: B.13 1/3 days
Explanation: 5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
ANSWER:B
Question: If |x| = 5x - 3, then x = ?
A.1
B.1/2
C.2
D.-1/2
Answer: C.2
Explanation: Answer: A
Approach:
Substituted option A i.e x=1. Inequality satisfied.
C
Question: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4,5 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY5?
A.12/15
B.5/6
C.4/5
D.7/3
Answer: A.12/15
Explanation: If a number is divisible by 5 the last 1 digits of the number has 5.
If the number ends with 15: Number of possibilities = 4*3 * 2 * 1 = 24
number ends with 25: Possibilities = 4*3 * 2 * 1 = 24
number ends with 35: Possibilities =24
number ends with 45: Possibilities =24
Total number of possibilities with restriction = 24*4= 96
Total number of possibilities without restriction = 5! = 120
Probability = 96/120 = 12/15
Answer: A
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
A.150
B.997
C.266
D.288
Answer: A.150
Explanation: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer:A
Question: Kid have 8 black balls and 8white balls. He is trying to arrange a ball in a row then in how many ways can he arrange these balls in a row so that balls of different colors alternate?
A.(8!)^2
B.2×(8!)
C.2×(8!)^2
D.2^2
Answer: C.2×(8!)^2
Explanation: 8 black balls can be arranged in 8! ways ...(A)
Now we need to arrange white balls such that white balls and black balls are positioned alternatively. i.e., we can arrange 8 white balls either in the 8 positions marked as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I as shown below.
8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H in 8! ways.
8 white balls can be arranged in the 8 positions marked as B,C,D,E,F,G,H,I in 8! ways.
8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I in 8!+8!=2×8! ways ...(B)
From (A) and (B),
required number of ways =8!×2×8!=2×(8!)^2
C
Question: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 6. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
A.8
B.9
C.10
D.11
Answer: D.11
Explanation: Since it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4.
so ans can either be 8 0r 12.
With 8 as answer - no of girls = 8
With 12 as answer - no of girls = 12
Now Class A has one more boy and two more girls than class B and also the ratio of boys to girls in Class B is 4 to 5.
So we are looking for number of girls in B to be divisible by 5.
With 8 as answer -> Girls = 8-2 = 6. (Not possible)
With 12 as answer -> Girls = 12-2 = 5.
So, answer = 11. ( D)
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
A.8000
B.8877
C.2877
D.2678
Answer: A.8000
Explanation: 8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000
Answer: A
Question: According to a recent student poll, 4/5 out of 25 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
A.29/30
B.4/49
C.2/7
D.45/49
Answer: A.29/30
Explanation: 20 students are interested, 5 are not interested
Prob = 1 - 5C2/25C2 = 1 - (5*4/(25*24))=1 - 1/30 = 29/30
Answer : A
Question: A gardener wants to plant trees in his garden in rows in such away that the number of trees in each row to be the same. If there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row?
A. 63 B. 28?
A.11
B.28
C.16
D.19
Answer: B.28
Explanation: Required number of trees
= 24/36 * 42 = 28.
Answer: B
Question: 3034 - (1002 / 20.04) = ?
A.2984
B.2983
C.2982
D.2981
Answer: A.2984
Explanation: Option A
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time Q will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did?
A.2 minute and 12 seconds.
B.two minutes.
C.44 seconds.
D.20 seconds.
Answer: D.20 seconds.
Explanation: Tom is running alone for 20 seconds.
So he will cover a distance of 20*2.5 = 50 m in 20 seconds=Q
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side
D is the answer
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
A.5 hours
B.6 hours
C.3 hours
D.9 hours
Answer: C.3 hours
Explanation: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.Answer: C
Question: A lends Rs. 2500 to B and a certain to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives Rs. 1120 as interest from B and C, then the sum lent to C is?
