mathewhe/aqua_rat huggingface dataset:
Question: There are 100 boxes numbered from 1 to 100. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
(A) 4650
(B) 4750
(C) 4850
(D) 4950
(E) 5050
Rationale: 1 green ball: 100 ways
2 green balls: 99 ways
3 green balls: 98 ways
4 green balls: 97 ways
etc...
95 green balls: 6 ways
96 green balls: 5 ways
97 green balls: 4 ways
98 green balls: 3 ways
99 green balls: 2 ways
100 green balls: 1 way
The total number of ways is 100*101/2=5050
The answer is E.
Answer: (E) 5050
Question: Playing kick-ball, 6 people are standing in a circle. two standing positions are considered different only when the position of the people are different relative to each other. what is the total number of possible standing positions in the group?
(A) a.5
(B) b.10
(C) c.24
(D) d.32
(E) e.120
Rationale: for 6 people seating arrangement around a circular table = (6-1)!
= 4!
= 5*4*3*2*1
=120
OA is E
Answer: (E) e.120
Question: All prime numbers are odd numbers
(A) True
(B) False
(C) All of these
(D) Cannot be determined
(E) None of these
Rationale: Explanation :
2 is even prime number. Answer : Option B
Answer: (B) False
Question: A man can row downstream at 35 kmph and upstream at 25 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 35, 3
(B) 25, 5
(C) 35, 4
(D) 5, 30
(E) 30, 5
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 35 --- (1)
and x - y = 25 --- (2)
From (1) & (2) 2x = 60 => x = 30, y = 5.
Answer:E
Answer: (E) 30, 5
Question: Which of the following values of x do not satisfy the inequality x2 - 3x + 2 > 0 at all ?
(A) 1 ≤ x ≤2
(B) -1 ≥ x ≥ -2
(C) 0 ≤ x ≤ 2
(D) 0 ≥ x ≥ -2
(E) None of these
Rationale: Explanation :
On solving x2 - 3x + 2 > 0 , we get ( x - 1 )( x - 2 ) > 0.
That is the roots are x = 1 or x = 2.
The equation assumes a positive value for all values which belong to the interval less than 1 and greater than 2
For x = 1 and x = 2, it becomes zero and for any value of x between 1 and 2 it becomes negative.
Answer : A
Answer: (A) 1 ≤ x ≤2
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 6
(C) 5
(D) 3
(E) 1
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer:A
Answer: (A) 8
Question: 3, 7, 15, 27, 43, ?
(A) 63
(B) 56
(C) 74
(D) 57
(E) 32
Rationale: The pattern is + 4, + 8, + 12, + 16, +20
Answer : A.
Answer: (A) 63
Question: The total number of digits used in numbering the pages of a book having 356 pages is
(A) 732
(B) 990
(C) 1098
(D) 960
(E) 1405
Rationale: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 257) = (9 + 180 + 771) = 960.
ANSWER:D
Answer: (D) 960
Question: 130 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 8 days
(B) 6 days
(C) 7 days
(D) 9 days
(E) 13 days
Rationale: 1 women's 1 day work = 1/910
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/910 + 10/140) = 1/13
5 women and 10 children will complete the work in 13 days.
Answer: E
Answer: (E) 13 days
Question: Five kilograms of oranges contained 90% of water. If the next day the concentration of water decreased by 10%, what was the new weight of the oranges, in kilograms?
(A)  4.9
(B)  4.8
(C)  2.5
(D)  2
(E)  0.2
Rationale: Five kilograms of oranges contained 90% of water. If the next day the concentration of water decreased by 10%, what was the new weight of the oranges, in kilograms?
(A) 4.9
(B) 4.8
(C) 2.5
(D) 2
(E) 0.2
If C is the answer, then the question means that the concentration of water the newt day became 80%.
Out of 5 kilograms 90%, or 4.5 kilograms was water and 0.5 kilograms was non-water.
The next day, after some water evaporated, oranges became 80% water and 20% of non-water, so the next day 0.5 kilograms of non-water composed 20% of oranges, which means that the new weight of the oranges was x*0.2=0.5 --> x=2.5 kilograms.
Answer: C.
Answer: (C)  2.5
Question: In a can, there is a mixture of milk and water in the ratio 3 : 7. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 7. Find the capacity of the can?
(A) 16.6
(B) 44
(C) 27
(D) 50
(E) 56
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 3/10 (T - 8)
After adding milk, quantity of milk in the mixture = 4/11 T.
4T/11 - 8 = 3/10(T - 8)
37T = 880- 264 => T = 16.6.
Answer:A
Answer: (A) 16.6
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1740?
