mathewhe/aqua_rat huggingface dataset:
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) 200
(B) 177
(C) 188
(D) 166
(E) 129
Rationale: Profit on first article = 20% of 1000
= 200.
Answer:A
Answer: (A) 200
Question: A retailer bought a machine at a wholesale price of $108 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?
(A) 81
(B) 100
(C) 120
(D) 135
(E) 144
Rationale: My solution: Wholesale Price= 108
Retail Price, be = x
He provides 10 % discount on Retail price= x-10 x/100
This Retail price = 20 % profit on Wholesale price
x-10 x/100 = 108+ 1/5(108)
x=144;
ANSWER:E
Answer: (E) 144
Question: A certain office supply store stocks 2 sizes of self-stick notepads, each in 7 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 6
(B) 8
(C) 16
(D) 84
(E) 92
Rationale: Notepads of the same color = 7 (we have 7 colors). As we have two sizes then total for the same color=7*2=14
Notepads of the different colors = 7C3=35 (we should choose 3 different colors out of 7). As we have two sizes then total for the different color=35*2=70
Total=70+14=84
Answer: D.
Answer: (D) 84
Question: Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/11 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
(A) 21
(B) 35
(C) 33
(D) 60
(E) 65
Rationale: The total number of the people in the room must be a multiple of both 7 and 11 (in order 3/7 and 5/11 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 11, which is 77.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 77 people in the room.
Therefore there are 3/7*77=33 people in the room under the age of 21.
Answer: C.
Answer: (C) 33
Question: In a game of billiards, A can give B 10 points in 50 and he can give C 40 points in 50. How many points can B give C in a game of 100?
(A) 18
(B) 27
(C) 25
(D) 75
(E) 17
Rationale: A scores 50 while B score 40 and C scores 10.
The number of points that C scores when B scores 100 = (100 * 10)/40 = 25
In a game of 100 points, B gives (100 - 25) = 75 points to C.
Answer: D
Answer: (D) 75
Question: At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 12 months?
(A)  2^3
(B)  3^2
(C)  2(3^10)
(D)  3(2^12)
(E)  3(10^2)
Rationale: 3*2^n where n is the #of month --> 3*2^12 Answer (D)
Answer: (D)  3(2^12)
Question: In a recent head-to-head run-off election, 18,000 absentee ballets were cast. 3/7 of the absentee ballets were thrown out and 2/9 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?
(A) 2,000
(B) 3,000
(C) 6,000
(D) 8,000
(E) 9,000
Rationale: 4/7 * 7/9 (total absentee votes) = 4/9 (total votes)=4/9*18000=8000
Answer is D
Answer: (D) 8,000
Question: A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 9,100 sedans in Anytown, how many motorcycles are there?
(A) 1260
(B) 2600
(C) 3600
(D) 4200
(E) 5200
Rationale: Let the total number of trucks = 3x
total number of sedans = 7x
total number of motorcycles = 2x
total number of sedans = 9100
=> 7x = 9100
=> x = 1300
total number of motorcycles =2x = 2*1300
=2600
Answer B
Answer: (B) 2600
Question: in a certain flower shop, which stocks four types of flowers, there are 1/4 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?
(A) 60
(B) 62
(C) 66.66
(D) 64
(E) 68
Rationale: Given :-
Violets - C/4
Carnations - C
Tulip - C/8
Rose - C/8
Total flowers in terms of C = C/4+C+C/8+C/8 = 3/2 C
Percentage of Carnations = C/3C/2 *100 =66.66%
Answer C
Answer: (C) 66.66
Question: 7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
(A) 17.5%
(B) 17.8%
(C) 18.1%
(D) 18.4%
(E) 18.7%
Rationale: The total amount of alcohol is 0.22(7) + 0.11(3) = 1.87 liters.
The percentage is 1.87 / 10 = 18.7 / 100 which is 18.7%
The answer is E.
Answer: (E) 18.7%
Question: 60 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.