A.2998
B.1500
C.2878
D.299
Answer: B.1500
Explanation: Let the sum lent to C be Rs. x. Then,
(2500 * 7 * 4) / 100 + (x * 7 * 4) / 100 = 1120
7/25 x = (1120 - 700) => x = 1500
Answer: B
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 54 kmph, find the speed of the stream?
A.77
B.18
C.14
D.12
Answer: B.18
Explanation: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 54/3 = 18 kmph.
Answer:B
Question: An engineering student has to secure 36% marks to pass. He gets 130 marks and fails by 14 marks. The maximum number of marks obtained by him is?
A.337
B.400
C.298
D.2798
Answer: B.400
Explanation: 130
14
-------
361------ 144
100%------? => 400
Answer:B
Question: Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 9.5 km apart, if they walk in the same direction?
A.19 hrs
B.14 hrs
C.15 hrs
D.17 hrs
Answer: A.19 hrs
Explanation: Sol.
to be 0.5 km apart, they take 1 hour.
To be 9.5 km apart, they take [1/0.5 * 9.5] hrs = 19 hrs.
Answer A
Question: Raju age after 23 years will be 5 times his age 5 years back, What is the present age of Raju
A.10 years
B.11 years
C.13 years
D.12 years
Answer: D.12 years
Explanation: Explanation:
Clearly,
x+23 = 5(x-5)
<=> 4x = 48 => x = 12
Option D
Question: Shop Offered 40% offer for every Shirt, Smith bought a shirt at Rs. 560. and What was the shop's original selling Price?
A.500
B.550
C.600
D.933
Answer: D.933
Explanation: SP* (60/100) = 560
SP= 9.33 * 100 => CP = 933
Answer:D
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
A.1:00pm, 220 km
B.1:00pm, 200km
C.2:00pm, 200 km
D.2:00pm, 220 km
Answer: C.2:00pm, 200 km
Explanation: Explanation:
When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.
ANSWER IS C
Question: If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
A.4 days
B.5 days
C.6 days
D.7 days
Answer: A.4 days
Explanation: Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, 6x + 8y = 1/10 and 26x + 48y = 1/2
Solving these two equations, we get : x = 1/100 and y = 1/200
(15 men + 20 boy)'s 1 day's work = (15/100 + 20/200) = 1/4
15 men and 20 boys can do the work in 4 days.
Answer = A
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
A.neither profit nor loss
B.1%
C.7%
D.6%
Answer: A.neither profit nor loss
Explanation: Explanation:
Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: A
Question: A Deer passed a certain tree at a constant speed of 50 miles per hour while being chased by a Cheetah. Then, 2 minutes later, the Cheetah passed the same tree at a constant speed of 60 miles per hour. If both animals maintained their speeds, how long after the Cheetah passed the tree did the Cheetah catch up with the deer?
A.30 min
B.3 min
C.1 hr
D.1 min
Answer: D.1 min
Explanation: When the Cheetah is at the tree, the deer is 50/30 miles ahead on the highway. (the distance covered in 2 min)
every hour, Cheetah runs 10miles more than the deer. how many hours will it takes it to cover 50/30 miles more? the answer is (50/30)/10 = 1/60=1 min
Answer D
Question: Peeta asks Katniss, 'It is 9 pm as per my watch right now.Do you know what will be the time 23, 999, 997 hours later?'
A.5 pm.
B.4 pm.
C.6 pm.
D.7 pm.
Answer: C.6 pm.
Explanation: Solution:
6pm
Explanation:
The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer C
Question: The quarter of the time from midnight to present time added to the half of the time from the present to midnight gives the present time. What is the present time?
A.9 hr 30 min
B.9 hr 36 min
C.9 hr 46 min
D.8 hr 36 min
Answer: B.9 hr 36 min
Explanation: let the present time be t
given that t/4+(24-t)/2=t
so time is 9 hr 36 min
ANSWER:B
Question: Of 70 players on a football team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
A.54
B.59
C.63
D.71
Answer: B.59
Explanation: 37 are throwers and right handed
1/3 of remaining 33, i.e 11 are left handed and remaining are right handed.
