mathewhe/aqua_rat huggingface dataset:
Question: A man covered a certain distance at a speed of 8 Kmph and returned at a speed of 4 Kmph. Find the average speed of whole journey?
(A) 5 2/3 Kmph
(B) 5 1/3 Kmph
(C) 5 4/3 Kmph
(D) 6 1/3 Kmph
(E) None
Rationale: Option 'B'
Answer: (B) 5 1/3 Kmph
Question: Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next?
(A) 14
(B) 15
(C) 21
(D) 23
(E) None of these
Rationale: Explanation:
In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.
Answer is B
Answer: (B) 15
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?
(A) 6: 00 p.m.
(B) 8: 00 p.m.
(C) 6: 00 a.m
(D) 8: 00 a.m.
(E) 10: 00 a.m.
Rationale: Given:
he number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 2 PM, we get 8 AM as the answer.
Option D
Answer: (D) 8: 00 a.m.
Question: In a 200 m race, A beats B by 20 m and c by 38m. In a race of 600 m B will beat C by
(A) 20 m
(B) 30 m
(C) 25 m
(D) 15 m
(E) 60 m
Rationale: It means, when A covers 200 m,
B covers only (200-20)=180 m
and C covers only (200-38)=162 m
=> When C covers 162 m, B covers 180 m
=> When B covers 600 m, C covers 162/180×600 = 540 m
Hence, B beats C by 600-540 = 60 metre
ANSWER:E
Answer: (E) 60 m
Question: When positive integer n is divided by 3, the remainder is 1. When n is divided by 5, the remainder is 4. What is the smallest positive integer p, such that (n + p) is a multiple of 11?
(A) 1
(B) 2
(C) 5
(D) 7
(E) 20
Rationale: When positive integer n is divided by 3, the remainder is 1 i.e., n=3x+1
values of n can be one of {1, 4, 7, 10, 13, 16, 19, 22..............49, 52, 59..................}
Similarly,
When n is divided by 5, the remainder is 5..i.e., n=5y+4
values of n can be one of {4, 9, 14, 19,...}
combining both the sets we get
n={4,19, 52, ...........}
What is the smallest positive integer p, such that (n + p) is a multiple of 11 or 11x
in case of n=4 p=7
so for min value of p, we take min value of n.
D is the answer.
Answer: (D) 7
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
(A) 1888
(B) 2766
(C) 2999
(D) 1900
(E) 1712
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer: D
Answer: (D) 1900
Question: If (x-10)(x-3) < 0, which of the following must be true?
(A) x^2 + 5x + 6 < 0
(B) x^2 + 5x + 6 > 0
(C) 5 - x < 0
(D) x - 5 < 0
(E) 10 - x > 0
Rationale: (x-10)(x-3)<0 can be written as (10-x)(x-3)>0
So,to inequality hold true multiple of (10-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<10
Answer Choice E matched which says 10-x>0 or x<10,which must be true (I started to look from E to A for making easy decision first)
Correct Answer E
Answer: (E) 10 - x > 0
Question: Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 25 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 6.24
(B) B) 13.1
(C) C) 10
(D) D) 15
(E) E) 24
Rationale: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/25 = 10*12/5 = 24
Time difference = 13.1
Ans:B
Answer: (B) B) 13.1
Question: By doing some calculation, 2+3=18, 3+5=42, 6+2=48 and find 5+6=??
(A) 74
(B) 70
(C) 72
(D) 76
(E) 78
Rationale: Given 2+3=18==> (2^2+3^2)+(2+3)=18
3+5=42==> (3^2+5^2)+(3+5)=42
6+2=48==> (6^2+2^2)+(6+2)=48
So 5+6=72==> (5^2+6^2)+(5+6)=72
ANSWER:C
Answer: (C) 72
Question: Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $880.What was original rent of friend whose rent is increased?
