divelab/Sys2Bench huggingface dataset:
Question: A cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
Options:
A)8.1
B)8.9
C)8.6
D)8.3
E)9.0
Rationale: Distance = d1 = x miles
Speed = s1 = 8 miles per hour
Time = t1 = Distance/ Speed = x/8
2. Going from B to A
Distance = d2 = x miles
Speed = s2 = 10 miles per hour
Time = t2 = Distance/ Speed = x/10
3. Average Speed = Total Distance/Total Time
Total Distance = x + x = 2x
Total Time = x/10 + x/8 = x (1/10 + 1/8) = =9x/40
Speed = 2x/(9x/40) = 80/9
= 8.9
Answer : B
Answer: B
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)2000
B)2781
C)2278
D)2081
E)2721
Rationale: Explanation:
(10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: A
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)2888
C)2771
D)1261
E)1121
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: A
Question: In some language, 'COLLEGE' is written as 'FSOPHKH' and 'SCHOOL' is wriiten as 'VGKSRP'. Then What is for "STUDENT"??
Options:
A)VXWHHRW
B)VXXHIRW
C)VXWHIRX
D)VXXHHRW
E)VXXHHRS
Rationale: In 'college' and "school'
1) odd letters has +3 letters more from the alphabets
2) even letter has +4 letters from the alphabets
ODD LETTERS EVEN LETTERS
-----------------------------
S--->V T--->X
U--->X D--->H
E--->H N--->R
T--->W
ANSWER:D
Answer: D
Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
Options:
A)15
B)25
C)35
D)45
E)55
Rationale: Explanation:
Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ l0) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years. Answer: C
Answer: C
Question: 4.036 divided by 0.02 gives :
Options:
A)10.09
B)1.06
C)10.06
D)201.8
E)100.9
Rationale: = 4.036/0.02
= 403.6/2
= 201.8
Answer is D.
Answer: D
Question: The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?
Options:
A)22
B)29
C)88
D)28
E)11
Rationale: Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1
= 29.
Answer:B
Answer: B
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 80 terms?
Options:
A)1
B)21
C)40/41
D)80/81
E)160/161
Rationale: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a80 = 1/80 - 1/81
The sum of these terms is 1-1/81 = 80/81
The answer is D.
Answer: D
Question: A box contains ten bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
Options:
A)5/21
B)9/21
C)7/21
D)6/21
E)8/21
Rationale: Required probability = (5C3 . 5C1)/10C4 = (10 * 5)/210
= 5/21
Answer:A
Answer: A
Question: A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
Options:
A)11
B)12
C)10
D)13
E)10.5
Rationale: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
Ans- C
Answer: C
Question: If 25th of August in a year is Thursday, the number of Mondays in that month is
Options:
A)4
B)5
C)2
D)3
E)1
Rationale: Explanation:
Given that 25th August = Thursday
Hence 29th August = Monday
So 22nd,15th and 8th and 1st of August also will be Mondays
Number of Mondays in August = 5
Answer: Option B
Answer: B
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 7 hats randomly out of the drawer and returning each hat before taking out the next one?
Options:
A)3/4
B)5/8
C)9/16
D)17/32
E)35/64
Rationale: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue-blue-blue-blue.
The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2*1/2 = 1/128
There are 7C3 = 35 such cases so we need to multiply this by 35.
P(exactly 3 red hats) = 35*1/128 = 35/128
Clearly the probability of getting exactly 3 blue hats will also be 35/128.
The sum of the probabilities is 35/128+35/128 = 70/128 = 35/64
The answer is E.
Answer: E
Question: Set A contains all the even numbers between 12 and 50 inclusive. Set B contains all the even numbers between 112 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
Options:
A)2000
B)2550
C)5050
D)6275
E)11325
Rationale: Set A contains 12,14 , 16 ... 50
Set B contains 112 , 114 , 116 ... 150
Number of terms in each set = 20
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*20 = 2000
Answer A
Answer: A
Question: A person incurs 20% loss by selling a watch for $1000. At what price should the watch be sold to earn 20% profit?
