RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Tom, who has 50 math questions, will get 7 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 3 points per question. Then, which of the following can be the score if he solves all the 50 questions?
A.190
B.193
C.194
D.195
Answer: A.190
Explanation: Let x be the correctly answered questions. y be the wrongly answered/ skipped ones.
We have x + y = 50;
Score = 7x-3y
3x+3y = 150; 7x-3y = Score;
==> 10x = 150+Score;
check for answer choices where 150+Score is divisible by 10
Choice (A) 190 fits the equation !
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 7 days. B can do the work alone in?
A.19
B.12
C.11
D.42
Answer: D.42
Explanation: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/7
6/x = 1/7 => x = 42
So, B takes 21 hours to finish the work.
Answer: D
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5
B.2.7
C.2.9
D.2.3
Answer: A.2.5
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer: A
Question: Charlie, a painter, has 9 jars of paint: 4 are violet, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions:
1) C1, if the paint contains 2 jars of brown paint and no violet paint
2) C2, if the paint contains 3 jars of brown paint.
3) J1, if the paint contains at least 2 jars of violet paint
4) J2, if the paint contains exactly 1 jar of violet paint
What is the probability that the new colour will be a shade of J (J1 or J2)?
A.37/42
B.35/42
C.37/21
D.74/21
Answer: A.37/42
Explanation: the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2
For C1-3C2(Brown)*2C1(Yellow)=3*2=6
For C2-3C3(all brown)=1
Total=9C3=84
1-7/84=77/84= 37/42
Answer : A
Question: The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?
A.33
B.94
C.77
D.266
Answer: B.94
Explanation: Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 --- (1)
10b + a = 10a + b - 45
45 = 9a - 9b => a - b = 5 --- (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.
Answer: B
Question: Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 25kmph and Prasanna moves southward at a speed of 35 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
A.11
B.50
C.60
D.27
Answer: C.60
Explanation: Explanation:
We know 60 min = 1 hr
Total northward Laxmi's distance = 25kmph x 1hr = 25 km
Total southward Prasanna's distance = 35kmph x 1hr = 35 km
Total distance between Prasanna and Laxmi is = 25 + 35 = 60 km.
Answer: C
Question: A boatman goes 4 km against the current of the stream in 4 hour and goes 1 km along the current in 20 minutes. How long will it take to go 6 km in stationary water?
A.5 hours
B.1 hours
C.3 hours
D.2 hours
Answer: C.3 hours
Explanation: Speed upstream =4/4=1 km/hr
Speed downstream = 1/(20/60)=3 km/hr
Speed in still water = 1/2(3+1)=2 km/hr
Time taken to travel 6 km in still water =6/2=3 hours
ANSWER:C
Question: Vijay bought 160 shirts at the rate of Rs. 210 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
A.s.225
B.s.288
C.s.485
D.s.267
Answer: D.s.267
Explanation: Total CP per shirt = 210 + 1400/160 + 1.75 + 320/160 = Rs. 222.5
SP = CP[(100 + profit%)/100]
= 222.5 * [(100 + 20)/100] = Rs.267.
Answer:D
Question: If 0.2 of a number is equal to 0.08 of another number, the ratio of the numbers i
A.2 : 3
B.2 : 5
C.3 : 20
D.20 : 3
Answer: B.2 : 5
Explanation: Sol.
0.2A = 0.08 B â‡” A / B = 0.08 / 0.20 = 8/20 = 2/5
âˆ´ A : B = 2 : 5.
Answer B
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in
A.3 days
B.4 days
C.4 1/5 days
D.5 days
Answer: A.3 days
Explanation: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
A
Question: Which number can we add to 859722 to get a number exactly divisible by 456?
A.294
B.306
C.318
D.338
Answer: A.294
Explanation: 859722 / 456 = 1885 with a remainder of 162.
We need to add 456 - 162 = 294
The answer is A.
Question: What will be 90 percent of a number whose 200 percent is 90 ?