(A) 800
(B) 900
(C) 1600
(D) 1100
(E) 1200
Rationale: 0.2X = 4(880-800)
0.2X = 320
X = 1600
Answer C
Answer: (C) 1600
Question: Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 65.4 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
(A) 0.08
(B) 1.0
(C) 1.1
(D) 1.5
(E) 41.8
Rationale: Change in production of motor vehicles = 65.4 - 3.9 = 61.5 million in 41 years (1987 - 1946)
average increase per year = 61.5/41 = 1.5 million (apporx.)
Answer (D)
Answer: (D) 1.5
Question: If C + D = 15 and C and D are any numbers, which of the following is a possible value for 8C + 5D?
(A) 99
(B) 29
(C) 0
(D) 09
(E) 19
Rationale: c + d = 15
8c + 5d = 3c + 5C + 5d = 5(c+d) + 3C = 5(15) + 3C=75 + 3C= c=-25
Now 3C is a multiple of 3, so the right answer should be 75 + multiple of 3.
c+d=15=-25+d=15=d=40
So, 0 is the right answer
Hence, C is the right answer.
Answer: (C) 0
Question: If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average T(arithmetic mean) annual increase in the index over this period?
(A)  (x + 100)/18
(B)  x/18
(C)  (100 − x)/18
(D)  (x − 100)/18
(E)  100x/18
Rationale: CPI in end of 1967 = 100
CPI in end of 1985 = x
Number of years = 18
Average annual increase in CPI T= (x-100)/18
Answer D
Answer: (D)  (x − 100)/18
Question: Each side of a certain parallelogram has length 8. If the area of the parallelogram is 24. Which of the following is the measure of one of its angles?
(A) 22
(B) 45
(C) 60
(D) 90
(E) 120
Rationale: area of a parallelogram = b*h
b*h=24
h=24/8=3
sin theta =opp/hyp = 3/8
theta = sin inv of 3/8 = 22 deg
A
Answer: (A) 22
Question: Find out the wrong number in the given sequence of numbers.
52, 51, 48, 43, 34, 27, 16
(A) 22
(B) 34
(C) 77
(D) 99
(E) 21
Rationale: Explanation:
Subtract 1, 3, 5, 7, 9, 11 from successive numbers.
So, 34 is wrong.
Answer: B) 34
Answer: (B) 34
Question: Two pipes P and Q can fill a tank in 5 hours and 10 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 4 hours 20 min
(B) 5 hours 49 min
(C) 3 hours 20 min
(D) 3 hours 22 min
(E) 3 hours 42 min
Rationale: Explanation:
Part filled by P in 1 hour = 1/5
Part filled by Q in 1 hour = 1/10
Part filled by (P + Q) in 1 hour = ( 1/5 + 1/10) = (3/10)
Time taken to fill the tank is (10/3) = 10/3*60 = 200 mins = 3 hrs 20 mins
ANSWER C
Answer: (C) 3 hours 20 min
Question: log3 N+log6 N what is 3 digit number N that will be whole number
(A) 629
(B) 729
(C) 829
(D) 929
(E) 216
Rationale: No of values N can take is 1
6^3=216
ANSWER:E
Answer: (E) 216
Question: What is the smallest positive integer x such that 450x is the cube of a positive integer?
(A) 2
(B) 15
(C) 30
(D) 60
(E) 120
Rationale: 450 = 2 x 3^2 x 5^2 now we need two 2s, one 3 and one 5 to make it perfect cube.
So x= 2^2 x 3 x 5 = 60.
Answer is C.
Answer: (C) 30
Question: There are 35 students in a hostel. If the no. of students increases by 10, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) 304.5
(B) 340.9
(C) 342.9
(D) 345.9
(E) 380.9
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 10) = x – 1
or, 35x + 42 = 45x – 45
or, x = 8.7
Thus the original expenditure of the mess = 35 x 8.7 = Rs. 304.5
A
Answer: (A) 304.5
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 50% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
(A) 1.8 lakh
(B) 1.1 lakh
(C) 1.9 lakh
(D) 8.1 lakh
(E) 6.1 lakh
Rationale: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.5 = 4.5 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 4.5 - 1.2 = 3.3 lakh
Average SP of all the 3 cars = 1.1 lakh
Answer: B) 1.1 lakh
Answer: (B) 1.1 lakh
Question: For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
(A) 12%
(B) 26%
(C) 29%
(D) 30%
(E) 60%
Rationale: In the first plot 20% of 300 seeds germinated, so 0.20 x 300 = 60 seeds germinated.