(A) Rs.1000
(B) Rs.1550
(C) Rs.1510
(D) Rs.1500
(E) None of these
Rationale: Explanation:
1740 = P [1 + (5*16/5)/100]
P= 1500
Answer: Option D
Answer: (D) Rs.1500
Question: A camera lens filter kit containing 5 filters sells for $87.50. If the filters are purchased individually, 2 of them are priced at $16.45 each, 2 at $14.05 each, 1 at $19.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?
(A) 7%
(B) 8%
(C) 9%
(D) 10%
(E) 11%
Rationale: Cost of kit = $87.50
If filters are purchased individually - $16.45*2 + $14.05*2 + $19.50 = $80.50
Amount saved = $87.50 - $80.50 = $7
Required %age = ($7/$87.50)*100 = 8%
So, the correct answer is B.
Answer: (B) 8%
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?
(A) 120
(B) 240
(C) 360
(D) 480
(E) 720
Rationale: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want 6C!/2 -> 720/2 = 360
ANS:C) 360
Answer: (C) 360
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
(A) 8/15
(B) 7/15
(C) 2
(D) 1/15
(E) 1/10
Rationale: A's 1 day's work =1/15
B's 1 day's work =1/20
(A + B)'s 1 day's work =(1/15+1/20)=7/60	.
(A + B)'s 4 day's work =(7/60 x 4)=7/15.
Therefore, Remaining work =(1 -7/15	)=8/15.
Answer: Option A
Answer: (A) 8/15
Question: 9 friends bought a shopping mall for 12 million dollars. If the all businessman have to pay the same amount and none of them have amount smaller than $1, how much money would they have to pay?
(A) 11,999,997
(B) 12,000,000
(C) 12,000,002
(D) 12,000,003
(E) 12,000,004
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 12,000,000 = 12 and 9 is divisible by 9.
Hence, we need to remove 3 to this number for it to be divisible by 9
Correct Option: A
Answer: (A) 11,999,997
Question: A man can reach a certain place in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. Find his speed.
(A) 4 1/2km/hr
(B) 5 km/hr
(C) 5 1/2km/hr
(D) 6 km/hr
(E) none
Rationale: Sol.
Let the speed be x km/hr. Then,
30x-30*14/15x = 10
⇔ 2x = 10
⇔ x = 10/2
= 5 km/hr
Answer B
Answer: (B) 5 km/hr
Question: Nicky and Cristina are running a 200 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
(A) 35
(B) 30
(C) 45
(D) 40
(E) 50
Rationale: The distance traveled by both of them is the same at the time of overtaking.
3(t+12) = 5t
t=18.
Cristina will catch up Nicky in 18 seconds.
So in 18 seconds Cristina would cover = 18*5 = 90 meter.
Now Time taken my Nicky to cover 90 meter = 90/3 = 30 Seconds.
B
Answer: (B) 30
Question: X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ4, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9
(A) I only
(B) II only
(C) III only
(D) I , II and III
(E) I and II only
Rationale: it can be a combination of 6,8 or 7,7 or 5,9
I choose D as an answer.
Answer: (D) I , II and III
Question: Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that
ball is white
(A) 1
(B) 2/3
(C) 1/3
(D) 4/3
(E) None of these
Rationale: Explanation:
Total cases = 10 + 20 = 30
Favourable cases = 20
So probability = 20/30 = 2/3
Answer: B
Answer: (B) 2/3
Question: Pandi and Rani invested in a business. They earned some profit which they divided in the ratio of 3:2. If Pandi invested Rs.30, 000, the amount invested by Rani is:
(A) Rs. 65,000
(B) Rs. 20,000
(C) Rs. 80,000
(D) Rs. 90,000
(E) Rs. 60,000
Rationale: Invested by Rani = 30000/3*2 = 20000
Answer : B
Answer: (B) Rs. 20,000
Question: If (5 - x)/(7 + x) = x, what is the value of x^2 + 8x - 5?
(A) -4
(B) -3
(C) -2
(D) -1
(E) 0
Rationale: (5-x) = x*(7+x)
(5-x) = 7x+x^2
0 = x^2+8x-5
The answer is E.
Answer: (E) 0
Question: In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students T in the class?
(A) A)10
(B) B)12
(C) C)15
(D) D)20
(E) E)25
Rationale: the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C)
Answer: (C) C)15
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
(A) 1/3 rd
(B) 2/5 th
(C) 2/3 rd
(D) 1/5 th
(E) 2/5 th
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
ANSWER:A
Answer: (A) 1/3 rd
Question: If p - q = 2 and
p2+q2=26
, find the value of pq.
