divelab/Sys2Bench huggingface dataset:
Question: In the first week of the Year, ancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that ancy saved during the 52 weeks?
Options:
A)$1,326
B)$1,352
C)$1,378
D)$2,652
E)$2,756
Rationale: In the first week of the Year, ancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Answer: C
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Options:
A)35.55 km/hr
B)36 km/hr
C)71 km/hr
D)71.11 km/hr
E)70 km/hr
Rationale: Total time taken =((160/64)+(160/80))hrs=9/2hrs.
Average speed =(320 x2/9)km/hr= 71.11 km/hr.
ANSWER D
Answer: D
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.60 per kg. What will be his gain percent?
Options:
A)8 1/7 %
B)2 1/3 %
C)10 %
D)8 1/8 %
E)8 1/9 %
Rationale: C.P. of 1 kg = 420/70 = Rs. 6
S.P. of 1 kg = Rs. 6.60
Gain % = 0.60/6 * 100 = 10
= 10 %
Answer:C
Answer: C
Question: A trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent?
Options:
A)No profit No loss
B)4% profit
C)2% loss
D)2% profit
E)None of these
Rationale: Let CP of an article = RS. 100
MP= Rs. 120
Discount = 20%
SP = M[(100 - d%)/100] = 120(80/100) = Rs. 96
Clearly, the trader gets 4% loss.
ANSWER:E
Answer: E
Question: In how many different ways can 6 identical blue pants and 6 identical red pants be shared among 12 children such that each child receives a pant?
Options:
A)47900
B)4790016
C)479001
D)47900160
E)479001600
Rationale: GGG RRR
Therefore total number of ways is
12! but there are two groups of 3 identical things.
Therefore total number of "different" ways is
12!/ (6!) (6!) = 479001600 ANS:E
Answer: E
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Options:
A)17:6
B)17:3
C)17:1
D)17:9
E)17:4
Rationale: P:Q = 85000 : 15000
= 17:3.
Answer:B
Answer: B
Question: Mamuni went to the movies nine days ago. She goes to the movies only on Thursday. What day of the week is today?
Options:
A)Sunday
B)Tuesday
C)Thursday
D)Saturday
E)Friday
Rationale: Clearly, Nine days ago, it was Thursday.
Today is Saturday
ANSWER:D
Answer: D
Question: Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined Bobby had:
Options:
A)A profit of $10
B)A profit of $8
C)A loss of $8
D)A loss of $10
E)Neither a profit nor a loss
Rationale: Cost of the first stock: 96/1.2=80, so profit from it 96-80=16
Cost of the second stock: 96/0.8=120, so loss from it 96-120=-24
Overall loss 16-24=-8
Answer: C.
Answer: C
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
Options:
A)5/7
B)5/9
C)5/6
D)5/4
E)5/2
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9
Answer:B
Answer: B
Question: A train 125 m long passes a man, running at 9 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)11
B)50
C)88
D)65
E)54
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 9) km/hr. x - 9 = 45 ==> x
= 54 km/hr.
Answer:E
Answer: E
Question: If an object travels at three feet per second, how many feet does it travel in one hour?
Options:
A)3488
B)10800
C)12788
D)1800
E)2881
Rationale: Explanation:
If an object travels at 2 feet per second it covers 3x60 feet in one minute, and 3x60x60 feet in one hour.
Answer = 10800
Answer: B) 10800
Answer: B
Question: In how many ways can 7 people, A, B, C, D, E, F, G be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
Options:
A)384
B)396
C)576
D)4944
E)696
Rationale: Number of total arrangements = 7!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
7! - (4!*2*2) = 5040 - (24*2*2) = 4944
Answer D
Answer: D
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A)18/35
B)18/67
C)18/78
D)18/33
E)18/28
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A
Answer: A
Question: a person purchased four cloth average price of cloth is 300.price of its three cloths are 350,400,200 respectively what will be the price of fourth cloth?