Basically, out of 70, only 11 are left handed and remaining 70-11= 59 are right handed.
B is the answer
Question: . There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?
A.10420
B.11
C.11760
D.11640
Answer: C.11760
Explanation: We need to select 5 men from 8 men and 6 women from 10 women
Number of ways to do this
= 8C5 × 10C6
= 8C3 × 10C4 [∵ nCr = nC(n-r)]
=((8×7×6)/(3×2×1))*((10×9×8*7)/(4×3×2×1))
=56×210
=11760
ANSWER:C
Question: Out of 7 people working on a project, 3 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
A.17/20
B.21/25
C.23/30
D.31/35
Answer: D.31/35
Explanation: P(no graduates) = 4C3 / 7C3 = 4/35
P(at least one graduate) = 1- 4/35 = 31/35
The answer is D.
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
A.22
B.88
C.27
D.20
Answer: D.20
Explanation: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20.Answer: D
Question: A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
A.21%
B.77%
C.44%
D.16%
Answer: A.21%
Explanation: g% = 10 + 10 + (10*10)/100
= 21%
Answer: A
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
A.0 sq m
B.8 sq m
C.2 sq m
D.8sq m
Answer: A.0 sq m
Explanation: Explanation:
S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer: Option A
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
A.Rs.49
B.Rs.40
C.Rs.44
D.Rs.42
Answer: C.Rs.44
Explanation: Explanation:
π (152 - 132) = 176
176 * 1/4 = Rs.44
Answer: Option C
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 75 <=> 5x - 25 = 75 <=> x = 20.
Therefore, Length of the rectangle = 20 cm.
Answer is D
Question: A six-sided die is rolled once. What is the probability that the number rolled is an odd number greater than 2?
A.2 / 6
B.1 / 2
C.3 / 3
D.4 / 5
Answer: A.2 / 6
Explanation: 2 / 6
correct answer A
Question: What is the principal sum?
I. The sum amounts to Rs. 780 at a rate of 8% p.a. at S.I.
II. The sum amounts to Rs. 1000 in 5 years at S.I.
III. The rate of interest is 8% p.a.
A.I and III only
B.II and III only
C.I and II only
D.Any two of the three
Answer: B.II and III only
Explanation: Explanation:
Clearly, Only the statement II and III is needed and cant be able to find by using I statement
Answer: B
Question: X can do 1/4 of a work in 10 days, Y can do 40% of work in 40 days and Z can do 1/3 of work in 13 days. Who will complete the work first?
A.D
B.F
C.X
D.Z
Answer: D.Z
Explanation: Whole work will be done by X in 10*4 = 40 days.
Whole work will be done by Y in (40*100/40) = 100 days.
Whole work will be done by Z in (13*3) = 39 days
Therefore, Z will complete the work first. The answer is D.
Question: How many different arrangements of A, B, C, D, and E are possible where A is adjacent to neither B nor D?
A.96
B.60
C.48
D.36
Answer: D.36
Explanation: Total # of permutation of 5 distinct letters will be 5!=120;
Glue A and B together, consider it to be one unit: {AB}{C}{D}{E} --> # of permutation of these 4 units will be 4!=24, A and B within its unit also can be arranged in 2 ways : {AB} or {BA}, so total # of ways to arrange A, B, C, D, and E so that A and B to be together will be 4!*2=48;
The same for A and D: total # of ways to arrange A, B, C, D, and E so that A and D to be together will be 4!*2=48;
Now, the above 48+48=96 cases will contain the arrangements when A is adjacent to both B and D, so we should subtract this cases to get rid of the double counting. The # of case when A is adjacent to both B and D will be: consider {BAD} {C}{E} --> # of permutation of these 3 units will be 3!, {BAD} also can be arranged in 2 ways: {BAD} or {DAB}, so total # of ways to arrange A, B, C, D, and E so that A is adjacent to both B and D will be 3!*2=12;
The # of arrangements when A is adjacent to neither B nor D will be total-(48+48-12)=120-84=36.