(A) 7
(B) 8
(C) 9
(D) 11
(E) 10
Rationale: Explanation:
We know
2ab=(a2+b2)âˆ’(aâˆ’b)2
2pq=26âˆ’4=22
=>pq=11
Option D
Answer: (D) 11
Question: A cylinder of height h is 5/6 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
(A) 25%
(B) 50%
(C) 60%
(D) 72%
(E) 100%
Rationale: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 5/6
New cylinder 3/5
So 3/5/5/6 = 3/5 *6/5= 0.72 or 72%.
Answer D
Answer: (D) 72%
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/6. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
(A) 116
(B) 146
(C) 152
(D) 162
(E) 170
Rationale: The probability of survival for each of the first 3 months of life is 1-1/6= 5/6, so of 200 newborn 200*5/6*5/6*5/6=~116 is expected to survive.
Answer: A.
Answer: (A) 116
Question: A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 200
(B) 210
(C) 240
(D) 250
(E) 260
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 34 = 15
x + 300 = 510
x = 210 m.
Answer: Option B
Answer: (B) 210
Question: If r<0, which of the following must be true?
(A) –100 < r < 100
(B) r ≤ –1
(C) r ≤ 1
(D) r^2 ≥ 1/4
(E) –100 < r < 0
Rationale: r is a negative number.
A. –100 < r < 100r can be a negative number less than -100
B. r ≤ –1r can be a fraction, in which case it would be greater than -1
C. r ≤ 1must be true since 1 is positive and r is negative
D. r^2 ≥ 1/4not true if r is a negative fraction like -1/5
E. –100 < r < 0r can be a negative number less than -100=C
Answer: (C) r ≤ 1
Question: What is the solution of the equations x - y = 0.1 and 1(x + y)-1 = 2 ?
(A) x = 0.3, y = -0.2
(B) x = 1, y = 0.1
(C) x = 2, y = 1.1
(D) x = 1.2, y = 0.3
(E) None
Rationale: Answer
x - y = 0.1 ...(i)
and 1(x + y)-1=2
⇒ 1/ (x + y) = 2
⇒ 2(x + y) =1
⇒ x + y = 1/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 0.3
and y = -0.2
Correct Option: A
Answer: (A) x = 0.3, y = -0.2
Question: Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent Q of all the possible subcommittees that include Michael also include Anthony?
(A)  20%
(B)  30%
(C)  40%
(D)  50%
(E)  60%
Rationale: The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability Q= 1/5+4/5*1/4 = 2/5.C
Answer: (C)  40%
Question: 78 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?
(A) 10^7
(B) 10^8
(C) 10^9
(D) 10^10
(E) 10^11
Rationale: 78 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 78=80, 48=50, 25,075=25,000 are derived, which makes (78)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is B.
Answer: (B) 10^8
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18900. A's share is?
(A) 6300
(B) 2765
(C) 6000
(D) 1298
(E) 1261
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18900 = 6300
Answer:A
Answer: (A) 6300
Question: What is the 4 digit no. in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is 3 times the second?
(A) 1123
(B) 1234
(C) 1349
(D) 1455
(E) 1567
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349
Question: $2,000 is deposited in a savings account that pays 4% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?
(A) $2125.15
(B) $2083.12
(C) $2184.22
(D) $2150.84
(E) $2080.80
Rationale: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2
So,
new time=2periods and new rate=4/2=2%
Now,
CA=2000(1+2/100)^2=$2080.80
Hence answer is E
Answer: (E) $2080.80
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) 287
(B) 369
(C) 125
(D) 279
(E) 361
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2
= Rs.125
Answer:C
Answer: (C) 125
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 2.6 sec
(C) 2.7 sec
(D) 2.8 sec
(E) 2.9 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: Option A
Answer: (A) 2.5 sec
Question: What is the probability of flipping a fair coin four times and the coin landing on heads on exactly two flips?
(A) 1/6
(B) 3/4
(C) 1/3
(D) 2/5
(E) 3/8
Rationale: Probability = (Favorable combination)/(Total combination)
Favorable combination = (HHTT, HTHT, HTTH,THHT,THTH,TTHH) ==> 6
Total combination = 16 (2^4)
Probability = (6)/(16) = 3/8
(E)
Answer: (E) 3/8
Question: A bus trip of 360 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip?
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: The time is the distance/speed. The time difference is 1 hour.
360/V - 360/(V+5) = 1
360(V+5) - 360V = (V)(V+5)
1800 = (V)(V+5)
40*45 = (V)(V+5)
V = 40 mph
The answer is B.
Answer: (B) 40
Question: By selling 10 pencils for a rupee a man loses 15%. How many for a rupee should he sell in order to gain 15%?
