RikoteMaster/aqua-rat-mcqa huggingface dataset:
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.80/8
B.80/7
C.80/1
D.80/3
Answer: B.80/7
Explanation: 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
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
A.123
B.127
C.235
D.305
Answer: B.127
Explanation: Explanation:
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127. Answer: B
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
A.285m
B.207m
C.280m
D.270m
Answer: D.270m
Explanation: Speed =72 x5/18 m/sec= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
x + 250/26=20
x + 250 = 520
x = 270m
Answer D
Question: 6^7 is equal to which of the following?
A.279,936
B.148,752
C.149,660
D.510,662
Answer: A.279,936
Explanation: A is the correct answer. We do not really need to calculate it. The last digit for 6^7 will be 6. Hence A is the correct answer
Question: The perimeter of one square is 48 cm and that of another is 28 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
A.13√4
B.13√2
C.23√2
D.13.9√2
Answer: D.13.9√2
Explanation: 4a = 48 4a = 28
a = 12 a = 7
a2 = 144 a2 = 49
Combined area = a2 = 193 => a = 13.9
d = 13.9√2
Answer: D
Question: A family consists of two grandparents, two parents and 6 grandchildren. The average age of the grandparents is 60 years, that of the parents is 30 years and that of the grandchildren is 5 years. What is the average age of family?
A.5/7years
B.B)21
C.C)30
D.D)33
Answer: B.B)21
Explanation: Required average
= (60 x 2 + 30 x 2 + 5 x 6 )/(2 + 2 + 6)
= (120 + 60 + 30)/10
= 210/10
= 21 years.
Answer is B
Question: In a rectangular axis system, what is the area of a parallelogram with the coordinates: (2,2), (8,2), (3,5), (9,5) ?
A.18.
B.28.
C.35.
D.49.
Answer: A.18.
Explanation: Delta x will give us the dimension of one side of the parallelogram = 8-2= 6 unit
Delta y will give us the dimension of the other side of parallelogram = 5-2=3 unit
Area of parallelogram = 6*3 = 18
ANSWER IS A
Question: If six machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job?
A.45
B.60
C.72
D.80
Answer: C.72
Explanation: using the std formula
m1d1h1/w1=m2d2h2/w2
substituting the values we have
6*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)
4=10/3*x
x=6/5 hour
so 72 minutes
ANSWER:C
Question: A man can row a boat at 24 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 100 km downstream?
A.24/8
B.25/8
C.23/8
D.21/8
Answer: B.25/8
Explanation: Speed downstream = 24 + 8 = 32 kmph.
Time required to cover 60 km downstream = d/s = 100/32
= 25/8 hours.
Answer: B
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 600. What is the manager's monthly salary ?
A.Rs.16003
B.Rs.16029
C.Rs.11288
D.Rs.14100
Answer: D.Rs.14100
Explanation: Explanation:
Manager's monthly salary Rs. (2100 * 21 - 1500 * 20) = Rs.14100.
Answer: D
Question: A box contains 50 balls, numbered from 1 to 50. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
A.1/4
B.3/8
C.1/2
D.5/8
Answer: A.1/4
Explanation: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2
My answer is: 1/4
A
Question: In the first week of last month, Company X realized an average wholesale profit of $2856 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?
A.$3
B.$4
C.$7
D.$13
Answer: D.$13
Explanation: The key operator that everyone seems to have missed is the average. The average profit of $2856 per day is equivalent to a total profit of $19992 for the whole week.
Therefore, the difference between sale price and cost per unit is equal to $19992, which is divisible by all of the answer choices, except for 13.
So, D is the answer.
Question: In what time will a train 100 m long cross an electric pole, it its speed be 126 km/hr?
A.2.5
B.2.9
C.2.4
D.2.85
Answer: D.2.85
Explanation: Speed = 126 * 5/18 = 35 m/sec
Time taken = 100/35
= 2.85 sec.
Answer:D
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
A.78 2/11%
B.18 2/11%
C.58 2/11%
D.18 2/11%
Answer: B.18 2/11%
Explanation: Explanation:
13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer:B
Question: Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = 2
(II) y = 4
(III) x + y = 0
A.I
B.II
C.III
D.I and II
Answer: B.II
Explanation: y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
B
Question: A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1840 had it been put at the rate of interest compounded annually?
A.4.5
B.3.5
C.3
D.2
Answer: D.2
Explanation: We can form equations as following:
Initial amount = P, Total amount after interest = T, Interest per year = I
T = P+I
Given T1 = P+2I = 1400
T2 = P+ 5I = 2000
From this we get, P = 1000I = 200 $
Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually)
consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$.
To get a 440 $ compound interest the duration have to be > 1 year and < 3 years.
Only option fitting : Option D.
Question: A sells a radio to B at a gain of 10% and B sells to c at a gain of 5%.If C pays Rs.462 for it,what did it cost to A?