In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.
Since 60 + 70 = 130 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (130/500) x 100%, or 26%.
Answer: B.
Answer: (B) 26%
Question: A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 10 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
(A) 5:00
(B) 5:34
(C) 5:42
(D) 6:00
(E) 6:24
Rationale: C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15 = 45 minutes have passed.
C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60 = 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.
C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.
C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of 4/3 * 2/3 * 5/4 * 45 = 50 minutes.
C4 loses 10 minutes every hour.
In 6 hours, C4 will lose 6*10 = 60 minutes = 1 hour.
Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 6pm.
The correct answer is D.
Answer: (D) 6:00
Question: Machine X takes 80 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce
(A) 100
(B) 65
(C) 25
(D) 11
(E) 2.25
Rationale: Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 80
So, x = 80.
Hence 6x = 6*80 = 480 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/480
= 2.25
Hence option (E).
Answer: (E) 2.25
Question: Factor 3x3 - x2y +6x2y - 2xy2 + 3xy2 - y3 =
(A) (3x - 2y)(x + y)
(B) (3x - y)(x + y)(x - y)
(C) (3x - y)(x + y)2
(D) (3x - y)(x2 + y2)
(E) none
Rationale: Solution:
3x3 - x2y + 6x2y - 2xy2 + 3xy2 - y3=
x2(3x - y) + 2xy(3x - y) + y2(3x-y) =
(3x - y)(x2 + 2xy + y2)=
(3x - y)(x + y)2
Answer C
Answer: (C) (3x - y)(x + y)2
Question: The maximum number of students among them 1234 pens and 874 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
(A) 91
(B) 2
(C) 1001
(D) 1911
(E) None of these
Rationale: Explanation:
Required number of students = H.C.F of 1234 and 874 = 2. Answer: B
Answer: (B) 2
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 58 Kmph
(B) 68 Kmph
(C) 78 Kmph
(D) 55 Kmph
(E) 65 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
ANSWER:B
Answer: (B) 68 Kmph
Question: 20 balls are numbered 1 to 20. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
(A) 7/30
(B) 3/14
(C) 9/38
(D) 4/21
(E) 5/26
Rationale: P(1st ball is even) = 10/20
P(2nd ball is also even) = 9/19
P(both balls are even) = 10/20 * 9/19 = 9/38
The answer is C.
Answer: (C) 9/38
Question: A man can row downstream at the rate of 10 Km/hr and upstream at 4 Km/hr. Find man's rate in still water and the rate of current?
(A) 9,6
(B) 7,3
(C) 9,3
(D) 6,6
(E) None of these
Rationale: Explanation:
Rate of still water = 1/2 (10 + 4) = 7 Km/hr
Rate of current = 1/2 (10-4) = 3 Km/hr
Answer: Option B
Answer: (B) 7,3
Question: What is the next number of the following sequence
10,8,18,16,34,32,....
(A) 44
(B) 66
(C) 55
(D) 77
(E) 48
Rationale: 10
10-2=8
8+10=18
18-2=16
16+18=34
34-2=32
32+34=66
answer will be 66
ANSWER:B
Answer: (B) 66
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 380$
(C) 420$
(D) 450$
(E) 480$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 55 ) = 21 + 429 => 450
Hence answer will be (D) 450
Answer: (D) 450$
Question: Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point?
