mathewhe/aqua_rat huggingface dataset:
Question: 20, 22, 26, 34, 41, 46, 56, 67, __?
(A) 72
(B) 80
(C) 88
(D) 68
(E) 78
Rationale: next no. = previous + (sum of digits)
20 + (2+0) = 22
22 + (2+2) = 26
26 + (2+6) = 34
-
-------
56 +(5+6) = 67
67 +(6+7) = 80
ANSWER:B
Answer: (B) 80
Question: If -1<x<0, what is the median J of these six numbers listed below
1/x^3,1/x^2, 1/x,x, x^2,x^3
(A) 1/x
(B) x^2
(C) x^2(x+1)/2
(D) J=x(x^2+1)/2
(E) x^2/2x
Rationale: My approach: Put any value between -1 and 0. you will get the answer. lets say 0.5. so the list will be as follows:
-8,-2,-0.5,-0.125 and last two numbers will be positive so need to see that.
median will be between -0.5 and -0.125.
So, (x^3+x)/2 (D).
Answer: (D) J=x(x^2+1)/2
Question: Two trains of length 100 meters and 200 meters are 140 meters apart. They are moving towards each other on parallel tracks, at speeds of 54 km/h and 72 km/h. After how many seconds will the trains meet?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: The speeds are 54000/3600 = 15 m/s and 72000/3600 = 20 m/s
The relative speed is 35 m/s.
time = 140 / 35 = 4 seconds
The answer is B.
Answer: (B) 4
Question: A train is moving at a speed of 60km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?
(A) 30sec
(B) 45sec
(C) 36sec
(D) 29sec
(E) 52sec
Rationale: Speed of the train = 60*5/18 = 50/3 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(50/3) =30sec
Answer is A
Answer: (A) 30sec
Question: In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number Y of employees who take the subway to work?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: P/3 + F/4 = P/3 + (48-P)/4 = 12 + P/2
P/3 + F/3 = (P+F)/3 = 48/3 = 16
P/4 + F/4 = 12
P/3 + F/3 > P/3 + F/4 > P/4 + F/4
--> 16> 12 + P/12 > 12
GREATEST Possible Y: 12 + p/12 = 15 --> p = 36 ( integer --> good)
15 or D is the answer
Answer: (D) 15
Question: The ratio of cats to dogs to birds to fish is 7:8:9:10. There are no other types of animals in the pet store.which of the following cannot be the total number of animals in the store?
(A) 68
(B) 102
(C) 136
(D) 170
(E) 210
Rationale: The parts add up to 7 + 8 + 9 + 10 = 34, so we know that any possible number of total answers must be a multiple of 34. All five answer choices are multiples of 34:
(A) 68= 34*2
(B) 102= 34*3
(C) 136= 34*4
(D) 170= 34*5
(E) 210 = not multiple of 34
Answer: (E) 210
Question: A students was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?
(A) 3
(B) 7
(C) 17
(D) 31
(E) 10
Rationale: Solution
Clearly, we have (3+11+7+9+15+13+8+19+17+21+14+x/12)	=12
Number in place of x is
137+x=144
x= 144-137
x= 7.
Answer B
Answer: (B) 7
Question: Excluding stoppages, the speed of a train is 42 kmph and including stoppages it is 27 kmph. Of how many minutes does the train stop per hour?
(A) A)19.42
(B) B)20.42
(C) C)21.42
(D) D)22.42
(E) E)23.42
Rationale: Explanation:
T = 15/42 * 60 = 21.42
Answer: Option C
Answer: (C) C)21.42
Question: Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they which are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then, how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects ?
(A) 8
(B) 10
(C) 15
(D) 22
(E) 25
Rationale: total number arrangement without any restriction is 2^5=32
nymber of arrangement in which blue balls are adjacent =bb,bb,bb,bb,bbb,bbb,bbb,bbbb,bbbb,bbbbb=10
hence required number= 32-10=22
ANSWER:D
Answer: (D) 22
Question: Ajay spends 25 per cent of his salary on house rent, 5 percent on food, 10 percent travel, 10 percent on clothes and the remaining amount of Rs.32000 is saved. What is Ajayâ€™s income?
(A) Rs.60000
(B) Rs.80500
(C) Rs.64000
(D) Rs.70500
(E) None of these
Rationale: Explanation:
Savings = Income â€“ expenditure
100 â€“ (25+5+10+10) = 50%
50% of income = Rs.32000
:. Income = 32000x 100/50 = Rs. 64000.