(A) 190
(B) 200
(C) 210
(D) 1770
(E) 230
Rationale: 1st person will shake hand with 59 people
2nd person will shake hand with 58 people
3rd person will shake hand with 57 people
......
total no. of handshakes = 59+58+57+...+3+2+1 = 19*(19+1)/2 = 1770
or, if there are n persons then no. of shakehands = nC2 = 60C2 = 1770
ANSWER: D
Answer: (D) 1770
Question: A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Explanation :
Let the number of horses =x
Then the number of pigeons =80−x.
Each pigeon has 2 legs and each horse has 4 legs.
Therefore, total number of legs =4x+2(80−x)=260.
=>4x+160−2x=260.
=>2x=100.
=>x=50.
Answer : C
Answer: (C) 50
Question: A motorcyclist X drives along a circular fence at a rate of 2 rounds per hour and another motor cyclist Y at a rate of 4 rounds per hour. After how long they will cross each other for the first time?
(A) 10 min
(B) 20 min
(C) 30 min
(D) 40 min
(E) None of these
Rationale: Explanation :
Since X and Y move in the same direction they cross each other when there is a difference of two round between the two. Relative speed of X and Y=4-2=2.
Time taken to complete one round at this speed = 1/2 hour
= 30minutes
Answer : C
Answer: (C) 30 min
Question: A train is moving at 4/5 of its usual speed. The train is 45 minutes too late. What is the usual time (in hours) for the train to complete the journey?
(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Rationale: new time = d / (4v/5) = 5/4 * usual time
45 minutes represents 1/4 of the usual time.
The usual time is 4* 45 minutes = 3 hours.
The answer is E.
Answer: (E) 3
Question: If 3 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
(A)  -7
(B)  -6
(C)  -3
(D)  1
(E)  6
Rationale: The phrase “3 is one solution of the equation” means that one value of x is 3. Thus, we first must plug 3 for x into the given equation to determine the value of k. So we have
3^2 + (3)(3) + k = 10
9 + 9 + k = 10
18 + k = 10
k = -8
Next we plug -8 into the given equation for k and then solve for x.
x^2 + 3x – 8 = 10
x^2 + 3x – 18 = 0
(x+6)(x-3) = 0
x = -6 or x = 3
Thus, -6 is the other solution. Answer B.
Answer: (B)  -6
Question: The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 14000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
(A) Rs. 7000
(B) Rs. 8000
(C) Rs. 8600
(D) Rs. 9000
(E) None
Rationale: Answer
Average salary
= 8000 + 5000 + 14000 + 7000 + 9000 / 5
= Rs. 8600
Correct Option: C
Answer: (C) Rs. 8600
Question: If two women starting from same point, walking in the opposite directions with 8km/hr and 7km/hr as average speeds respectively. Then the distance between them after 3 hours is?
(A) 23
(B) 33
(C) 43
(D) 53
(E) 63
Rationale: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (8Ã— 3) + (7Ã— 3)
= 24+ 21
= 43 Km
Answer:C
Answer: (C) 43
Question: When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following T is a possible value for x + y?
I. 18
II. 19
III. 20
(A) I only
(B) II only
(C) T=III only
(D) II and III only
(E) None
Rationale: TIP FOR SUCH QUESTIONS: Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about
i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as
m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7
i.e. Min Value of x = 8
AND
i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as
n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11
i.e. Min Value of y = 12
i.e. Minimum Value of x+y = 8+12 = 20
Hence III only can be True
Answer: Option
C
Answer: (C) T=III only
Question: If |x^2 − 30| = x, which of the following could be the value of x?
(A) -6
(B) -5
(C) 1
(D) 5
(E) 15
Rationale: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.
First, let's assume that x^2-30 is negative.
-(x^2 -30) = x
x^2 + x - 30 = 0
(x+6)(x-5) = 0
x = 5 or x = -6 (However, x can not be negative.)
Then x = 5 is a possible value for x.
The answer is D.
Answer: (D) 5
Question: The average of 11 results is 45, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
(A) 114
(B) 116
(C) 117
(D) 118
(E) 119
Rationale: 1 to 11 = 11 * 45 = 495
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 495=114
ANSWER:A
Answer: (A) 114
Question: On a map the distance between two mountains is 312 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 25 inch from the base of the mountain. How many km is he from the base of the mountain?