(A) 20sec
(B) 15sec
(C) 30sec
(D) 24sec
(E) 1min
Rationale: They meet every 360/7+8 = 24sec
Answer is D
Answer: (D) 24sec
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 12
(B) 9
(C) 8
(D) 6
(E) 5
Rationale: A's 1 hour's work = 1 ;
4
(B + C)'s 1 hour's work = 1 ;
3
(A + C)'s 1 hour's work = 1 .
2
(A + B + C)'s 1 hour's work = ( 1 + 1 ) = 7 .
4 3 12
B's 1 hour's work = ( 7 - 1 ) = 1 .
12 2 12
Therefore A alone will take 12 hours to do the work.
Answer: (A) 12
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream?
(A) 60/18
(B) 30/29
(C) 60/12
(D) 60/13
(E) 30/82
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 120/26
= 60/13 hours.
Answer:D
Answer: (D) 60/13
Question: Given that 268x74= 19432, find the value of 2.68x.74.
(A) 1.9432
(B) 1.0025
(C) 1.5693
(D) 1.0266
(E) None
Rationale: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9432
Answer A
Answer: (A) 1.9432
Question: There is a truck driver starts from one place to pick another person at
another place. The driver goes to that place by 6 AM and then picking him
he returns back.one day the other person woke a bit early and started
walking towards the first place.one the way he meets truck driver and joins
him and both went back to the first place. This day the other person came
20 min early to the time he usually comes to the first place?Tell the time
when the driver met the second person that day?
(A) 5.10 AM
(B) 5.20 AM
(C) 5.40 AM
(D) 5.50 AM
(E) 5.30 AM
Rationale: Given that the first person reaches the first place by 6.00 AM
But,one day the second person reached the place 20 min early.
and met the first person on the way ad reached the stop at 6.00 AM.
Therfore,They would have met at 5.50 AM.
ANSWER:D
Answer: (D) 5.50 AM
Question: The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 675 sq meters, then what is the width (in meters) of the rectangular plot?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: Area = L*W = 3W^2 = 675
W^2 = 225
W = 15
The answer is B.
Answer: (B) 15
Question: How many different positive integers exist between 10^9 and 10^10, the sum of whose digits is equal to 2?
(A) 6
(B) 7
(C) 5
(D) 8
(E) 10
Rationale: So, the numbers should be from 1,000,000,000 to 10,000,000,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
1,000,000,001
1,000,000,010
1,000,000,100
1,000,001,000
1,000,010,000
1,000,100,000
1,001,000,000
1,010,000,000
1,100,000,000
9 numbers.
2. One 2 and the rest are 0's:
2,000,000,000
1 number.
Total = 10 numbers.
Answer: E
Answer: (E) 10
Question: List K consists of 14 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 12
Rationale: Answer = D = 8
If least = -4, then largest = 9
Range = 9 - 1 = 8
Answer: (D) 8
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 18
(B) 99
(C) 77
(D) 66
(E) 25
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18
Question: A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $120,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $150,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
(A) $3,500
(B) $5,000
(C) $2,500
(D) $9,700
(E) $10,000
Rationale: Team K's contract = $120,000 + $120,000*1.2 + $120,000*1.2*1.2 + $50,000 = $486,800
Team L's contract = $150,000 + $150,000*1.1 + $150,000*1.1*1.1 = $496,500
The difference = $9,700.
Answer: D.
Answer: (D) $9,700
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 62.3
(C) 62.7
(D) 62.2
(E) 62.9
Rationale: CP = 47.50
SP = 47.50*(125/100)
= 59.375
MP*(95/100)
= 59.375
MP = 62.5
Answer:A
Answer: (A) 62.5
Question: If each side of a square is increased by 6%, find the percentage change in its area?
(A) 10.68%
(B) 8.72%
(C) 9.28%
(D) 12.36%
(E) 11.91%
Rationale: let each side of the square be a , then area = a x a
New side = 106a / 100 = 53a /50
New area =(53a x 53a) / (50 x 50) = (2809a²/2500)
increased area== (2809a²/2500) - a²
Increase %= [(309a²/2500 ) x (1/a² ) x 100]% = 12.36%
answer :D
Answer: (D) 12.36%
Question: In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 100 and the slope of line segment AC is 4/3, what is the length of AB?