Answer: Option C
Answer: (C) Rs.64000
Question: A train 850 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 510
(B) 450
(C) 500
(D) 520
(E) 589
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (850 + x)/60 = 65/3
x = 450 m.
Answer: Option B
Answer: (B) 450
Question: Today is Monday. After 61 days, it will be:
(A) Sunday
(B) Saturday
(C) Friday
(D) Thursday
(E) Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer :B
Answer: (B) Saturday
Question: If n is a 18-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 3
II. n is divisible by 9
III. n is divisible by 18
(A) I only
(B) I , II and III only
(C) I and III only
(D) II and III only
(E) II
Rationale: Rule for divisibility by 3: The sum of the digits of the number should be multiple of 3
Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.
Rules for divisibility by 18: The sum of the digits should a multiple of 18
Consider no 11111111...18 times = The sum 18*1=18----> divisbible by 3,9 and 18
consider number to be 222....18 times, then sum of the no. 18*2=36 divisibly by 3,9 and 18
So why so because when you sum the numbers either you can add the digits 27 times or multiply the digit *18..
Note that since 18 is divisble by 18,9 and 3 and thus the sum of the nos will be divisible by all the nos.
Ans is B
Answer: (B) I , II and III only
Question: A train is moving at a speed of 120km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?
(A) 30sec
(B) 45sec
(C) 15sec
(D) 29sec
(E) 52sec
Rationale: Speed of the train = 120*5/18 = 100/3 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(100/3) =15sec
Answer is C
Answer: (C) 15sec
Question: Each writer for the local newspaper is paid as follows: a dollars for each of the first x stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits x+ a stories in a month earn than a writer who submits x+ b stories?
(A) (a – b)( a + b + x)
(B) a – b
(C) a^2 – b^2
(D) x( a – b)
(E) ax + bx – ax
Rationale: total earned for x+a stories =a + a(a+b)
total earned for x+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
=(a+b)(a-b) =a^2-b^2
answer is C
Answer: (C) a^2 – b^2
Question: An seller earns an income of Re 1 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 20th day of business, he earns an income of:
(A) 29
(B) 57
(C) 35
(D) 20
(E) 30
Rationale: 2nd day he earns = 3(2 – 1)
3rd day he earns = 3(3 – 1)
On 20th day he earns 3(20 -1) =57 rupees
ANSWER:B
Answer: (B) 57
Question: In a lottery, there are 10 prizes and 15 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/10
(B) 2/5
(C) 2/7
(D) 5/7
(E) None
Rationale: Solution
P(getting a prize)	= 10 / (10+15)
‹=› 10 / 25
‹=› 2 / 5.
Answer B
Answer: (B) 2/5
Question: If a man crosses a 600 m long street in 5 minutes. What is his speed?
(A) 5.2 km/hr
(B) 6.5 km/hr
(C) 7.2 km/hr
(D) 8.9 km/hr
(E) 9.8 km/hr
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
C
Answer: (C) 7.2 km/hr
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1123
(B) 1234
(C) 1452
(D) 1356
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 40 feet on a side. What will be the volume of the new building in cubic feet?
(A) 6,983,629 cubic feet
(B) 15,750 cubic feet
(C) 11550√3 cubic feet
(D) 15,750√3 cubic feet
(E) 3,937,500√3 cubic feet
Rationale: Volume of the Hexagon with side 200 and height 70 = Area * height
= 6*(sqrt(3)/4)(200^2)(70)
Volume of the center bull's eye that is similar in shape of a hexagon but side 50
= 6 * (sqrt(3)/4)(40^2)*70
Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(40^2)*70
Answer: (A) 6,983,629 cubic feet
Question: If e is a positive integer, Which of the following options must be divisible by 2?
(A) (e−1)*e*(e+1)
(B) e^2*(e−5)
(C) e^2*(e−5)
(D) (e^2−2)
(E) e(e+2)^3
Rationale: option A) (e−1)*e*(e+1) which represents the product of three consecutive integers
the product of 3 consecutive integers is divisible by both 2 and 3.
Answer is A
Answer: (A) (e−1)*e*(e+1)
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 22 overs to reach the target of 282 runs?
(A) 6.25
(B) 11.36
(C) 7.4
(D) 5
(E) 6
Rationale: Explanation:
Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 22
Run rate needed = 250/22=11.36
Answer: Option B
Answer: (B) 11.36
Question: Simple interest on a sum at 5% per annum for 2 years is Rs.120. The C.I. on the same sum for the same period is?