A.200
B.300
C.100
D.400
Answer: D.400
Explanation: Solution
C.P of radio to C=C.P of radio to A * (1+10/100)(1+5/100)
=> 462=C.P of radio to A * 110/100 *105/100
=>C.P of radio to A=(462*100*100)/(105*110)
=400
Answer D
Question: The average weight of man, women and children is 45 kg. If the average weight of man and women be 40 kg and that of women and children be 43 kg, thenthe weight of women?
A.29
B.30
C.31
D.35
Answer: C.31
Explanation: Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg.
C
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
A.11
B.18
C.16
D.88
Answer: C.16
Explanation: 10 * 15 + 36 – 26 = 160/10 = 16.Answer: C
Question: A man can row downstream at the rate of 30 Kmph and upstream at 10 Kmph. Find the man’s rate in still water and rate of current?
A.10
B.8.0
C.9.5
D.9.0
Answer: A.10
Explanation: Rate of still water = 1/2 (down stream + upstream)
= 1/2 (30 + 10) = 20 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (30 - 10)
= 1/2 (20)
= 10 kmph
Answer is A.
Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 4 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
A.30
B.20
C.18
D.12
Answer: D.12
Explanation: 21-12 < no of hrs < 21-6
9< no of hrs < 17.
D
Question: If w and u are two positive integers and w/u = 2.20, then w can equal which one of the following?
A. 15
B. 28
C. 33
D. 30
Answer: C. 33
Explanation: w/u = 2.20 = 220/100 = 11/5
So, p COULD equal 33
Answer: C
Question: Out of eight consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels?
A.3150
B.3360
C.3580
D.3720
Answer: B.3360
Explanation: 8C2 x 3C3 x 5! = 3360
The answer is B.
Question: he average of 25 numbers is zero. Of them, at the most, how many may be greater than zero?
A.0
B.1
C.24
D.19
Answer: C.24
Explanation: Average of 25 numbers = 0.
Sum of 25 numbers (0 x 25) = 0.
It is quite possible that 24 of these numbers may be positive and if their sum is a the 25th number is (-a).
Answer: Option C
Question: John tossed a fair coin 3 times. What is the probability that the outcome was “tails” exactly twice?
A.1/8
B.1/4
C.3/8
D.1/2
Answer: C.3/8
Explanation: Total number of outcomes = 2*2*2 = 8
Number of favorable outcomes = Number of ways two places (for tails) can be chosen out of 3 slots = 3C2 = 3
So probability = 3/8
Alternative
Probability of getting tail in single toss = 1/2
Probability of getting head in single toss = 1/2
Probability of getting First Tail = 1/2
Probability of getting Second tail (Such that first tail has occurred, this incidentally is also the probability when first was head and second is tail) = 1/2 * 1/2 = 1/4
Probability of getting Third Head ( such that first was tail and second was tail) = 1/2 * 1/2 * 12 = 1/8
As you can notice the probability will be 1/8 whatever the sequence of Heads and tails.
We can arrange 2 Tails and one head in 3 ways (3C2 ways OR (3P3)/2! OR enumeration, whichever method you prefer to get here)
Since the favorable even can happen in either of these 3 ways, so Probability = 3 * 1/8 = 3/8
Answer:C
Question: A machine can filled a tank in 25 minutes and another machine can empty it in 50 minutes. If the tank is already half full and both the taps are opened together, then the tank is filled in how many minutes?
A.25min
B.20min
C.10min
D.15min
Answer: A.25min
Explanation: T = 1/2 (25*50 / 50-25) = 25 minutes
Tank is filled in 25 minutes
Answer is A
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?
A.120 metres
B.180 metres
C.324 metres
D.250 metres
Answer: D.250 metres
Explanation: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50 x 15/3 m = 250 m.
ANSWER : OPTION D
Question: A committee of 5 is to be selected from among 5 boys and 4 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
what is the answer choice and how?
A.105
B.225
C.209
D.350
Answer: C.209
Explanation: I'm sure there is some problem with the question.
R U sure its atleast one boy and not atleast 1 boy and 1 girl?
if its 1 boy and 1 girl
6C1*4C1 + 6C2*4C2 + 6C3*4C3 + 6C4*4C4
6*4 + 15*6 + 20*4 + 15*1
24 + 90 + 80 + 15
209
C
Question: In a class of 39 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
A.6
B.8
C.10
D.12
Answer: C.10
Explanation: 26 + 20 - 17 = 29
39 - 29 = 10 play neither
Answer is C
Question: The average of first 12 even numbers is?