A.144
B.72
C.40.5
D.None of these
Answer: C.40.5
Explanation: Answer
∵ 200% of N = 90
⇒ N = (90 x 100) / 200 = 45
∴ 90% of N = (90 x 45) / 100 = 40.5
Correct Option: C
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 11 units?
A.140 sq.units
B.170 sq.units
C.154 sq.units
D.940 sq.units
Answer: C.154 sq.units
Explanation: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 11 units
Area of the rectangle = lb = 14 * 11 = 154 sq.units
Answer: Option C
Question: A set of numbers has the property that for any number t in the set, 3t + 1 is in the set. If -1 is in the set, which of the following must also be in the set?
I. -3
II. 10
III. 5
A. I only
B. II only
C. I and II only
D. II and III only
Answer: B. II only
Explanation: The question is which of the followingmustbe in the set, notcouldbe in the set.
If -1 is in the set so must be 3*-1+1=-2, as -2 is in the set so must be 3*-2+2=-4, as -4 is in the set so must be 3*-4+2=10 and so on.
Answer: B.
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 120 pages?
A.8 hours 15 mins
B.8 hours
C.9 hours
D.7 hours
Answer: C.9 hours
Explanation: Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 120 pages when Anil and Suresh work together = 120 × 3 /40 = 9
= 9 hour
Answer is C.
Question: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 27 percent ryegrass, what percent of the weight of this mixture is X ?
A. 10%
B. 13.33 %
C. 40%
D. 50%
Answer: B. 13.33 %
Explanation: ---------------->Ryegrass
X-------------->	40%
Y-------------->	25%
M(mixture)---->27%
0.4X + (M-X)0.25 = 0.27M
0.15X = 0.02M
X = 0.1333M
X = 13.33% of M
B
Question: Calculate the number of revolutions a circular wheel of 4.6 m radius will make to travel a distance of 1 km?
A.28414.2
B.28914.2
C.21914.2
D.28944.2
Answer: B.28914.2
Explanation: 2 * 22/7 * 4.6 * x = 28914.3
x = 1000
Answer: B
Question: In a certain lottery, the probability that a number between 1 and 15, inclusive, is drawn is 1/3 . If the probability that a number 1 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 15 is drawn?
A.2/3
B.1/3
C.1/4
D.1/6
Answer: A.2/3
Explanation: You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 1 or larger
Set 2: Number 15 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or less OR both)
2/3 + P(Set 2) - 1/3 = 1
P(Set 2) = 2/3
Answer A
Question: What is the Area? If The volume of a Square is 22cm.
A.1
B.Not sufficient data
C.5
D.11
Answer: B.Not sufficient data
Explanation: The answer is not efficient data to calculate. There is no volume in Square. So we can't determine the area.
Answer is option B
Question: 7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.
A.200
B.300
C.400
D.500
Answer: B.300
Explanation: 1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc
This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7)
You have 1*9*9 = 81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81 = 243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once.
In each of these numbers, 7 is written once. Therefore, 243 times.
2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77
In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7).
There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers.
In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.
3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it.
Therefore, the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300
Option B
Question: what comes next?
7, -35, -34, -3, 15, 16, 4
A.-20
B.-15
C.5
D.21
Answer: A.-20
Explanation: 7*-5=-35, then -35+1=-34
-3*-5=15,then 15+1=16
so 4*-5=-20
ANSWER:A
Question: The sum of two numbers is 84, and one of them is 12 more than the other. What are the two numbers?
A.48, 36
B.36, 48
C.32, 48
D.48, 32
Answer: B.36, 48
Explanation: 2x = 84 − 12
= 72.
x = 72/2
= 36.
This is the first number. Therefore the other number is
x + 12 = 36 + 12 = 48.
The sum of 36 + 48 is 84.
Answer is B.
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
A.176 cm
B.800 cm
C.126 cm
D.269 cm
Answer: B.800 cm
Explanation: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square
= 4 * 200
= 800 cm.
