mathewhe/aqua_rat huggingface dataset:
Question: In a covering a certain distance the speed of A and B are in the ratio of 6: 9, A takes 20 min more, than B to reach the destination. The time taken by A to reach the destination is:
(A) 1 Hour
(B) 2 Hours
(C) 1.5 Hours
(D) 2.5 Hours
(E) 3 Hours
Rationale: Let the speed of A and B are 6x Kmph
and 9x Kmph respectively,
Let the total distance to travel = y Km
y/6x - y/9x = 1/3
y/x(1/18 = 1/3
y = 6x
Required time = 6x/6x = 1 hour
Answer A.
Answer: (A) 1 Hour
Question: In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
(A)  215,000
(B)  216,000
(C)  217,000
(D)  218,000
(E)  219,000
Rationale: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 7-2 = 5 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 5 = 216,000. Hence B.
Answer: (B)  216,000
Question: 9 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
(A) 40587
(B) 60451
(C) 16152
(D) 24325
(E) 40320
Rationale: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 9
hence ans = 8 factorial = 40320
hence E
Answer: (E) 40320
Question: A is twice as fast as B. If B alone can do a piece of work in 24 days, in what time can A and B together complete the work?
(A) 10
(B) 12
(C) 6
(D) 2
(E) 8
Rationale: A can do the work in 24/2 i.e., 12 days.
A and B's one day's work = 1/12+ 1/24 = (2 + 1)/24 = 1/8
So A and B together can do the work in 8 days.
Answer: E
Answer: (E) 8
Question: The expression (5x-2)/(x+3) is equivalent to which of the following?
(A) (5-2)/3
(B) 5 – (2/3)
(C) 5 – (x)/(x+3)
(D) 5 – (17)/(x+3)
(E) 5 + (17)/(x+3
Rationale: iven asked to find the value of (5x-2)/(x+3)...
Now take X as 1 then we get 3/4...
From the options check which one gets the same 3/4.
From option D = 5 – (17)/(x+3) => 5 - (17)/(1+3) => 3/4.. All other options will result in some other value..
Answer: D is the correct option
Answer: (D) 5 – (17)/(x+3)
Question: From a group of 7 women and 6 men, five persons are to be selected to form a committee so that at least 3 women are there in the committee. In how many ways can it be done?
(A) A)650
(B) B)656
(C) C)696
(D) D)724
(E) E)756
Rationale: From a group of 7 women and 6 men, five persons are to be selected with at least 3 men.
Hence we have the following 3 options.
We can select 5 women ...(option 1)
Number of ways to do this = 7C5
We can select 4 men and 1 man ...(option 2)
Number of ways to do this = 7C4 × 6C1
We can select 3 women and 2 men ...(option 3)
Number of ways to do this = 7C3 × 6C2
Total number of ways
= 7C5 + (7C4 × 6C1) + (7C3 × 6C2)
= 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ]
=
7
×
6
2
×
1
+
7
×
6
×
5
3
×
2
×
1
×
6
=7×62×1+7×6×53×2×1×6
+
7
×
6
×
5
3
×
2
×
1
×
6
×
5
2
×
1
+7×6×53×2×1×6×52×1
=
21
+
210
+
525
=
756
=21+210+525=756
E)
Answer: (E) E)756
Question: There are 9 color balls at a row. From that how many ways can 9 different color balls be arranged in a row so that black, white, red and green are never together?
(A) 223600
(B) 214600
(C) 566600
(D) 786789
(E) 345600
Rationale: Total number of ways in which 9 different colour balls can be arranged in a row
=9! ⋯(A)
Now we will find out total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are always together.
We have total 9 balls. Since black, white, red and green balls are always together, group these 4 balls together and consider as a single ball. Hence we can take total number of balls as 6. These 6 balls can be arranged in 6! ways.
We had grouped 4 balls together. These 4 balls can be arranged among themselves in 4! ways.