(A) 8.39
(B) 6.39
(C) 7.39
(D) 9.39
(E) 2.39
Rationale: 85% --- 10115% --- ?85/115 * 10 = 7.39Answer: C
Answer: (C) 7.39
Question: 4,6,8,10,12,....
(A) 58
(B) 14
(C) 61
(D) 62
(E) 63
Rationale: 2*2=4
3*2=6
4*2=8
5*2=10
6*2=12
7*2=14
ANSWER:B
Answer: (B) 14
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.2. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?
(A) 0.36
(B) 0.24
(C) 0.28
(D) 0.48
(E) 0.72
Rationale: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )
=0.6*0.2+0.4*0.3+0.6*0.2
= 0.12+0.12+0.12
=0.36
A
Answer: (A) 0.36
Question: JOHN and Antony can finish the work 36 days if they work together. They worked together for 24 days and then Antony left. JOHN finished the remaining work in another 24 days. In how many days JOHN alone can finish the work?
(A) 30 days
(B) 72 days
(C) 70 days
(D) 80 days
(E) 90 days
Rationale: Amount of work done by JOHN and Antony in 1 day = 1/36
Amount of work done by JOHN and Antony in 24 days = 24 Ã— (1/36) = 2/3
Remaining work â€“ 1 â€“ 2/3 = 1/3
JOHN completes 1/3 work in 24 days
Amount of work JOHN can do in 1 day = (1/3)/24 = 1/72
=> JOHN can complete the work in 72 days
Answer : B
Answer: (B) 72 days
Question: A cycle is bought for Rs.750 and sold for Rs.1080, find the gain percent?
(A) 22
(B) 44
(C) 99
(D) 88
(E) 11
Rationale: 750 ---- 180
100 ---- ? => 44%
Answer:B
Answer: (B) 44
Question: The sum of first four prime numbers is?
(A) 17
(B) 23
(C) 24
(D) 28
(E) 30
Rationale: Required sum = (2 + 3 + 5 + 7) = 17.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
A
Answer: (A) 17
Question: If x is equal to the sum of the integers from 50 to 60, inclusive, and y is the number of EVEN integers from 50 to 60, inclusive, what is the value of x+y ?
(A) 171
(B) 281
(C) 391
(D) 491
(E) 611
Rationale: sum s= n/2{2a+(n-1)d} = 11/2{2*50+ (11-1)*1} =11*55=605 =X
number of even number =( 60-50)/2 +1 = 6= Y
X+Y = 605+6 =611
E
Answer: (E) 611
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 5 men and 2 women will do that task.
(A) 6/7
(B) 3/10
(C) 3/18
(D) 3/16
(E) 3/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
5 m +2 w =12 w
Answer is 12/14 =6/7
Answer: A
Answer: (A) 6/7
Question: Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 14 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.
(A) 50 days
(B) 100 days
(C) 120 days
(D) 110 days
(E) 90 days
Rationale: Rate of both = 1/20
Together they do = 1/20*14 = 7/10
Left work = 1 - 7/10 = 3/10
Adam completes 3/10 work in 10 day
so he took 10*10/3 = 100/3 days to complete the left work alone.
Thus the rate of adam is 3/100
Rate of Micheal = 1/20 - 3/100 = 1/50
Thus micheal takes 50 days to complete the whole work.
ans. A
Answer: (A) 50 days
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 360 votes. Find the number of votes casted to the winning candidate?
(A) 456
(B) 744
(C) 930
(D) 1200
(E) 1400
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 360
62% -------- ? => 930
ANSWER:C
Answer: (C) 930
Question: Alfred buys an old bike for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the bike for Rs. 5800, his gain percent is?
(A) 5 5/11%
(B) 5%
(C) 5/7%
(D) 6%
(E) 6/11%
Rationale: Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % = 300	x 100	%	= 5	5	%
5500	11
A)
Answer: (A) 5 5/11%
Question: Diane find 2 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
(A) 5
(B) 7 and a half
(C) 10
(D) 12 and a half
(E) 15
Rationale: We know that 2.5 cans = 25/10 is used to paint 1/3 of a room. We need to find how much paint we'll need in order to paint the rest of the room (1-1/3=2/3) and 1 room more, hence 2/3+1=5/3
25/10 : 1/3 = x : 5/3
(25/10)*(5/3) = (1/3)*x
25/6=x/3
6*x=25*3
x=75/6
x=12.5
ANSWER:D
Answer: (D) 12 and a half
Question: Two cars, Car1 and Car2 move towards each other from Q and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Q starting from Y?
(A) 15.5 sec
(B) 8.4 sec
(C) 33.6 sec
(D) 31.11 sec
(E) 16.8 sec
Rationale: Q--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance QY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D
Answer: (D) 31.11 sec