(A) 10.89
(B) 14.81
(C) 14.8
(D) 14.82
(E) 14.12
Rationale: Explanation:
Since 312 inch = 136 km
So 1 inch = 136/312 km
So 25 inch = (136 Ã— 25)/ 312 = 10.89 km
Answer: A
Answer: (A) 10.89
Question: A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 8 members, then what is the exact number of researchers required?
(A) 23
(B) 22
(C) 21
(D) 20
(E) 19
Rationale: alternatively, we have
8*3-2( because james is included in all the three teams)
=22
B
Answer: (B) 22
Question: A train 110 m long is running with a speed of 82 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 8 sec
(D) 4.5 sec
(E) 2 sec
Rationale: Speed of train relative to man = 82+ 6
= 88 km/hr.
= 88 * 5/18 = 24.44 m/sec.
Time taken to pass the men = 110 /24.44
= 4.5 sec.
Answer:D
Answer: (D) 4.5 sec
Question: Average score for Virat Kohli in a series of 10 matches is 38.9 runs. If the average for first six matches comes out to be 42 what is his average in the last 4 matches of the series?
(A) 34.25
(B) 35
(C) 33.25
(D) 34.25
(E) None of these
Rationale: Explanation:
Average runs scored by Virat Kohli in 10 matches: Total runs scored/10—(1)
Average runs scored by Virat Kohli in 6 matches: (Total runs in 6 matches)/6
=> 42 = Runs/6
=>252 runs
Using (1):
=>38.9 = Runs/10
=>389 runs
Runs scored in rest 4 matches: 389 - 252 runs
=> 137 runs
Average runs scored by Virat Kohli in 4 matches: 137/4 = 34.25 runs
ANSWER A
Answer: (A) 34.25
Question: If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true?
(A) Each of r + s, r + t, and s + t is prime.
(B) Each of r + 3, s + 3, and t + 3 is prime.
(C) Each of r, s, and t is prime.
(D) The average (arithmetic mean) of r, s, and t is prime.
(E) r + s = t
Rationale: the question asks could be!!!!
this means that if at least one option works, it is the answer.
3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer.
Answer: (C) Each of r, s, and t is prime.
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 144 m and they cross each other in 12 sec, then the speed of each train is?
(A) 22
(B) 77
(C) 36
(D) 88
(E) 19.2
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (144 + 144)/12 => x = 12
Speed of each train = 12 m/sec.
= 12 * 18/5 =19.2 km/hr.
Answer: E
Answer: (E) 19.2
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2234
(B) 3245
(C) 3456
(D) 4567
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.
(A) 70 km/hr
(B) 60 km/hr
(C) 10 km/hr
(D) 20 km/hr
(E) 30 km/hr
Rationale: Explanation:
We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
Lets solve it.
Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S*T = 48 * 5/6 = 40 km
New time will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40*3/2 kmph = 60kmph
Answer: B
Answer: (B) 60 km/hr
Question: The positive numbers w, x, y, and z are such that x is 25 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?
(A) 15.2%
(B) 16.2%
(C) 20.0%
(D) 23.2%
(E) 24.8%
Rationale: My strategy is same as theDobermanbut instead take z=100, which makes life a bit easy. As:
z=100
y=120 (20% greater than z)
z=144(20% greater than y)
Now calculate w 20% less than z = 144*80/100= 115.2
Now by just looking, relation between w and z:
w-z/z*100 = 16.2 - Answer B
Answer: (B) 16.2%
Question: You buy a piece of land with an area of âˆš100, how long is one side of the land plot?
(A) 28
(B) 29
(C) 10
(D) 31
(E) 32
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 100.
Answer C
Answer: (C) 10
Question: A bag has 10 blue balls and 15 black balls. How many black balls must be removed from the bag so that 50 percent of the balls in the bag shall be black?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Suppose x black balls need to be removed from the bag.
After x black balls are removed, the bag shall have (15 - x) black balls and the same 10 blue balls; and the total number of balls shall be (15-x) + 10 = 25 - x
Now we want the 50 percent of balls in the bag to be black.
This means 50 percent of (25 - x) should be equal to the number of black balls which is (15 - x).
This means,
50 % of (25 - x) = (15 - x)
Solving above equation we get x = 5.