Options:
A)$1000
B)$950
C)$1500
D)$1150
E)$1250
Rationale: Let the new selling price be $x
(100-loss%): (1st S.P.) = (100+gain%):(2nd S.P.)
(100-20)/1000 = (100+20)/x
x = 120*1000/80 = 1500
Answer is C
Answer: C
Question: What is the greatest power that 4 can be raised to so that the resulting number is a factor of 24!?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: the number of 4s in 24!= 24/4=6..
ans E
Answer: E
Question: A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. The rate per annum is?
Options:
A)5 5/9
B)5 5/7
C)5 5/2
D)5 5/8
E)5 5/1
Rationale: Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 3 years.
Rate = (100 * x) / (x * 6 * 3) = 5 5/9 %.
Answer:A
Answer: A
Question: Two pipes can fill a tank in 10 hours and 12 hours. While the 3rd pipe empties the full tank in 20hours. If all the 3 pipes are open in how much time will the tank be filled?
Options:
A)6hr
B)5hr
C)7hr 30min
D)8hr 20min
E)9hr
Rationale: Net part filled in 1 hour = 1/10 + 1/12 - 1/20 = 8/60 = 2/15
The tank will be full in 15/2 hours = 7hr 30min
Answer is C
Answer: C
Question: A particular parking garage is increasing its rates by 25 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
Options:
A)15%
B)18%
C)20%
D)25%
E)30%
Rationale: Let x be the original number of days that Bob used the garage.
Let P be the original cost per day.
Let N*x be the new number of days that Bob uses the garage.
N*x*1.25P = x*P
N*x = x/1.25 = 0.8x, thus a 20% reduction.
The answer is C.
Answer: C
Question: Which pair of numbers has least and maximum frequency in the given sequence?
8 7 5 6 4 5 8 3 8 6 7 2 3 5 8 3 5 7 6 4 7 6 5
Options:
A)3 and 8
B)4 and 5
C)2 and 6
D)2 and 5
E)2 and 7
Rationale: frequency means how many times the number occured in the given series
here they asked about least and max frequency
so in the given pair 2 occurs 1 time and 5 occurs 5 times
ANSWER:D
Answer: D
Question: What is the diference between the place value and face value of 3 in the numeral 1375?
Options:
A)295
B)297
C)300
D)310
E)312
Rationale: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
B
Answer: B
Question: Which of the following integers is NOT a divisor of x if x = (21)(3^6) – (109)?
Options:
A)2
B)5
C)18
D)19
E)25
Rationale: (21)(3^6) is divisible by 3 but 109 is not divisible by 3.
Therefore (21)(3^6) - 109 is not divisible by 3 and thus not divisible by 18.
The answer is C.
Answer: C
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)299
B)288
C)240
D)775
E)2321
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m. Answer: C
Answer: C
Question: Mr. Smith calculated the average of 10 three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 19.8 The difference between the unit digit and hundreds digit of that number is :
Options:
A)2
B)6
C)5
D)3
E)4
Rationale: Since the average increased by 29.7 and there were a total of 10 numbers, it means the incorrect number was 198 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 198
99c - 99a = 99(c - a) = 198
198 = 99*2 = 99(c - a)
So c - a = 2
Answer (A)
Answer: A
Question: A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)3kmph
B)4kmph
C)5.1kmph
D)6kmph
E)7kmph
Rationale: M = 5.5
S = 1.5
DS = 7
US = 4
AS = (2 * 7 * 4) /11 = 4
Answer:C
Answer: C
Question: A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
Options:
A)2/91
B)3/52
C)5/25
D)8/45
E)7/56
Rationale: n(s)=no of ways of drawing 3 balls out of 15
15C3 = 15*14*13/3*2*1
==>455
n(E)=5C3=5C2 = 5*4/2*1 = 10
p(E) =n(E)/n(S)=10/455 = 2/91
ANSWER A
Answer: A
Question: Working alone, pump A can empty a pool in 4 hours. Working alone, pump B can empty the same pool in 6 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?