Hence, total number of ways in which 9 different colour balls be arranged in a row so that black, white, red and green balls are always together
=6!×4! ⋯(B)
From (A) and (B),
Total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are never together
=9!–6!×4!=6!×7×8×9−6!×4!=6!(7×8×9–4!)=6!(504–24)=6!×480=720×480=345600
E
Answer: (E) 345600
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
(A) 76
(B) 21
(C) 26
(D) 28
(E) 11
Rationale: Explanation:
Lot the total number of workers be v Then,
8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21.
Answer: B
Answer: (B) 21
Question: The area of a triangle is with base 4m and height 8m?
(A) 11
(B) 10
(C) 787
(D) 16
(E) 12
Rationale: 1/2 * 4 * 8 = 16 m2
Answer: D
Answer: (D) 16
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 400 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 400xy
(B) 400y - x
(C) 400x - y
(D) 400x/y
(E) 400y/x
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
400 = d/(x*pi)
d = 100 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (400 * x * pi) / (y*pi) = 400x/y
Answer (D)
Answer: (D) 400x/y
Question: A pupil's marks were wrongly entered as 73 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
(A) 56
(B) 80
(C) 20
(D) 25
(E) 26
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (73 - 45)
=> X/2 = 28
=> X = 56.
ANSWER:A
Answer: (A) 56
Question: Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?
(A) 20
(B) 90
(C) 10
(D) 80
(E) 70
Rationale: D
80
We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300
D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.
Answer: (D) 80
Question: The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 180,000. What was the percent increase in the cost of the home?
(A) 60%
(B) 50%
(C) 55%
(D) 40%
(E) 33.3%
Rationale: Percentage Increase = Increase in price / original price *100= (180000-120000)/120000*100=50%
Answer: B
Answer: (B) 50%
Question: a boy average marks in five subject is 60.he score 90 in math,in physics he scores 95.in rest three in how much maximum subject he can score more than or equal to 95.
(A) 1
(B) 2
(C) 3
(D) 0
(E) 4
Rationale: addition of marks of all five subject=300.
math+physics=185
sum of three subject marks=300-185=115
here it is clearly visible that he can only score more than 95 in one subject if he will score more than 95 in two then it will exceed 115 because marks are not in negative.
answer A
Answer: (A) 1
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is?
(A) 75
(B) 78
(C) 80
(D) 82
(E) 86
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86
E)
Answer: (E) 86
Question: A and B entered into a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months C joins the business with a capital of Rs. 21000. The share of B exceeds that of C, out of a total profit of Rs. 26400 after one year by
(A) Rs. 3200
(B) Rs. 3400
(C) Rs. 3600
(D) Rs. 3800
(E) None of these
Rationale: Explanation:
A:B: C = 16000*3 + 11000*9:12000*3 + 17000*9:21000*6
= 147:189:126 = 7:9:6
Difference of B and C’s shares =
Rs. [26400 * (9/22) — 26400 * (6/22))
= Rs. 3600
Option C
Answer: (C) Rs. 3600
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 500?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^8 = 256 < 500, then the greatest possible length of integer z is 8.
The answer is C.
Answer: (C) 8
Question: X and Y are two points respectively on sides AB and AC of triangle ABC such that XY is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium XYCB is 25:144 and BC=13 cm, then find the length of XY.
(A) 12
(B) 13
(C) 14
(D) 11
(E) 5
Rationale: ABC and AXY are similar triangles.
So (side of ABC/side of AXY)^2=169/25
side of ABC/side of AXY = 13/5
So the length of XY = 5
Answer - E
Answer: (E) 5
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $6.30?
(A) 426
(B) 430
(C) 443
(D) 410
(E) 486
Rationale: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 6.3$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 0.3 $ left. so we buy 10 individual envelopes. If we add up the numbers, we get 400+10=410 envelopes. Answer D
Answer: (D) 410
Question: A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 20 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.
(A) 34
(B) 32
(C) 36
(D) 38
(E) 40
Rationale: Let the speed of bus be v - 20, speed of taxi be v
The bus travelled a total of 8 hrs and taxi a total of 3 hrs.
Hence 8 * (v-20) = 3v
8v - 160 = 3v
5v = 160
v = 32 mph
B
Answer: (B) 32
Question: The average temperature from Tuesday to Friday is 48°C and from Wednesday to Saturday is 52°C. If the temperature on Tuesday is 42°C, what was it on Saturday?