Ans E
Answer: (E) 5
Question: Richard traveled the entire 60 miles trip. If he did the first 2 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour?
(A) 20mph
(B) 24mph
(C) 30mph
(D) 32mph
(E) 55mph
Rationale: Average speed=sum of distance/sum of time. If he travelled the first 2 miles at 24 miles/hr, it would take 0.083 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 60miles/(0.083+1)hrs=55miles/1hr.
Therefore, the answer is E.
Answer: (E) 55mph
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 770 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
(A) 191
(B) 193
(C) 195
(D) 212
(E) 213
Rationale: Total movies submitted are 770.
As per question we need to take 1/4 of 770 to be considered for top 10 movies = 192.25
approximate the value we 193
IMO option B is the correct answer...
Answer: (B) 193
Question: Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h
(A) 20 seconds
(B) 3
(C) 4
(D) 1
(E) 5
Rationale: swim in still water at = 3
speed of river= 1.4
US = 3 - 1.4= 1.6
Distance = 8
T = 8/1.6 = 5
Answer: E
Answer: (E) 5
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 25 seconds. The speed of the train is:
(A) 45 km/hr
(B) 50 km/hr
(C) 95 km/hr
(D) 55 km/hr
(E) 56 km/hr
Rationale: Speed of the train relative to man = (125/25) m/sec =25 m/sec. [(25 * (18/5)] km/hr = 90 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr.
ANSWER:C
Answer: (C) 95 km/hr
Question: One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 225cm when it touches the floor on third time. What is the value of the original height?
(A) 80cm
(B) 90cm
(C) 100cm
(D) 120cm
(E) 130cm
Rationale: when Ball comes down, Then i have indicated the distance covered in green
when Ball goes up, Then i have indicated the distance covered in red
Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h
h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 225
2.5 h = 225
h = 90.
B is the answer.
Answer: (B) 90cm
Question: A machine can finish a work in 18days and 2nd machine can finish the work in 15days. 2nd machine worked for 10days and left the job. In how many days, 1st machine can finish the remaining work?
(A) 4days
(B) 6days
(C) 8days
(D) 10days
(E) 5days
Rationale: 2nd machine 10days work = 1/15*10 = 2/3
Remaining work = 1 - 2/3 = 1/3
now 1/18 work is done by 1st machine in 1day
1/3 work is done by 1 machine in 18*1/3 = 6days.
Answer is B
Answer: (B) 6days
Question: Find the missing number in the given sequence : 5,10,15,?,?,30,35
(A) 18 & 28
(B) 16 & 22
(C) 17 & 23
(D) 16 & 24
(E) 20 & 25
Rationale: 5+5=10
10+5=15
15+5=20
20+5=25
25+5=30
30+5=35
ANSWER:E
Answer: (E) 20 & 25
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections W of the 4 items can Amanda make?
(A) 9
(B) 12
(C) 14
(D) 15
(E) 60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
W=3*20=60
E. 60
Answer: (E) 60
Question: In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, those whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?
(A) 19
(B) 41
(C) 21
(D) 57
(E) 26
Rationale: Answer
We need to find out the number of students who took at least one of the three subjects and subtract that number from the overall 120 to get the number of students who did not opt for any of the three subjects.
Number of students who took at least one of the three subjects can be found by finding out A U B U C, where A is the set of those who took Physics, B the set of those who took Chemistry and C the set of those who opted for Math.
Now, AUBUC = A + B + C - (A n B + B n C + C n A) + (A n B n C)
A is the set of those who opted for Physics = 120/2 = 60 students
B is the set of those who opted for Chemistry = 120/5 = 24
C is the set of those who opted for Math = 120/7 = 17.
The 10th, 20th, 30th..... numbered students would have opted for both Physics and Chemistry.
Therefore, A n B = 120/10 = 12
The 14th, 28th, 42nd..... Numbered students would have opted for Physics and Math.
Therefore, C n A = 120/14 = 8
The 35th, 70th.... numbered students would have opted for Chemistry and Math.
Therefore, B n C = 120/35 = 3
And the 70th numbered student would have opted for all three subjects.
Therefore, AUBUC = 60 + 24 + 17 - (12 + 8 + 3) + 1 = 79.