Options:
A)132
B)138
C)144
D)150
E)156
Rationale: Pump A can empty (1/4) of the pool per hour.
Pump B can empty (1/6) of the pool per hour.
Together the pumps can empty 1/4+1/6=5/12 of the pool per hour.
1 pool / (5/12) pool per hour = 12/5 hours = 144 minutes.
The answer is C.
Answer: C
Question: The ratio of spinsters to cats is 2 to 7. If there are 55 more cats than spinsters, how many spinsters are there?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: Let 2x be the number of spinsters. Then 7x is the number of cats.
7x-2x=55
x=11 and the number of spinsters is 2(11)=22.
The answer is C.
Answer: C
Question: If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are
the E odds that x^2+y^2>1?
Options:
A)1. pi/4
B)2. E=pi/16
C)3. E=1-pi/4
D)4. 1-pi/16
E)5.4-pi
Rationale: area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi.
then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1)
total outcomes = 4
therefore probability = (4-pi)/4
C
Answer: C
Question: A charity collected $1,299 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
Options:
A)60
B)64
C)66
D)68
E)69
Rationale: Min fund = 20
Total = 1299
The closest multiple of 20 to 1299 is : 63
Which implies 63 people gave 20 and 1 person gave 39
Ans. B
Answer: B
Question: (168% of 1265) ÷ 6 = ?
Options:
A)A)354
B)B)175
C)C)225
D)D)375
E)E)524
Rationale: Explanation :
? = (168 x 1265/100) ÷ 6 = 212520/600 = 354
Answer : Option A
Answer: A
Question: A 13% stock yields 8%.The market value of the stock is :
Options:
A)Rs. 72
B)Rs. 92
C)Rs. 162.50
D)Rs. 116.50
E)None of these
Rationale: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 13, investment = Rs.(100/8X13)= Rs. 162.50
∴ Market value of Rs. 100 stock = Rs.162.50
Answer C
Answer: C
Question: In what ratio must tea of Rs.42 per kg be mixed with tea of Rs.50 per kg so that cost of mixture is Rs.45 per kg?
Options:
A)5:3
B)3:5
C)2:3
D)3:4
E)1:2
Rationale: 50-45:45-42=5:3
ANSWER:A
Answer: A
Question: The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 70 with him, what was the average amount with the group before his joining the group?
Options:
A)s. 25.6
B)s. 70/3
C)s. 16.6
D)s. 26/3
E)s. 25
Rationale: Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 70. So, the amount with remaining 6 people = 210 - 70 = Rs. 140
The average amount with them = 140/6 = Rs. 70/3
ANSWER:B
Answer: B
Question: The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 60% more than the price of the other, what is the price of each of these two oranges?
Options:
A)Rs 5, Rs 7.50
B)Rs 8, Rs 12
C)Rs 10, Rs 16
D)Rs 12, Rs 14
E)None of these
Rationale: Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 60% of x) = Rs. x + 3/5x = Rs. 8x/5
So, x + 8x/5 = 26
13x = 130
x = 10.
The prices of the two oranges are Rs. 10 and Rs. 16
Answer : C
Answer: C
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
Options:
A)29
B)378
C)20
D)30
E)121
Rationale: M = 20
S = 10
DS = 20 + 10 = 30
Answer: D
Answer: D
Question: The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
Options:
A)120
B)298
C)272
D)827
E)278
Rationale: 4*5*6
= 120
Answer:A
Answer: A
Question: Pipe A can fill a tank in 2 hours, pipe B in 4 hours and pipe C in 4 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)1
C)3
D)4
E)5
Rationale: Answer:	Part filled by A + B + C in 1 hour = 1/2 + 1/4 + 1/4= 1/1
All the three pipes together will fill the tank in 1 hours.
Answer: B
Answer: B
Question: If a person walks at 10 km/hr instead of 5 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
Options:
A)50 km
B)76 km
C)20 km
D)16 km
E)97 km
Rationale: Let the actual distance traveled be x km. Then,
x/5 = (x + 20)/10
5x - 100 =>x = 20 km.