Options:
A)300
B)250
C)200
D)400
E)275
Rationale: sum of price of all cloth=300*4=1200
sum of price of three cloth=350+400+200=950
price of fourth cloth=1200-950=250
answer B
Answer: B
Question: Mrs. Mary. invested $36,000; part at 5%, and part at 8%. The total interest on the investment was $2,520. How much did she invest at each rate?
Options:
A)x=$15,000, y =$30,000
B)x=$16,000, y =$32,000
C)x=$12,000, y =$24,000
D)x=$5,000, y =$10,000
E)x=$13,000, y =$26,000
Rationale: I approached this question like a mixture problem.
I don't like the wordingpartat 5% andpartat 8% because we have variables x and y in the answer choices and I have no idea which one is x or y.
Anyway here's how I did it.
0.05(x) + 0.08(y) = 0.07(x+y)
0.01(y) = 0.02(x)
y = 2x
Note: 0.07(x+y) because $2,520 is 7% of 36,000
In which answer choice is y = 2(x)
Answer C
Answer: C
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?
Options:
A)11
B)10
C)9
D)8
E)7
Rationale: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $324 per week
36x =324
x =9
Correct Option : C. 9
Answer: C
Question: What is the difference between the compound interest on Rs.12000 at 30% p.a. for one year when compounded yearly and half yearly?
Options:
A)399
B)383
C)270
D)288
E)133
Rationale: When compounded annually, interest
= 12000[1 + 30/100]1 - 12000 = Rs.3600
When compounded semi-annually, interest
= 12000[1 + 15/100]2 - 12000 = Rs.3870
Required difference = 3870- 3600 = Rs.270
Answer: C
Answer: C
Question: Of three numbers, the third is twice the first and the second is 4 times the first. If their average is 77, the smallest of the three numbers is:
Options:
A)18
B)25
C)20
D)32
E)33
Rationale: Explanation:
Let first number be x.
So,2nd no. = 4x & 3rd no.=2x.
So,x+4x+2x=77 × 3 = 231
7x = 231
x = 231/7
Hence,smallest Number x=33
Answer: E
Answer: E
Question: A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
Options:
A)4 days
B)8 days
C)2 days
D)12 days
E)6 days
Rationale: Suppose A, B and C take x,	x/2 and x/3 days respectively to finish the work.
Then,1/x+ 2/x + 3/x = 1/2
6/x = 1/2
x = 12.
So, B takes (12/2) = 6 days to finish the work
ANSWER:E
Answer: E
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.48, find the sum of money?
Options:
A)288
B)262
C)246
D)205
E)267
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 48
41 ---- ? => Rs.246
Answer: C
Answer: C
Question: The ratio between the current age of A and B is 6:7. If B is 4 years old than A. What will be the ratio of the ages of A and B after 4 years?
Options:
A)7:8
B)8:9
C)4:6
D)4:8
E)5:8
Rationale: A
7:8
If A’s age and B’s age will be 6A years and 7A years correspondingly
Then, 7A – 6A = 4
A = 4
Needed ratio = (6A + 4) : (7A + 4)
= 28 : 32
= 7 : 8
Answer: A
Question: How many seconds does Sandy take to cover a distance of 700 meters, if Sandy runs at a speed of 18 km/hr?
Options:
A)100
B)120
C)140
D)160
E)180
Rationale: 18 km/hr = 18000 m / 3600 s = 5 m/s
time = 700 / 5 = 140 seconds
The answer is C.
Answer: C
Question: Company P had 15 percent more employees in December than it had in January. If Company P had 500 employees in December, how many employees did it have in January?
Options:
A) 391
B) 435
C) 410
D) 423
E) 445
Rationale: D = number of employees in December
J = number of employees in January
J x 1.15 = D
J x 1.15 = 500
J = 500/1.15
J = 50,000/115 = 435
Thus B is the correct answer.
Answer: B
Question: Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 25 hours after they passed each other the ratio of the speeds of the two trains was
Options:
A)2:1
B)3:2
C)4:3
D)5:2
E)1:2
Rationale: Explanation:
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 5 : 2. Answer: D
Answer: D
Question: Two-fifths of thirty per cent of one-fourth of a number is 15. What is 20 per cent of that number?