A.19
B.18
C.16
D.13
Answer: D.13
Explanation: Sum of 12 even numbers = 12 * 13 = 156
Average = 156/12 = 13
Answer:D
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
A.28%
B.25%
C.23%
D.45%
Answer: B.25%
Explanation: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 60,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
A.70,000
B.60,000
C.128,000
D.90,000
Answer: C.128,000
Explanation: The distance traveled by each tyre:
4/5 * 1, 60, 000km = 128,000 km. C
Question: A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much
A.0.60 loss
B.0.70 loss
C.0.80 loss
D.0.50 loss
Answer: C.0.80 loss
Explanation: CP when profit of 25% = 12.8
CP when loss of 20% = 20
Total CP = 32.8
Total SP = 32.00
Total loss = 0.80
ANSWER:C
Question: If PINTU is coded as 79523 in a certain code language, how would you code MINTU in the same language?
A.13426
B.14236
C.49523
D.14263
Answer: C.49523
Explanation: 1 2 3 4 5 6 7 8 9
a b c d e f g h i
j k l m n o p q r
s t u v w x y z
sooo...MINTU is 49523...
ANSWER:C
Question: 14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish
A.1 day
B.2 days
C.3 days
D.4 days
Answer: B.2 days
Explanation: 14 men make toy in 5 days
after 1 day 14 more worker join
m1/m2=d2/d1
14/28=d2/4
=2 day
ANSWER:B
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 61 unique alphanumeric case sensitive characters.
A.63^4
B.62^5
C.62(61^4)
D.63(62^4)
Answer: C.62(61^4)
Explanation: Total number of passwords = number of 4 character password +number of 5 character password
= 61^4 + 61^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=61^4(1+ 61)
=61^4 * 62
Answer C
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
A.16%
B.16.66%
C.18.23%
D.19%
Answer: B.16.66%
Explanation: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $50. What is the percent decrease?
A.20%
B.30%
C.50%
D.70%
Answer: C.50%
Explanation: The is always the difference between our starting and ending points. In this case, it’s 100 – 50 = 50. The “original” is our starting point; in this case, it’s 100. (50/100)*100 = (0.5)*100 = 50%.
C
Question: Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.4500. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?
A.Rs.750, Rs.2250
B.Rs.2000, Rs.750
C.Rs.750, Rs.2000
D.Rs.800, Rs.1250
Answer: A.Rs.750, Rs.2250
Explanation: Minu’s one day’s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18
Anu’s wages: Binu’s wages: Minu’s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2
Minu’s share = Rs.4500* 2/12 = Rs.750
Anu’s share = Rs.4500* 6 /12 = Rs.2250
ANSWER:A
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 55 kmph when will the owner over take the thief from the start?
A.A)1.33
B.B)5
C.C)7
D.D)5
Answer: A.A)1.33
Explanation: Explanation:
|-----------20--------------------|
55 40
D = 20
RS = 55 – 40 = 15
T = 20/15 = 1.33 hours
Answer: Option A
Question: Ed and Flora drive at constant speeds toward each other on a highway. Ed drives at a constant speed of 31 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Ed is 120 km away from Flora at 6 am, and also 120 km away from Flora at 11 am, then how fast is Flora driving (in kilometers per hour)?
A.13
B.15
C.17
D.19
Answer: C.17
Explanation: Ed and Flora complete 240 km / 5 hours = 48 km/hour
Flora's speed is 48-31=17 km/hour
The answer is C.
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
A.4 hrs 29 min
B.4 hrs 24 min
C.8 hrs 24 min
D.4 hrs 44 min
Answer: B.4 hrs 24 min
Explanation: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer:B
Question: The area of the largest circle that can be drawn inside a square of side 98 Cm in length is:
A.8600
B.3646
C.7546
D.7636
Answer: C.7546
Explanation: Radius of required circle = 49 Cm
its area = 22/7 × 49 × 49
154 × 49 = 7546 Cm(power)2
Answer is C.
Question: SI on a sum of money for 2yrs at 5% per annum is Rs.50, what is the CI on the same at the same rate & for the same time?
A.Rs. 34.24
B.Rs. 41.25
C.Rs. 51.25
D.Rs. 59
Answer: C.Rs. 51.25
Explanation: Sum = Rs. 50 x 100 = Rs. 500.
2 x 5
Amount
= Rs. 500 x 1 +	5 2
100
= Rs. 500 x	21	x	21
20	20
= Rs. 551.25
C.I. = Rs. (551.25 - 500) = Rs. 51.25
C
Question: A bowl contains many kinds of fruit. In the bowl there are twice as many pears then there are oranges, and twice times as many plums as oranges. If the total number of pieces of fruit is X, then how many oranges are in the bowl as a fraction of X
A.X/2
B.X/3
C.X/4
D.X/5
Answer: D.X/5
Explanation: Since X equals the number of fruit, X = pears + oranges + plums.
Since there are twice as many pears as oranges, then pears = 2*oranges.