Answer: C
Answer: C
Question: A two digit number, digits interchange places and the new number is added to the original number, then the resulting number will be divisible by?
Options:
A)10
B)11
C)13
D)15
E)16
Rationale: Let the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.
B
Answer: B
Question: if 5 boys take two hours to water the garden, then how long should 10 boys take to water the same type of garden?
Options:
A)80 min
B)50 min
C)30 min
D)65 min
E)60 min
Rationale: if 5 boys take an hour to water the garden, then
10 boys will take 5*120/10 = 60 mins to water the same type of garden.
ANSWER:E
Answer: E
Question: A train 125 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)40
B)50
C)51
D)79
E)80
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 6) km/hr.
x - 6 = 45 => x = 51 km/hr.
Answer: Option C
Answer: C
Question: Eight family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
Options:
A)1040
B)1240
C)1440
D)1640
E)1840
Rationale: Let's consider Michael and Bobby as one unit.
There are 7! possible arrangements of 7 units.
Around a table, there would be repetitions of each arrangement, so we divide by 7.
Then there are 6! arrangements around a circular table.
For each arrangement, Michael and Bobby can switch places, so we multiply by 2.
The number of arrangements is 6!*2 = 1440.
The answer is C.
Answer: C
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 160 m, in what time will they cross other travelling in opposite direction?
Options:
A)17 sec
B)12 sec
C)16 sec
D)15 sec
E)18 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (160 + 160)/20 = 16 sec.
Answer:C
Answer: C
Question: Excluding stoppages, the speed of a train is 50 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour?
Options:
A)82
B)17
C)12
D)24
E)18
Rationale: Explanation:
T = 20/50 * 60 = 24
Answer: Option D
Answer: D
Question: How many arrangements can be made out of the letters of the word 'ENGINEERING' ?
Options:
A)277200
B)92400
C)69300
D)23100
E)45380
Rationale: The word 'ENGINEERING' contains 11 letters, namely 3E, 3N, 2G, 2I and 1R.
∴ Required number of arrangements = 11!/(3!)(3!)(2!)(2!)(1!) = 277200.
Answer is A
Answer: A
Question: From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 10 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
Options:
A) 38
B) 39
C) 40
D) 41
E) 42
Rationale: 1.10x=45 --> 11/10*x=45 --> x=45*10/11=450/11=~41.
Answer: D.
Answer: D
Question: On a map, 1 centimeter represents 17 kilometers. Two cities 663 kilometers apart would be separated on the map by how many centimeters?
Options:
A)15
B)27
C)39
D)270
E)480
Rationale: X=663/17= 39
Answer: C
Answer: C
Question: In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-one students are registered for History, twenty-six students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
Options:
A)13
B)10
C)9
D)8
E)7
Rationale: A U B U C = A + B + C - AB-BC-AC + ABC
68 = 21 + 26+ 34 -AB-BC-AC +3 => AB+BC+AC = 16
Exactly Two classes = AB+BC+AC - 3ABC = 16 -3*3 = 7
Hence E
Answer: E
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 18 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
Options:
A)72
B)50
C)60
D)Data inadequate
E)None of these
Rationale: E+H+G+M/4âˆ’E+S+M+H/4=18
â‡’ G - S = 72
Answer A
Answer: A
Question: Which is longest: a foot, a yard or an inch?
Options:
A)a yard
B)inch
C)foot
D)feet
E)cm
Rationale: 3 feet = 1 yard
12 inches = 1 foot
answer A
Answer: A
Question: If p and q are integers, such that p < 3 < q, and s is a nonnegative integer, which of the following must be true?
Options:
A)p^2 < q^2
B)p + q = 0
C)sp < sq
D)sp ≠ sq
E)p/q < s
Rationale: We're told that P < 0 < Q and that S is a NON-NEGATIVE INTEGER. We're asked which of the following MUST be true.