Options:
A)90
B)150
C)100
D)120
E)None of these
Rationale: Let the number = x
2⁄5 × 30⁄100 × x⁄4 = 15
or x=15×5×100/2×30=500
20% of 500 = 100
Answer C
Answer: C
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 must he travel to reach A at 1 PM?
Options:
A)13 kmph
B)15 kmph
C)12 kmph
D)16 kmph
E)18 kmph
Rationale: 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
Answer: C
Question: At the end of the day one market stall had 16 apples and 48 oranges left. Another market stall had 36 apples and 24 oranges left. What is the difference between the percentages of apples left in the two market stalls?
Options:
A)39%
B)37%
C)38%
D)35%
E)40%
Rationale: D
35%
First stall 16 out of 64= 25%.
Second stall 36 out of 60 = 60%.
Difference in percentages = 35%.
Answer: D
Question: If 2^5, 3^3, and 14^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
Options:
A)26
B)39
C)42
D)65
E)168
Rationale: Here 156 has three two's
two three's
and one 14
rest of them must be in w
so w= 14*3*4 = 168
Smash E
Answer: E
Question: If a car went the first third of the distance at 60 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?
Options:
A)38 kmh
B)40 kmh
C)42 kmh
D)44 kmh
E)50 kmh
Rationale: Assume D/3 = 240 (this number is convenient because it is divisible by 60, 24 and 48)
So:
240 = 60*T1 = 4 hrs
240 = 24*T2 = 10 hrs
240 = 48*T3 = 5 hrs
T = T1 + T2 + T3 = 19 hrs
D = RT
(240*3) = R*19
R = 38
ANSWER: A
Answer: A
Question: A candidate appearing for an examination has to secure 35% marks to pass paper I. But he secured only 42 marks and failed by 23 marks. What is the maximum mark for paper I?
Options:
A)110
B)120
C)186
D)140
E)150
Rationale: he secured 42 marks nd fail by 23 marks so
total marks for pass the examinatn=65
let toal marks x
x*35/100=65
x=186
ANSWER:C
Answer: C
Question: A man swims downstream 42 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)2
B)8
C)9
D)6
E)10
Rationale: 42 --- 3 DS = 14
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (14 + 6)/2 =10
Answer: E
Answer: E
Question: Suppose you want to buy three loaves of bread that cost $2.25 each
and a jar of peanut butter that costs $2. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $14. How much money will you have left
over?
Options:
A)$1.50
B)$2.50
C)$5.25
D)$4.50
E)$5.50
Rationale: The jelly is extra information. 14.00 â€“ 3 x 2.25 â€“ 2.00 =
14.00 â€“ 6.75 â€“ 2.00 = 5.25.
You have $5.25 left.
correct answer C
Answer: C
Question: A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 600. Find the sum?
Options:
A)7000
B)7029
C)2778
D)2800
E)5000
Rationale: Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100 = 600 => 36x/100 - 24x/100 =600
=> 12x/100 = 600 => x = 5000.Answer:E
Answer: E
Question: A number is divided by 406 leaves remainder 115 , What will be the reminder when it will be divided by 29?
Options:
A)28
B)99
C)27
D)26
E)81
Rationale: Let the number be N.
So N = 406x + 115.
Now divide this number by 29. As 406 is exactly divisible by 29, we have to divide 115 by 29 and find the remainder. So remainder = 28
Answer:A
Answer: A
Question: The average of 11 results is 42, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
A)121
B)156
C)144
D)125
E)123
Rationale: 1 to 11 = 11 * 42= 462
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 â€“ 462 = 144
Answer:C
Answer: C
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
Options:
A)432
B)212
C)252
D)992
E)212
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432 Answer:A
Answer: A
Question: A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 2 a rupee. Find his net profit or loss percent?