Answer: D.
Question: A boy asked a girl her name she replied your name is behind your scooty Behind the scooty is written 7.3 3.3 9.3 2.3 What is her name
A.RIAE
B.RIAF
C.RIAG
D.RIBF
Answer: B.RIAF
Explanation: 7.3=21=r
3.3 =9=i
9.3=27%26=1=a
2.3=6=f
ANSWER=RIAF
ANSWER:B
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.79.7
B.79.9
C.79.5
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 jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the direction opposite to that in which the train is going ?
A.3.6sec
B.18sec
C.36sec
D.72sec
Answer: C.36sec
Explanation: Solution
Speed of train relative to jogger =(45-9)km/hr =36km/hr
(36*5/18)m/sec = 10 m/sec
Distance to be covered = (240 +120)m= 360m
∴ Time taken =(360/10)sec= 36 sec
Answer C
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 24 hrs and a machine of type S does the same job in 12 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
A.3
B.4
C.6
D.8
Answer: B.4
Explanation: Type R completes 1/24 of the job each hour.
Type S completes 1/12 of the job each hour.
Together R and S complete 1/24 +1/12 = 1/8 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/8) = 1 job completed
n = 4
The answer is B.
Question: How many ways are there to split a group of 10 students into two groups of 5 students each? (The order of the groups does not matter)
A.104
B.126
C.148
D.172
Answer: B.126
Explanation: 10C5 = 252
If we consider these groups, each group will be counted twice.
The number of ways to choose 2 groups of 5 is 252/2 = 126
The answer is B.
Question: In a graduating class, 40 percent of the students are male. In this class, 40 percent of the male students and 30 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
A.0.66
B.0.72
C.0.78
D.0.84
Answer: A.0.66
Explanation: Let x be the total number of students.
The number students who are younger than 25 is 0.6*0.4x+0.7*0.6x = 0.66x
The answer is A.
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
A.5M
B.4M
C.9M
D.2M
Answer: D.2M
Explanation: Explanation:
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: Option D
Question: How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.26 sec
B.30 sec
C.24 sec
D.19 sec
Answer: C.24 sec
Explanation: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 400 * 3/50
= 24 sec.
Answer:C
Question: In 2008, the profits of Company N were 8 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
A.150%
B.105%
C.120%
D.124.2%
Answer: A.150%
Explanation: the profit 0f 2009 interms of 2008 = 0.8*15/8*100=150%
A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
A.298 m
B.178 m
C.197 m
D.150 m
Answer: D.150 m
Explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time
= 50/3 * 9
= 150 m
Answer:D
Question: How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
A.254
B.100
C.132
D.503
Answer: B.100
Explanation: 1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be ‘n’.
Therefore, using ‘n’ alphabets we can form n * n * n = n^3 distinct 3 digit initials.
Note distinct initials is different from initials where the digits are different.
For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This n^3 different initials = 1 million
i.e. n^3 = 106 (1 million = 106)
=> n^3 = (102)^3 => n = 102 = 100
Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.
Ans:B
Question: The sum of the present age of Henry and Jill is 43. What is their present ages if 5 years ago Henry was twice the age of Jill?
A.and 27
B.and 24
C.and 22
D.and 29
Answer: A.and 27
Explanation: Let the age of Jill 5 years ago be x, age of Henry be 2x
x+5 + 2x+5 = 43
x = 11
Present ages will be 16 and 27
Answer : A
Question: Diana can buy watches at a price of M dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of T by selling N watches, then in terms of M and T and N, what is the percent of the markup from her buy price to her sell price?
A.100-N/T
B.NMT/100
C.N-M/100T
D.100T/(NM)
Answer: D.100T/(NM)
Explanation: Algebraic Solution:If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (T/N)/M *100 = 100T/(NM)
Answer : D