Number of students who opted for none of the three subjects = 120 - 79 = 41.
choice is (B)
Answer: (B) 41
Question: 1+1
(A) 9
(B) 8
(C) 3
(D) 0
(E) 2
Rationale: E
Answer: (E) 2
Question: Walking at 5/6 of its usual speed, a train is 10 minutes too late. Find its usual time to cover the journey.
(A) 50 min
(B) 20 min
(C) 1 hour
(D) 30 min
(E) 45 min
Rationale: new speed = 5/6 of the usual speed
new time taken = 6/5 of the usual time taken
so, ( 6/5 of the usual time ) - ( usual time ) = 10min
1/5 of the usual time = 10min
usual time = 10*5 = 50 min
correct option is A
Answer: (A) 50 min
Question: A can do a work in 16 days. A and B can do it in 8 days. How many days can B alone can do the work?
(A) 1/16
(B) 32
(C) 16
(D) 8
(E) 1/8
Rationale: Ans is:C
A's 1 day's work =1/16
(A + B)'s 1 day's work =1/8
B's 1 day's work =1/8-1/16=1/16
Therefore whole work can be done by B in 16 days. Ans:C
Answer: (C) 16
Question: The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home?
(A) 60%
(B) 50%
(C) 55%
(D) 40%
(E) 33.3%
Rationale: Increase = 168000-120000 = 48000
% increase = 48000*100/120000 = 40%
Answer: option D
Answer: (D) 40%
Question: A group of tourists wants to visit only three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.
(A) 18
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: The number of ways to choose three cities is 4C3=4.
The number of itineraries for each group of 3 cities is 3!.
So the number of itineraries to three cities is 4*3!=24.
The answer is B.
Answer: (B) 24
Question: Forty ladies and fifty gentlemen are present at a party. There are 30 couples among them. If a lady and a gentleman is selected at random, what is the probability that they will be a couple?
(A) 3/200
(B) 1/100
(C) 1/50
(D) 1/40
(E) 1/20
Rationale: In how many ways we can select a woman and a man from 40 women and 50 men? In 40*50 = 2,000 ways.
We have a total of 30 couples so, the probability of selecting a couple is 30/2,000 = 3/200.
Ans- A
Answer: (A) 3/200
Question: Next number in the series is 1 , 2 , 4 , 13 , 31 , 112 , ?
(A) 221
(B) 222
(C) 223
(D) 224
(E) 225
Rationale: In
Base 5
1 (1), 2(2) , 4(4) , 13(8) , 31(16) , 112(32) ,224(64)
ANSWER:D
Answer: (D) 224
Question: How many 2 digit numbers that do not contain the digit 2 are there?
(A) 72
(B) 68
(C) 84
(D) 96
(E) 124
Rationale: Applying combinations....8 * 9 = 72...
8 for first digit...cant be 0 or 2
9 for 2nd ....cant be 2
ANSWER: A
Answer: (A) 72
Question: In traveling from a dormitory to a certain city, a student went 1/2 of the way by foot, 1/4 of the way by bus, and the remaining 6 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
(A) 35
(B) 24
(C) 14
(D) 24
(E) 12
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/2x + 1/4x + 6
x - 1/2x - 1/4x = 6
x = 24km
Option: D
Answer: (D) 24
Question: Find remainder if (67^67 +67) is divided by 68
(A) 60
(B) 62
(C) 66
(D) 72
(E) 78
Rationale: => (6767 + 1) is divisible by (67 + 1)
=> (6767 + 1) is divisible by 68
=> (6767+1) ÷ 68 gives a remainder of 0
=> [(6767+1) + 66] ÷ 68 gives a remainder of 66
=> (6767 + 67) ÷ 68 gives a remainder of 66
C
Answer: (C) 66
Question: in a soccer bet,we play 4 teams.first team odd 1.26,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?
(A) 219.5
(B) 225.5
(C) 235.01
(D) 266.74
(E) 669.0
Rationale: in the case we won the bet,we have:
1.26* 5.23* 3.25* 2.0*5.00=219.50
we will win 219.50
so correct answer is A)219.50
Answer: (A) 219.5