P = -2
Q = 2
S = 0
Answer A: P^2 < Q^2.... 4 < 1 NOT TRUE
Answer B: P+Q=0... -2+1 = -1 NOT TRUE
Answer C: SP < SQ... 0 < 0 NOT TRUE
Answer D: SP ≠ SQ... 0 = 0 NOT TRUE
Answer E: P+Q=0 This IS TRUE
B
Answer: B
Question: A grocer stacked apples in a pile. The bottom layer was rectangular with 3 rows of 5 apples each. In the second layer from the bottom, each apple rested on 4 apples from the bottom layer, and in the third layer, each apple rested on 4 apples from the second layer. Which of the following is the maximum number of apples that could have been in the third layer?
Options:
A) 5
B) 3
C) 6
D) 2
E) 1
Rationale: Bottom Layer = 5 x 3 = 15
IInd Layer = (5-1) x (3-1) = 8
IIIrd Layer = (4-1) x (2-1) = 3
Answer = 3 = B
Answer: B
Question: The radius of a sphere is increased by 50%. The increase in surface area of the sphere is :
Options:
A)168
B)125
C)186
D)197
E)191
Rationale: Explanation:
Take radius 100. Then surface area is 4 × ππ × 100 × 100.
After increase radius by 50% the radius becomes100 + 50% of 100 = 150
Then new surface area is 4 × ππ × 150 × 150
Then put the values into formula of percentage = 4π1502−4π10024π1002×1004π1502−4π10024π1002×100 = 125%
Answer: B
Answer: B
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)9
B)8
C)7
D)6
E)65
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: B
Question: How much is 80% of 40 is greater than 2/5 of 25?
Options:
A)22
B)27
C)18
D)12
E)81
Rationale: (80/100) * 40 â€“ (2/5) * 25
32 - 10 =22
Answer:A
Answer: A
Question: Given two sets A = {1,1,2,2,7,7} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
Options:
A)1/5
B)1/6
C)1/2
D)1/3
E)1/4
Rationale: One way to look at it:
The number from set A can be ANYTHING.
The number selected from set B will determine whether the sum is odd or even.
For example, if a 2 is selected from set A, we need a 0 from set B to get an even sum.
If a 7 is selected from set A, we need a 1 from set B to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)
= P(select ANY number from set A)xP(select the number from set B that makes the sum even)
= 1x1/2
= 1/2
= C
Answer: C
Question: Of the three-digit integers greater than 700, how many have distinct digits?
Options:
A) 216
B) 82
C) 80
D) 45
E) 36
Rationale: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700);
A. all digits are distinct = 3*9*8=216
Answer: A
Answer: A
Question: Find the compound interest on $ 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly
Options:
A)824
B)824.36
C)824.32
D)824.24
E)824.26
Rationale: Principal = $ 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount = $ [10000 * (1+(2/100))4] = $(10000 * (51/50) * (51/50) * (51/50) * (51/50))
= $ 10824.32.
:. C.I. = $ (10824.32 - 10000) = $ 824.32.
Answer C.
Answer: C
Question: There are n cities. What is the number of airlines that connected 5 different cities (airline from city A to city B is different with airline from city B to city A)?
Options:
A)n(n-1)
B)n(n+1)
C)n(n-1)/2
D)n(n-3)
E)n2
Rationale: First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-4). Hence, the answer is n(n-4), which makes A an answer choice.
D
Answer: D
Question: What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?
Options:
A)1/15
B)2/15
C)4/15
D)7/15
E)None of these
Rationale: Explanation :
Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30
Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15.
For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number.
So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6
Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24
So total probability = 24/90 = 4/15
Answer : C
Answer: C
Question: The sale price of a trolley bag including the sale tax is Rs. 280. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:
Options:
A)Rs 200
B)Rs 220
C)Rs 260
D)Rs 280
E)None of these
Rationale: Explanation :
112% of S.P. = 280
S.P. = Rs.(280x 100/112) = Rs.250.
C.P. = Rs (100/125x 250) = Rs 200
Answer : A
Answer: A