(A) 52°C
(B) 55°C
(C) 58°C
(D) 51°C
(E) 53°C
Rationale: Temperature on Tuesday + Wednesday + Thursday + Friday = 4 x 48°C = 192°C
Temperature on Tuesday = 42°C
Thus, Wednesday + Thursday + Friday = (192°C - 42°C) = 150°C
Temperature on Wednesday + Thursday + Friday + Saturday = 4 × 52°C = 208°C
Thus, Saturday’s temperature = 208 - 150°C = 58°C
ANSWER:C
Answer: (C) 58°C
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 5.5), (8, 0), (0, -5.5), (-8, 0)?
(A) 56
(B) 88
(C) 112
(D) 116
(E) 120
Rationale: Ares of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 8+8= 16
Length of 2nd diagonal= 5.5+5.5= 11
Area= 1/2*16*11= 88
B is the answer
Answer: (B) 88
Question: A man engaged a servant on the condition that he would pay him Rs.600 and a uniform after one year service. He served only for 9 months and received uniform and Rs.400, find the price of the uniform?
(A) s.80
(B) s.85
(C) s.90
(D) s.100
(E) s.200
Rationale: 9/12 = 3/4 * 600 = 450
400
-------------
50
1/4 -------- 50
1 --------- ? => Rs.200
ANSWER:E
Answer: (E) s.200
Question: If a young child was 17 months old one year ago, how old was the child, in months, x months ago?
(A) x − 29
(B) x − 12
(C) 17 − x
(D) 24 − x
(E) 29 − x
Rationale: The child's age today is 17 months + 12 months = 29 months
x months ago, the child's age was (29 - x) months old.
The answer is E.
Answer: (E) 29 − x
Question: When positive integer N is divided by positive integer J, the remainder is 11. If N/J = 724.04, what is value of J?
(A) 140
(B) 150
(C) 260
(D) 275
(E) 280
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 724.04
Here 724 is the quotient.
Given that Remainder = 11
So, 724.04 = 724 + 11/J
So, J = 275
Answer: (D) 275
Question: Find the side of the largest possible square slabs which can be paved on the floor of a room 2 m 50 cm long and 1 m 50 cm broad. Also find the number of such slabs to pave the floor.
(A) 25, 20
(B) 30, 15
(C) 50, 15
(D) None of these
(E) 75,35
Rationale: Explanation:
HCF (250, 150) = 50 cm
The number slabs = 250 *150/ 50*50
=15
Answer: C
Answer: (C) 50, 15
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 88
(E) 98
Rationale: Explanation:
We have: l = 20 ft and lb = 680 sq. ft.
So, b = 34 ft.
Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.
Answer: D
Answer: (D) 88
Question: A farmer brought 76 cows, the price of each cow being the same and then sold 20 cows at a profit of 15%, 40 cows at a profit of 19% and the remainder at a profit of 25% making a total profit of Rs.26,280. What is the cost price of each cow?
(A) Rs.1000
(B) Rs.1800
(C) Rs.1500
(D) Rs.1400
(E) Rs.2500
Rationale: Let cost price of each Cow is x.
Total Cost of 76 Cows = 76x.
SP of 20 Cows = 20x + 15% of 20x
SP of 20 Cows = 20x + 3x = 23x
SP of 40 Cows = 40x + 19% of 40x = 47.6x
SP of remaining cows (16 cows) = 16x + 25% of 16x = 20x
Total selling price of 76 cows = 23x + 47.6x + 20x = 90.6x.
Total Profit = Rs. 26280
Total SP - Total CP = Total Profit
90.6x - 76x = 26280
14.6x = 26280
x = 1800.
CP of each Cow is Rs. 1800.
ANSWER :OPTION B
Answer: (B) Rs.1800
Question: Bus 1 and Bus 2 run between cities A and B. Bus 1 leaves city A at the same time Bus 2 leaves city B,
each at a constant rate of speed. Their first meeting is 60 miles from city A. After reaching their
respective destinations and immediately turning around, their second meeting is 30 miles from city B.