Answer:B
Question: A total of 22 men and 28 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
A. 31
B. 31.5
C. 32.6
D. 32.5
Answer: C. 32.6
Explanation: Let Aw = average age of women
Average = (Number of men X average age of men + Number of women X average age of women)/total number of people
35 * 50 = 22 * 38 + 28 * Aw
=>1750 = 836 + 28 Aw
=> 28 Aw = 914
=>Aw = 32.6
Answer C
Question: Sara and Alan start a company with Rs.100000 and Rs.50000 respectively. how should they share their profits at the end of one year?
A.2:1
B.3 by 4
C.3:8
D.3:1
Answer: A.2:1
Explanation: The ratio of the investments made by A and B =
100000: 50000=> 2:1.Answer: A
Question: A natural number has 43 divisors (excluding 1 and itself) . What is the maximum number of distinct prime factors it can have ?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: no. of total divisors=43+2=45
If N=a^p*b^q*c^r.... then the number of factors of N = (p+1)(q+1)(r+1) ....
45=3*3*5
distinct prime factors are 3 and 5
ANSWER:A
Question: The cost of 16 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
A.Rs 52.50
B.Rs 56
C.Rs 58.50
D.Rs 64.75
Answer: A.Rs 52.50
Explanation: Explanation :
Let the required cost be Rs. x. Then,
More packets, More cost (Direct Proportion)
More weight, More cost (Direct Proportion)
Packets 16 : 27
Weight 900 : 1000 :: 28 : x
(16 x 900 x x) = (27 x 1000 x 28)
x = (27 x 1000 x 28) /16 x 900
= 105 /2
= 52.50
Answer A
Question: The least number which should be added to 1800 so that the sum is exactly divisible by 5,6,4 and 3 is :
A.3
B.13
C.23
D.30
Answer: D.30
Explanation: Solution
L.C.M. of 5,6,4 and 3 = 60. on dividing 1800 by 60, the remainder is 30.
∴ Number to be added = (60-30) = 30. Answer D
Question: A man sells a book at 5% profit. If he had bought it at 5% less and sold it for Re 1 less, he would have gained 10%. The cost price of the book is
A.Rs 200
B.Rs 150
C.Rs 250
D.Rs 240
Answer: A.Rs 200
Explanation: Let the C.P of the article be Rs X
Profit = 5%
Therefore, S.P. = X + 5 % of X = 21X / 20
If C.P would have been (X - 5% of X), i.e.,
Rs 19 X / 20 and S.P would have been Rs [ (21 X / 20) - 1 ],
Then, gain % = 10 %
Therefore, [ { ( 21 X / 20) - 1 } - 19 X / 20 ] / (19 X /20 ) x 100 = 10
(2 X - 20 / 19 X) x 100 = 10
=> X = 200
ANSWER:A
Question: If x, y, and g are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=g and if x is less than y, which of the following could be the value of g?
A.10
B.12
C.15
D.18
Answer: D.18
Explanation: Answer choice C: g= 15
(10x + 20y)/(x+y) = 15
10x + 20y = 15x + 15y
5y = 5x
y = x
Doesn't work because the problem states that x<y.
We need y to be larger, so let's try answer choice D: g=18
10x + 20y = 18x + 18y
2y = 8x
y/x = 8/2
Success! x<y.
The correct answer is D.
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 7. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
A.60
B.120
C.160
D.200
Answer: C.160
Explanation: A:B:C:D=2x:3x:5x:10x, for some positive number x. Total time 2x+3x+5x+10x=20x.
If 2x = 30 then 20x = 300;
If 3x = 30 then 20x = 200;
If 5x = 30 then 20x = 120;
If 10x = 30 then 20x = 60;
Only answer choices which is not obtained is 160.
Answer: C.
Question: An alloy is to contain Steel and Iron in the ratio 5:2. The Iron required to be melted with 35kg of Steel is?
A.12kg
B.14kg
C.15kg
D.20kg
Answer: B.14kg
Explanation: Let the required quantity of steel be x kg
5:2::35:x
5x =2*35
x = 14kg
Answer is B
Question: A pharmaceutical company received $2 million in royalties on the first $20 million in sales of and then $9 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
A.8%
B.15%
C.45%
D.52%
Answer: B.15%
Explanation: (9/108)/(2/20) = 30/54 = 55,5% it means that 9/108 represents only 83,3%. Therefore a decrease of 15%.