Options:
A)34 %
B)30 %
C)50 %
D)150 %
E)33%
Rationale: The total number of mangoes bought by the shopkeeper be 10.
If he buys 5 a rupee, his CP =2
He selling at 2 a rupee, his SP = 5
Profit = SP - CP = 5 - 2 = 3
Profit Percent = 3/2 * 100 = 150 %
Answer:D
Answer: D
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is :
Options:
A)Rs. 1386
B)Rs. 1764
C)Rs. 1575
D)Rs. 2268
E)None of these
Rationale: Solution
Let P.W. be Rs. x. Then, S.I on Rs. X at 16% for 9 months = Rs. 189.
∴ xX 16x9/12x1x100 = 189 or x = 1575.
∴ P.W = Rs. 1575.
∴ Sum due =P.W + T.D. = Rs. (1575+189) = Rs. 1764.
Answer B
Answer: B
Question: What will come in place of the x in the following Number series? 2, 7, 10, 22, 18, 37, 26, x
Options:
A)224
B)35
C)36
D)42
E)52
Rationale: There are two series here
2, 10, 18, 26, ... (Increase by 8)
7, 22, 37, ... (Increase by 15)
Hence, next term is 37+15 = 52
E
Answer: E
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is b + 2?
Options:
A)b -3
B)b- 6
C)b- 1
D)b
E)b+ 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= b+2
n= b+1
1st integer= b+1-4= b-3
A is the answer
Answer: A
Question: 5% of (25% of $1600) is?
Options:
A)$20
B)$30
C)$45
D)$15
E)$60
Rationale: 5% of (25% of $1600) = 5/100 (25/100 * 1600) = $20
Answer is A
Answer: A
Question: The volume of a cube is 343 cc. Find its surface.
Options:
A)864
B)556
C)294
D)287
E)267
Rationale: a3 = 343 => a = 7
6a2 = 6 * 7 * 7 = 294
Answer:C
Answer: C
Question: Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nickel is worth $0.5, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Andrew’s pocket?
Options:
A)3
B)10
C)18
D)20
E)21
Rationale: E.
Let number of quarters be q. Therefore , dimes are 3q and nickels are 18q.
Total value = 18q(.5) + 3q(0.1) + .25q =9.55q
Given total value = 10.15
therefore, 9.55q=10.15 or q=1
Number of dimes = 3q = 3
Answer : A
Answer: A
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 41 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
Options:
A)140
B)175
C)210
D)245
E)280
Rationale: In 72 minutes, car X travels 42 miles.
Car Y gains 6 miles each hour, so it takes 7 hours to catch car X.
In 7 hours, car X travels 245 miles.
The answer is D.
Answer: D
Question: a, b are positive integers. The remainder of a to be divided by 5 is 4 and the remainder of b to be divided by 3 is 1
Which is possible to be the remainder of a*b to be divided by 24
Options:
A)a) 2
B)b) 4
C)c) 8
D)d) 12
E)e) 20
Rationale: Two ways to do it...
a=5x+4..
b=3y+1.
1) convenient way..
Take x and y as 0, and you will get a*b as 4*1=4
Answer : B
Answer: B
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 12 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)A)17.33
B)B)2
C)C)18
D)D)16
E)E)13.21
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
12/(x + 4) + 12/(x - 4) = 2
x = 13.21
Answer:E
Answer: E
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.
Options:
A)10 cm
B)20cm
C)30 cm
D)40 cm
E)50 cm
Rationale: Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 75 <=> 5x - 25 = 75 <=> x = 20.
:. Length of the rectangle = 20 cm.
Option B
Answer: B
Question: In a company of 200 employees, 120 are females. A total of 100 employees have advanced degrees and the rest have a college degree only. If 40 employees are males with a college degree only, how many employees are females with advanced degrees?
Options:
A)60
B)70
C)80
D)90
E)100
Rationale: The number of males is 200-120=80.
The number of males with advanced degrees is 80-40=40.
The number of females with advanced degrees is 100-40=60.
The answer is A.