What is the distance in miles between city A and city B?
(A) 90
(B) 120
(C) 125
(D) 150
(E) 180
Rationale: let d=distance between cities A and B
bus 1 distance to first meeting=60 miles
bus 1 distance from first to second meeting=(d-60)+30=d-30 miles
bus 2 distance to first meeting=d-60 miles
bus 2 distance from first to second meeting=60+(d-30)=d+30 miles
because both buses take the same time for the pre-meeting leg, and
the same time for the inter-meeting leg, and their speeds remain
constant, their ratios between pre-meeting distance and inter-meeting
distance should be the same
therefore, 60/(d-30)=(d-60)/(d+30)
d^2=150d
d=150 miles
D
Answer: (D) 150
Question: If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?
(A) 87
(B) 40
(C) 37
(D) 28
(E) 26
Rationale: A.M. of 75 numbers = 35
Sum of 75 numbers = 75 * 35 = 2625
Total increase = 75 * 5 = 375
Increased sum = 2625 + 375 = 3000
Increased average = 3000/75 = 40.
Answer:B
Answer: (B) 40
Question: A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1300. How many workers were part of the latter production run?
(A) A)6
(B) B)10
(C) C)9
(D) D)15
(E) E)23.5
Rationale: The daily average production is given by 5n + 20- given
In the first k days, 500 units are produced
= (5n+20)K =500
k = 500/5n+20...................................1
5 workers were added = 5(n+5)+20 = 5n +45
cumulative is 1300 .. thus for the current period = 1300 -500 = 800
(5n+45)K= 800
k = 800/5n+45........................................2
equate 1 and 2
500/5n+20 = 800 /5n+45
500(5n+45) = 800(5n+20)
25n + 225 = 40n + 160
-15n = -65
n = 4
thus n+5 = 9
hence C
Answer: (C) C)9
Question: A car started running at a speed of 36 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
(A) 45 km
(B) 76 km
(C) 25 km
(D) 15 km
(E) 30 km
Rationale: A
45 km
The total distance covered by the car in the first 10 hours = 36 + 38 + 40 + 42 + 44 + 46 + 48+ 50 + 52 + 54= sum of 10 terms in AP whose first term is 36 and last term is 54 = 10/2 [36 + 54] = 450 km.
Answer: (A) 45 km
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
(A) 5/26
(B) 5/78
(C) 5/21
(D) 5/56
(E) 5/12
Rationale: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252
= 5/21
Answer:A
Answer: (A) 5/26
Question: Kristy, Amy, and Blair are going on a cross-country road trip from Washington to Maine. The total driving time is 48 hours. Each driver will drive 6 hours daily and in the remaining hours of the day the group will sight-see and explore. They will sleep in the car when they are not driving. They all have driver's licenses, but Amy is scared of driving in unfamiliar places and would prefer not to take the wheel. How much sooner would the group arrive in Maine, in hours, if Amy chose to drive, compared to just Kristy and Blair?
(A) 12
(B) 24.76
(C) 31.92
(D) 36.92
(E) 24
Rationale: All three girls calculation: 3 girls x 6 hours = 18 hours of driving per day, 6 nondriving hours/day
48 total trip hours divided by 18 daily driving hours = 2.67 days / driving rotations
2.67 x 24 (hours in one day) = 64.08 total hours for road trip
2 girls calculation: 2 girls x 6 hours = 12 hours of driving per day, 12 nondriving hours/day
48 total trip hours divided by 12 daily driving hours = 4 days / driving rotations
4 x 24 (hours in one day) = 96 total hours for road trip
FINAL ANSWER: 96 hours (2 girls total) minus 64.08 (3 girls total) = ANSWER C: The group would arrive in Maine 31.92 hours sooner if all three drove.
Answer: (C) 31.92
Question: P, Q and R can do a work in 10 , 12 and 15 days respectively. What is the share ratio of P, Q and R respectively?
(A) 6 : 5 : 7
(B) 6 : 5 : 4
(C) 6 : 5 : 3
(D) 6 : 4 : 5
(E) 4 : 5 : 6
Rationale: The ratio of their working rates = 1/10 : 1/12 : 1/15 = 6 : 5 : 4.