Answer B
Question: If 5 spiders can catch five flies in five minutes, how many flies can hundred spiders catch in 100 minutes?
A.100
B.1000
C.500
D.2000
Answer: D.2000
Explanation: 5 × 5 × x = 100 × 100 × 5 ⇒ x = 2000.
Answer: D.
Question: A train 125 m long passes a man, running at 7 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
A.52 km/hr
B.17 km/hr
C.76 km/hr
D.50 km/hr
Answer: A.52 km/hr
Explanation: 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 - 7) km/hr.
x - 7 = 45 => x = 52 km/hr.
Answer: A
Question: A project scheduled to be carried out over a single fiscal year has a budget of $18,000, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $6500. By how much was the project over its budget?
A. $500
B. $540
C. $1,050
D. $1,380
Answer: A. $500
Explanation: Difficulty level: 600
Each month's budget = 18000/12 = 1500
Budget for 4 months = 4*1500 = 6000
Actual amount spent = 6500
Amount spent over the budget = 6500 - 6000 = 500
Answer (A),
Regards,
Question: 2 pipes can separately fill a tank in 20hrs and 30hrs respectively. Both the pipes are opened to fillthe tank, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
A.10 hrs
B.12 hrs
C.16 hrs
D.18 hrs
Answer: C.16 hrs
Explanation: 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
C
Question: A millionaire bought a job lot of hats 1/4 of which were brown. The millionaire sold 2/3 of the hats including 4/5 of the brown hats. What fraction of the unsold hats were brown.
A.1/60
B.1/15
C.3/20
D.3/5
Answer: C.3/20
Explanation: If initially he had x hats.
x/4 were brown.
sold x*2/3 hats. left with x/3 hats.
sold (x/4)*((4/5) = x/5 brown hats and left with x/4-x/5= x/20 brown hats.
Fraction of brown hats in total remaining hats = (x/20)/(x/3) = 3/20 hats
ANSWER:C
Question: A train running at the speed of 36 km/hr crosses a pole in 9 seconds. What is the length of the train?
A.286
B.278
C.90
D.150
Answer: C.90
Explanation: Speed=(36 * 5/18) m/sec = (10) m/sec Length of the train
= (Speed x Time) = (10 * 9) m
= 90 m.
Answer:C
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 8:6:4. If there are in all Rs.114, the number of 25 paisa coins is?
A.52
B.62
C.72
D.86
Answer: C.72
Explanation: 8x 6x 4x
50 25 100
400x + 150x + 400x = 11400
950x = 11400
x = 12 => 6x = 72
Answer: C
Question: At a tanning salon, customers are charged $10 for their first visit in a calendar month and $4 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon?
A.$1220
B.$1160
C.$1300
D.$1340
Answer: B.$1160
Explanation: I get B. This question seems too straightforward for 600+. Am I missing something?
100 first-time visits --> 100(10) = $1000
30 + 10 = 40 subsequent visits --> 40(4) = $160
Total revenue: 1000+ 160 = $1160
The answer is B.
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 9.8?
A.12.6.
B.14.4.
C.15.8.
D.16.2.
Answer: A.12.6.
Explanation: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 9.8
= 6*0 + 2*7.2 + 8 - 9.8
= 0 +14.4 -1.8
12.6
Answer A
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 9 and 5 respectively, is:
A.16
B.127
C.235
D.305
Answer: A.16
Explanation: Explanation:
Required number = H.C.F. of (1657 - 9) and (2037 - 5)
= H.C.F. of 1648 and 2032 = 16. Answer: A
Question: 50% of a number is 10 less than 3/5th of that number. What is the number?