(A) 81.6
(B) 81.9
(C) 121.5
(D) 121.3
(E) 121.1
Rationale: SI = 60 + 60
CI = 60 + 60 + 1.5= 121.5
Answer: C
Answer: (C) 121.5
Question: Evaluate: 11110 + 24*3*10 = ?
(A) 90111
(B) 52631
(C) 11190
(D) 65321
(E) 11133
Rationale: According to order of operations, 24?3?10 (division and multiplication) is done first from left to right
24/2 = 8* 10 = 80
Hence
11110 + 24*3*10 = 11110 + 80 = 11190
correct answer C
Answer: (C) 11190
Question: A car moves at 64 km/hr. What is the speed of the car in meters per second ?
(A) 20 2/9m sec
(B) 17 2/9m sec
(C) 18 2/9m sec
(D) 19 2/9m sec
(E) 28 2/9m sec
Rationale: Explanation:
Speed=(64∗5/18)m/sec
=155/9 m/sec
=17 2/9msec
Option B
Answer: (B) 17 2/9m sec
Question: In an election between two candidates first candidate got 30% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
(A) 3700 votes
(B) 4000 votes
(C) 4900 votes
(D) 4980 votes
(E) 4990 votes
Rationale: Total = 100 %,
First person got 30%
second person got remaining 70 % of votes.
than 70 % = 2800
70% = 70Ã—40 = 2800
100% =100Ã—40 =4000 votes
B
Answer: (B) 4000 votes
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 65 sec
(B) 55 sec
(C) 48 sec
(D) 33 sec
(E) 12 sec
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125
= 48 sec.
Answer:C
Answer: (C) 48 sec
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car
(A) 960 km
(B) 950 m
(C) 906 km
(D) 906 m
(E) 950 m
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
ANSWER A
Answer: (A) 960 km
Question: If k and w are the dimensions of a rectangle that has area 40, and if k and w are integers such that k > w, what is the total number of possible values of k?
(A)  Two
(B)  Three
(C)  Four
(D)  Five
(E)  Six
Rationale: kw=40=40*1=20*2=10*4=8*5=--> k can take 4 values, namely: 8,10,20 and 40
Answer: C.
Answer: (C)  Four
Question: A and B can do a piece of work in 6 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 15.5 days
(B) 19.5 days
(C) 17.5 days
(D) 16.5 days
(E) 30 days
Rationale: C = 1/5 – 1/6 = 1/30 => 30 days
ANSWER:E
Answer: (E) 30 days
Question: Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?
(A) ab/(a+b)
(B) (a-b)/(a+b)
(C) b/(b-a)
(D) a/(a+b)
(E) b/(a+b)
Rationale: Let total work completion be denoted as 1.
Randy and Alvin can together complete work in ab/a+b hours.
Randy's 1hr work is 1/a.
Alvin's 1 hr work is 1/b.
Alvin's portion of total work = Alvin's 1hr work /total 1 hr work.
=(1/b)/((a+b)/ab)
=a/(a+b)
That's the portion of work Randy need not do.
ANSWER:D
Answer: (D) a/(a+b)
Question: Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
Answer: Option A
Answer: (A) 4
Question: The sum of two numbers is 25 and their difference is 13. Find their product?
(A) 104
(B) 114
(C) 315
(D) 325
(E) 335
Rationale: 114 is the ans
ANSWER:B
Answer: (B) 114
Question: A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
(A) 1 hour 40 minutes
(B) 1 hour 38 minutes
(C) 1 hour 20 minutes
(D) 1 hour 44 minutes
(E) 2 hour 20 minutes
Rationale: Let the distance and original speed be d km and k kmph respectively.
d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3
=> (5d - 4d)/4k = 1/3 => d = 4/3 k
Time taken to cover the distance at original speed
= d/k = 4/3 hours = 1 hour 20 minutes.
Answer: C
Answer: (C) 1 hour 20 minutes
Question: Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/2, what percent of the total number of the remaining employees would then be clerical?