Since there are twice as many plums as oranges, then plums = 2*oranges
Hence X = 2*oranges + oranges + 2*oranges, which simplifies to X = 5*oranges
Thus Oranges = X/5
Answer: D
Question: man walks at speed of 8 km/h 300 mtrs length train crosses man in 30 sec from back, find speed of train?
A.40 km/hr
B.44 km/hr
C.42 km/hr
D.43 km/hr
Answer: B.44 km/hr
Explanation: if speed of train is x kmph, then
relative speed =(x-8 ) km/hr = (x-8)*5/18 m/sec
(x-8)*(5/18)*30=300
x-8=36
x= 44 km/hr
ANSWER:B
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ?
A.13m
B.14m
C.15m
D.16m
Answer: A.13m
Explanation: Explanation:
the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is
=> mts.
ANSWER IS A
Question: Beginning in Town A, Biker Bob rides his bike 20 miles west, 6 miles north, 10 miles east, and then 18 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
A.28 miles
B.30 miles
C.26 miles
D.18 miles
Answer: C.26 miles
Explanation: Using Pythagoras we have one side i,e total distance traveled in north direction = 18+6=24m
other being the base ie distance traveled west- distance traveled eat=20-10=10 m
now this third side or the distance between town A and Town B=24^2+ 10^2=sq root 676=26m
Answer : C
Question: A sum of money lent out at S.I. amounts to Rs. 710 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
A.s.440
B.s. 586
C.s. 540
D.s. 740
Answer: B.s. 586
Explanation: S.I for 5 years = (1020 - 710) = Rs. 310.
S.I. for 2 years = 310/5 * 2 = Rs. 124.
Principal = (710 - 124) = Rs. 586.
ANSWER:B
Question: Which of the following fractions is greater than 2/3?
A.1. 12/50
B.2. 3/11
C.3. 2/9
D.4. 4/17
Answer: C.3. 2/9
Explanation: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
C
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
A. 20 B. 54
A.20
B.27
C.28
D.22
Answer: A.20
Explanation: There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee
= ⁶C₃ = (6 * 5 * 4)/6
= 20.
Answer:A
Question: Two numbers are respectively 40% and 60% more than a third number. What percentage is the first of the second?
A.72%
B.87.5%
C.63.7%
D.56.9%
Answer: B.87.5%
Explanation: Required answer = (100+x)/(100+y)*100 = 140*100/160 = 87.5%
Answer is B
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
A.12
B.24
C.C is elder than A
D.Data inadequate
Answer: A.12
Explanation: Solution
[(A+B) - (B+C)]	= 12
‹=›A - C
= 12.
Answer A
Question: Find a sum for first 7 prime numbers?
A.22
B.58
C.29
D.32
Answer: B.58
Explanation: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17) = 58
Note: 1 is not a prime number
Option B
Question: Set Q consists of the following five numbers: Q = {5, 8, 11, 21, 34}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}
A. I only
B. III
C. IIII
D. IIIII
Answer: D. IIIII
Explanation: (1)	Multiplying all the numbers change Standard Deviation
(2)	Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number there in the Set Q.
Set II: elements are multiplied by 2 and standard deviation changes.
Hence the answer is D.
Question: A number when divided by a divisor leaves a remainder of 25. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
A.12
B.13
C.35
D.38
Answer: D.38
Explanation: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+25
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 38
as D is also integer and 38 is a prime number, the D should be 38 to satisfy the above equation.
Hence answer is 'D'
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 4/7 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
A.0
B.1/15
C.2/15
D.1/20
Answer: D.1/20
Explanation: Suppose the water in each jug is L liters
CX x (1/5) = L
CX = 5L liters
CX is capacity of X
CY x (4/7) = L
CY = 7L/4 liters
CY is capacity of Y
Now, Y is 7L/4 - L empty = 3L/4 empty
So, we can put only 3L/4 water in jug Y from Jug X
Jug X's remaining water = L - 3L/4 = L/4
Fraction of X which contains water = water / CX
= (L/4)/ 5L
= 1/20
Answer will be D
Question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
A.700
B.721
C.702
D.703
Answer: B.721
Explanation: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.
Answer B
Question: The area of a triangle is with base 4m and height 5m?
A.11
B.10
C.787
D.122
Answer: B.10
Explanation: 1/2 * 4 * 5 = 10 m2
Answer: B
Question: If a and b are positive integers such that a/b = 1.92, which of the following must be a divisor of a?
A.19
B.13
C.9
D.8
Answer: C.9
Explanation: 1) A and B are positive INTEGERS
2) A/B = 1.92
A = 192
B = 100
192/100 = 1.92
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 96
B = 50
96/50 = 1.92
Dividing by 2 again:
48/25 = 1.92
There is no other way to reduce this fraction, so A must be a multiple of 48 and B must be an equivalent multiple of 25. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 48, we have to 'factor-down' 48. This gives us (6)(8). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Answer: C