Answer: B
Answer: (B) 6 : 5 : 4
Question: A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 30 percent, what is the discount rate on mysteries?
(A) 17.18%
(B) 12%
(C) 13%
(D) 14%
(E) 15%
Rationale: Let B be the discount on biographies and M be the discount on mysteries
So., B + M = 0.30 -----(1)
And
(20*5 + 12*3) - (20*5*(1-B) + 12*3*(1-M)) = 19
--> 100(1-(1-B)) + 36(1-(1-M) = 19
100B + 36M = 19 ------(2)
Solving 12., we get M = 0.1718 = 17.18
A
Answer: (A) 17.18%
Question: Amar started a business investing Rs. 34000/-. After 3 months, Vamsi joined him with a capital of Rs. 40000/-. At the end of the year, they make a profit of Rs. 17040/-. What will be Amar’s share in the profit?
(A) Rs. 9025/-
(B) Rs. 9052.5/-
(C) Rs. 9503.5/-
(D) Rs. 9504.5/-
(E) None of these
Rationale: Explanation:
Amar : Vamsi = (34000 * 12 : 40000 * 9)
= 408000 : 360000
= 408 : 300
= 51 : 45
Amar’s share = 17040 * 51/91 = 177.5 * 51 = Rs. 9052.5/-
Answer: Option B
Answer: (B) Rs. 9052.5/-
Question: A bag contains ten marbles of the same size: 3 are identical green marbles, 2 are identical red marbles, and the other 5 are five distinct colors. If 5 marbles are selected at random, how many distinct combinations Q of five marbles could be drawn?
(A)  41
(B)  51
(C)  62
(D)  72
(E)  82
Rationale: there will be different cases, which we will take one by one..
1)case 1 when all five colours are different-7c5=21..
2)case 2 when three different colours and 2 of same type=6c3*2=30..
3)case 3 when two different colours and 3 of same type=6c2=15..
4)case 4 when one different colours and 2 of two different colors=5c1*4!/2!2!=15...
5)case 4 when 3 of one type and 2 of other colour=1...
total Q-82 ans E
Answer: (E)  82
Question: If the greatest common divisor of (n+2)!, (n-1)!, and (n+4)! is 120, what is the value of n?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 3
Rationale: Notice that:
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
So, the smallest factorial must be 5! for the GCD to be 120
The smallest of the three factorials is (n-1)!
So, we need (n-1)! to equal 5!
This means that n = 6
If n = 6, then (n+2)!, (n-1)!, and (n+4)! become 8!, 5! and 10!
Let's CONFIRM this conclusion
8! = (1)(2)(3)(4)(5)(6)(7)(8) = (120)(6)(7)(8)
5! = (1)(2)(3)(4)(5) = 120
10! = (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) = (120)(6)(7)(8)(9)(10)
As you can see, 120 is a divisor of all three factorials.
In fact, 120 is the GREATEST COMMON divisor of all three factorials.
Answer: C
Answer: (C) 6
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
(A) 16:00.
(B) 18:00
(C) 20:00
(D) 22:00.
(E) 24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 3 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 6 hours
Time taken by both buses to meet again in St. Louis will be LCM of 3 and 6 = 6
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours
Answer B
Answer: (B) 18:00
Question: A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes?
(A) 35:1
(B) Either ;35:1
(C) Either 70;35:1
(D) Either 55;45:1
(E) Either 65;35:5
Rationale: Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B)
Answer: (B) Either ;35:1
Question: Let A be the event that a randomly selected two digit number is divisible by 2 and let B be the event that a randomly selected two digit number is divisible by 10. What is P(A and B)?
(A) 1/20
(B) 1/15
(C) 1/12
(D) 1/8
(E) 1/2
Rationale: P(A and B) = 1/2*1/10 = 1/20
The answer is A.
Answer: (A) 1/20
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 65 sec
(B) 16 sec
(C) 18 sec
(D) 13 sec
(E) 76 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken
= 280 * 2/35
= 16 sec
Answer:B
Answer: (B) 16 sec