(A) 25%
(B) 22.2%
(C) 20%
(D) 12.5%
(E) 11.1%
Rationale: Let's see, the way I did it was
1/3 are clerical out of 3600 so 1200 are clerical
1200 reduced by 1/2 is 1200*1/2
so it reduced 600 people , so there is 600 clerical people left
but since 600 people left, it also reduced from the total of 3600 so there are 3000 people total
since 600 clerical left / 3000 people total
you get (C) 20%
Answer: (C) 20%
Question: Find the odd man out. 445, 221, 109, 46, 25, 11, 4
(A) 25
(B) 109
(C) 46
(D) 221
(E) None of these
Rationale: Explanation :
To obtain next number, subtract 3 from the previous number and divide the result by 2
445
(445-3)/2 = 221
(221-3)/2 = 109
(109-3)/2 = 53
(53-3)/2 = 25
(25-3)/2 = 11
(11-3)/2 = 4
Clearly, 53 should have come in place of 46. Answer : Option C
Answer: (C) 46
Question: A trader bought a car at 20% discount on its original price. He sold it at a 60% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 28%
(B) 72%
(C) 12%
(D) 82%
(E) 16%
Rationale: Original price = 100
CP = 80
S = 80*(160/100) = 128
100 - 128 = 28%
Answer:A
Answer: (A) 28%
Question: A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?
(A) 37.9
(B) 37.2
(C) 37.1
(D) 37.82
(E) 37.8
Rationale: Assume the circumference of the circle is 200 meters. Hare and tortoise started at the same point but moves in the opposite direction. It is given that by that time tortoise covered 40 m (1/5th of the distance), Hare started and both met after hare has covered 25. This implies, in the time hare has covered 25m, hare has covered 200 - 40 - 25 = 135 meters.
So Hare : tortoise speeds = 25 : 135 = 5 : 27
Now Hare and tortoise has to reach the starting point means, Hare has to cover 175 meters and Tortoise has to cover only 25 meters in the same time.
As time =DistanceSpeed=2527=1755×KDistanceSpeed=2527=1755×K
Ie., Hare has to increase its speed by a factor K. Solving we get K = 37.8
Answer:E
Answer: (E) 37.8
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
(A) 5767
(B) 5760
(C) 5788
(D) 5768
(E) 5769
Rationale: 1/x - 1/6
= -1/8
x = 24 hrs
24 * 60 * 4
= 5760
Answer:B
Answer: (B) 5760
Question: Find the average of all prime numbers between 4 and 15.
(A) 30
(B) 4
(C) 9
(D) 8
(E) None
Rationale: Sol.
There are four prime numbers between 4 and 15.
They are 5, 7, 11, 13
âˆ´ Required average = [5 + 7 + 11 +13 / 4] = 36/ 4 = 9
Answer C
Answer: (C) 9
Question: A sports equipment store sold ping pong rackets for a total of $588. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold?
(A) 50
(B) 60
(C) 490
(D) 500
(E) 980
Rationale: Average price for a pair of rackets = $9.8
Total cost = $9.8*x = $588
x = 60 pairs were sold.
ANSWER:B
Answer: (B) 60
Question: A man drives at a speed of 40 miles/hr. His wife left 30 mins. late with 50 miles/hr speed. when will they meet ?
(A) 1 hours
(B) 2 hours
(C) 3 hours
(D) 4 hours
(E) 5 hours
Rationale: In 30 minutes the man would have droven 20 miles, when his wife starts. Now both are driving in the same direction. So speed of wife related to man is 10(50-40) miles/hr. So wife will cover 20 miles in 2 hours to meet the man.
ANSWER:B
Answer: (B) 2 hours
Question: Of the 800 employees of Company X, 20 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 10 percent ?
(A) 88.88
(B) 160
(C) 112
(D) 80
(E) 56
Rationale: The # oflong-termemployees is 20%*800=160.
After y of them retire new # oflong-termemployees would become 160-y.
Total # of employees would become 800-y.
We want 160-y to be 10% of 800-y --> 160-y=(800 -y)*10% --> y = 88.88.
Answer: A.
Answer: (A) 88.88
Question: Find the odd number
(A) 21
(B) 17
(C) 3
(D) 14
(E) 12
Rationale: Each of the numbers except 14 is an odd number.
The number '14' is the only EVEN number.
answer :D
Answer: (D) 14
Question: Rs.590 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?
(A) Rs.157
(B) Rs.150
(C) Rs.117
(D) Rs.119
(E) Rs.127
Rationale: A+B+C = 590
5A = 6B = 8C = x
A:B:C = 1/5:1/6:1/8
= 24:20:15
15/59 * 590 = Rs.150
Answer:B
Answer: (B) Rs.150
Question: In a group of 28 junior high school students, 7 take French, 9 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
(A) 7
(B) 6
(C) 9
(D) 4
(E) 8
Rationale: E
8
Add 7 + 9 + 4 to get 20.