A.100
B.50
C.150
D.200
Answer: A.100
Explanation: Let the number be x
Then, 3x/5 - (50% of x) = 10
3x/5-50x/100 = 10
x = 100
Answer is A
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
A.5/7
B.5/9
C.5/3
D.5/2
Answer: B.5/9
Explanation: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer:B
Question: If 16% of 40% of a number is 5, then the number is
A.200
B.225
C.78.125
D.320
Answer: C.78.125
Explanation: Explanation:
Let 16/100×40/100×a=5
a = 5×100×100/16×40=78.125
Correct Option: C
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189.The amount of the bill is
A.Rs. 1386
B.Rs. 1764
C.Rs. 1575
D.Rs. 2268
Answer: B.Rs. 1764
Explanation: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.189.
∴ x 16 x9/ 12x 1/100}= 189 or x = 1575.
∴ P.W. = Rs. 1575.
Answer B
Question: Two numbers are 30% and 37% are less than a third number .How much percent is the second number less than the first?
A.19%
B.80%
C.10%
D.90%
Answer: C.10%
Explanation: I II III
70 63 100
70 -------- 7
100 ------ ? => 10%
Answer:C
Question: Find the least value of 'a' so that 365a24 is divisible by 8.
A.9
B.8
C.0
D.2
Answer: C.0
Explanation: Explanation:
Given, number is divisible by 8 only if 'a24' is divisible by 8.
.: Least value of a is '0'.
Answer: Option C
Question: If the radius of a circle that centers at the origin is 5, how many M points on the circle have integer coordinates?
A. 4
B. 8
C. 12
D. 15
Answer: C. 12
Explanation: I understand this might not be required but I used the equation of a circle.
Since the origin is at 0, x^2+y^2=5^2.
X,Y could be +/- (0,5 or 5,0) - 4 possibilities.
X,Y could be +/- (3,4 or 4,3) - 8 possibilities.
Ans: M=C
Question: in a certain flower shop, which stocks four types of flowers, there are 1/3 as many violets as carnations, and 1/3 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.63
B.64.28
C.65
D.66
Answer: B.64.28
Explanation: Given :-
Violets - C/3
Carnations - C
Tulip - C/9
Rose - C/9
Total flowers in terms of C = C/3+C+C/9+C/9 = 14C/9
Percentage of Carnations = C/14C/9 *100 =64.28%
Answer B
Question: If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
5 – 9 + 8 × 3 ÷ 20 =
A.6
B.9
C.12
D.-2
Answer: B.9
Explanation: B 9
Question: A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
A.5.15 a.m
B.7.20 a.m
C.2.15p.m
D.3.45p.m
Answer: C.2.15p.m
Explanation: Suppose they meet x hours after 10 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x =	17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Ans: C
Question: The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?
A.33 1/3%
B.33 1/8%
C.33 6/3%
D.33 8/3%
Answer: A.33 1/3%
Explanation: 100
75
-------
75 ------- 25
100 ------ ? => 33 1/3%
Answer: A
Question: The expression rs+r is odd when the r and s are integers. Which of the following expressions must be even?
A.r
B.s
C.r + s
D.rs - r
Answer: B.s
Explanation: rs+r is odd
r and s are integers
If r were even rs+r would be even despite any value of s.
s can't be odd, so s must be even.
Ans : B
Question: The product of a and b is equal to 10 more than twice the sum of a and b. If b = 9, what is the value of b - a?
A.2
B.5
C.7
D.24
Answer: B.5
Explanation: ab= 10 + 2(a+b)
9a= 10+2a +18
7a= 28
a=4
b-a= 9-4=5
B is the answer
Question: Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate P in miles per hour for the entire trip?
A.P=26.7
B.P=30.0
C.P=40.0
D.P=53.3
Answer: C.P=40.0
Explanation: VERITAS PREPOFFICIAL SOLUTION
Correct Answer : C
Using the formula: Time = Distance/Rate, we find that Mike takes 4 hours to cover the first 320 miles of his trip. Since the 2nd 320 miles take 200% longer than the first, it takes Mike 8 hours longer, or 12 hours. (Note: 200% longer than the first half is not 200% of the first half.) The overall time is 4 hours + 12 hours or 16 hours. Since the definition of Average Rate = Total Distance Traveled/Total Time of Travel, Mike's average rate = 640/16 or 40 miles per hour.
Answer choice C is correct.