(A) 12
(B) 18
(C) 24
(D) 28
(E) 80
Rationale: Slope = Change in Vertical Direction/Change in Horizontal Direction = 4/3
Change in Vertical Direction = 4x = AB
Change in Horizontal Direction = 3x = BC
AB^2 + BC^2 = 100^2
16x^2 + 9x^2 = 10000
25x^2 = 400
x^2 = 400
x = 20
Therefore AB = 20*4 =80
Answer: E
Answer: (E) 80
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 7 runs. His new average is:
(A) 38 runs
(B) 37 runs
(C) 39 runs
(D) 40 runs
(E) 41 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 7
= 11x + 77 = 10x + 108
= x = 31.
New average = (x + 7) = 38 runs.
Answer:A
Answer: (A) 38 runs
Question: Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.0 km apart, if they walk in the same direction?
(A) 12 hrs
(B) 14 hrs
(C) 15 hrs
(D) 16 hrs
(E) None
Rationale: Sol.
to be 0.5 km apart, they take 1 hour.
To be 8.0 km apart, they take [1/0.5 * 8.0] hrs = 16 hrs.
Answer D
Answer: (D) 16 hrs
Question: If 50% of (x-y) = 30% of (x+y) then what percent of x is y?
(A) 15
(B) 20
(C) 18
(D) 26
(E) 25
Rationale: 50% of (x-y)=30% of(x+y) ==> (50/100)(x-y)=(30/100)(x+y)
==>5(x-y)=3(x+y) ==> 2x=8y => x=4y
therefore required percentage =((y/x) X 100)% = ((y/4y) X 100) =25%
Answer E.
Answer: (E) 25
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 388
(B) 150
(C) 288
(D) 269
(E) 271
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer:B
Answer: (B) 150
Question: Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 9x +3 = 0?
(A) 28.3
(B) 1.45
(C) 2.78
(D) 6.84
(E) 7.23
Rationale: a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab]/ab
a + b = -9/1 = -9
ab = 3/1 = 3
Hence a/b + b/a = [(-9)2 - 2(3)]/3 = 56/4 = 28.3.
A)
Answer: (A) 28.3
Question: If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is
(A) 5 km/hr
(B) 4 km/hr
(C) 2 km/hr
(D) 1 km/hr
(E) 3 km/hr
Rationale: Explanation:
Rate upstream = (15/3) kmph
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7 - 5)kmph = 1 kmph
Option D
Answer: (D) 1 km/hr
Question: Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 25 hours respectively. The ratio of their speeds is
(A) 2 : 3
(B) 4 : 3
(C) 6 : 7
(D) 9 : 8
(E) 5 : 4
Rationale: Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √25 : √16
= 5 : 4.
Answer E
Answer: (E) 5 : 4
Question: How many factors of 2475 are odd numbers greater than 1?
(A) 3
(B) 4
(C) 17
(D) 6
(E) 7
Rationale: prime factors of 330 are 2^1,3^2,5^2 and 11^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18
since we need odd divisors other than 1 =>18-1 = 17 odd divisors
C is the answer
Answer: (C) 17
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 11
(B) 190
(C) 188
(D) 177
(E) 121
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec ,Answer:B
Answer: (B) 190
Question: By selling 100 pencil, a trader gains the cost of 20 Pencil. Find his gain percentage?
(A) 26 1/3%
(B) 51 1/3%
(C) 20%
(D) 53 1/3%
(E) 34 1/3%
Rationale: C
20%
Let the CP of each pencil be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 20 pencil = Rs. 20
Profit% = 20/100 * 100 = 20%
Answer: (C) 20%
Question: If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000?
(A) $3500
(B) $5000
(C) $3150
(D) $7200
(E) $10000
Rationale: Saving = (45-30)% of 48000 = 7200.
Answer:D
Answer: (D) $7200