Then subtract 21 from the total students ⇒ 28 – 20 = 8.
Answer is E
Answer: (E) 8
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 81. What is that number
(A) 9
(B) 10
(C) 12
(D) 14
(E) 15
Rationale: Explanation:
=> 3(2x+9) = 81
=> 2x+9 = 27
=> x = 9
Answer: Option A
Answer: (A) 9
Question: If 3 machines can build a car in 12 hours, how fast can 4 machines do it?
(A) 10 hours
(B) 9 hours
(C) 8 hours
(D) 7 hours
(E) 11 hours
Rationale: 3 * 12 = 4 * x
x = 9 hours
Answer: B
Answer: (B) 9 hours
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
(A) 27 7/9m
(B) 27 m
(C) 33 m
(D) 23 4/9 m
(E) 25 m
Rationale: Relative speed = (40 - 20) km/hr = ( 20 x 5/18 ) m/sec = 50/9 m/sec.
Therefore Length of faster train = ( 50/9 x 5 ) m = 250/9 m = 27 7/9 m.
ANSWER A
Answer: (A) 27 7/9m
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) Rs.270
(B) Rs.185
(C) Rs.215
(D) Rs.380
(E) Rs.315
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
ANSWER:A
Answer: (A) Rs.270
Question: A student completes a 3 part exam as follows. The student completes section A in 10 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour?
(A) 5:2
(B) 4:1
(C) 4:3
(D) 3:2
(E) 2:1
Rationale: The time spent on section B and section C is 25 minutes each.
The ratio of C to A is 25:10 = 5:2
The answer is A.
Answer: (A) 5:2
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 80/9 sec
(B) 80/7 sec
(C) 30/7 sec
(D) 80/8 sec
(E) 81/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.Answer:B
Answer: (B) 80/7 sec
Question: 10 Arabian horses are split into pairs to pull one of the distinct 4 carts in a race. If each cart is assigned to a pair, how many different assignments of horses to carts are possible?
(A) 420
(B) 1260
(C) 5220
(D) 9450
(E) 113400
Rationale: # of ways 10 horses can be divided into 5 groups when order of the groups does not matter is: C210∗C28∗C26∗C24∗C225!=945C102∗C82∗C62∗C42∗C225!=945.
So we would have 945 different cases of dividing 10 horses into 5 groups:
1. A1A1, B1B1, C1C1, D1D1, E1E1 (each letter represent pair of horses);
2. A2A2, B2B2, C2C2, D2D2, E2E2;
...
945. A945, B945, C945, D945, E945.
Now, we want to assign a pair (a letter in our case) to one of 4 distinct carts. For each case (out of 945) P45=120 would represent # of ways to choose 4 pairs out of 5 when order matters (as carts are distinct). OR C45 choose 4 different letters out of 5 and 4! - # of ways to assign 4 different letters to 4 distinct carts: C45∗4!=120C.
So total # of different assignments would be 945∗120=113400
Answer: E.
Answer: (E) 113400
Question: The side of a square is increased by 25% then how much % does its area increases?
(A) 56.65 %
(B) 56.25 %
(C) 56.29 %
(D) 57.25 %
(E) 56.55 %
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer: B
Answer: (B) 56.25 %
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 1 hour?
(A) 100
(B) 120
(C) 150
(D) 180
(E) 240
Rationale: Answer = 4 * 60 = 240
Answer is E
Answer: (E) 240
Question: A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '1' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
(A) 65
(B) 60
(C) 50
(D) 70
(E) 80
Rationale: problem of combination 8C4 = 8!/4!*(8-4)! = 8*7*6*5*4!/4!*4! =70
D
Answer: (D) 70
Question: 3,8,18,38,78,__
(A) 158
(B) 156
(C) 154
(D) 150
(E) 148
Rationale: 8=3*2+2
18=8*2+2
38=18*2+2
78=38*2+2
158=78*2+2
ANSWER:A
Answer: (A) 158
Question: Two pipes A and B can separately fill a cistern in 60 minutes and 80 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 40 minutes. In how much time, the third pipe alone can empty the cistern?
(A) 90 min
(B) 100 min
(C) 240 min
(D) 120 min
(E) 130 min
Rationale: 1/40-(1/60+1/80)=-1/240
third pipe can empty in 240 minutes
ANSWER:C
Answer: (C) 240 min