Answer: A
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages?
Options:
A)16, 28, 35
B)16, 28, 36
C)16, 28, 39
D)16, 28, 34
E)16, 28, 31
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80 => x = 4
Their present ages are 16, 28 and 36 years respectively.Answer: B
Answer: B
Question: Pipes A and B can fill a tank in 4 and 6 hours. Pipe C can empty it in 8 hours. If all pipes are opened together, then the tank will be filled in?
Options:
A)3/2hr
B)24/7 hr
C)1hr
D)9/7hr
E)5/3hr
Rationale: Net part filled in 1 hour = 1/4 + 1/6 - 1/8 = 7/24
The tank will be full in 24/7 hr
Answer is B
Answer: B
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 20 on Wednesday, what would be the value of D calculated on the following Saturday?
Options:
A)2800
B)3400
C)3800
D)4200
E)4500
Rationale: On Saturday, the value would be 7*6*5*20 = 4200
The answer is D.
Answer: D
Question: A hall is 15 meters long and 15 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?
Options:
A)975.5
B)1250.5
C)1465.5
D)1687.5
E)1824.5
Rationale: 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 1687.5
The answer is D.
Answer: D
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
Options:
A)3.75
B)3.76
C)3.79
D)3.74
E)3.71
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer: A
Answer: A
Question: Possible arrangements for the word REVIEW if one E can't be next to the other.
Options:
A)100
B)200
C)300
D)400
E)500
Rationale: 1) All arrangements: 6!/2 = 360 (1/2 in order to exclude double counting as [E1, E2] is the same as [E2,E1])
2) All arrangements with two E together: 5!/2 = 60
3) All arrangements in which one E can't be next to the other: 360 - 60 = 300.
ANSWER:C
Answer: C
Question: A ball team plays games only against the other five teams in its league and always in the following order: John, Paul, George, Ringo and Pete. If the team’s final game of the season is against Ringo, which of the following could be the number of games in the team’s schedule?
Options:
A)18
B)12
C)24
D)72
E)81
Rationale: IMO 'C' is the answer.
Matches will be in multiples of 5x+4. The answer that satisfies this condition is C
Answer: C
Question: The radius of the wheel of a bus is 70 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
Options:
A)200
B)250
C)300
D)330
E)None of these
Rationale: Radius of the wheel of bus = 70 cm. Then,
circumference of wheel = 2πr = 140π = 440 cm
Distance covered by bus in 1 minute
= 66⁄60 × 1000 × 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 440 cm
∴ Revolutions per minute = 6600000/60×440 = 250
Answer B
Answer: B
Question: A grocer has a sale of Rs. 5266, Rs. 5744, Rs. 5864, Rs. 6122 and Rs. 6588 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5750?
Options:
A)4016
B)4076
C)4816
D)4916
E)5916
Rationale: Total sale for 5 months = Rs. (5266 + 5744 + 5864 + 6122+ 6588) = Rs. 29584.
Required sale = Rs. [ (5750 x 6) - 34500 ]
= Rs. (34500 - 29584)
= Rs. 4916.
ANSWER:D
Answer: D
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 90 and Rs. 80 respectively. The sum is:
Options:
A)1360
B)1450
C)720
D)1800
E)None
Rationale: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 90 * 80 / (90 - 80) = Rs.720.
Answer C
Answer: C
Question: How many different ways can you select a pilot and a co pilot if you have 80 people to choose from?
Options:
A) 199
B) 200
C) 398
D) 4950
E) 6320
Rationale: You are not just choosing two from 80. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (80C2) x 2 = 6320=E
Answer: E
Question: If B and C are digits and 8BC is a 3-digit number that is divisible by 4, which of the following is a possible product of B and C?
Options:
A)1
B)2
C)5
D)6
E)14
Rationale: Try with the options -
A. If BC = 1 , both B and C must be 1
B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3
C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3
D. If BC = 6 , then we can have the following possibilities
i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3
ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3
E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 4
Thus answer is (C)
Answer: C