mathewhe/aqua_rat huggingface dataset:
Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
A
Answer: (A) 1
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 8
(B) 7
(C) 9
(D) 6
(E) 5
Rationale: Let B joined for x months. Then
85000×12:42500×(x)=3:1
⇒850×12:425x=3:1
⇒850×12×1=3×425x
⇒850×4=425x
⇒x=8
Answer is A.
Answer: (A) 8
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3200, A will get:
(A) Rs.1200
(B) Rs.1500
(C) Rs. 1920
(D) Rs.2000
(E) None of these
Rationale: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3000/25 = 128
So, A’s amount = 120 × 15 = Rs.1920.
Answer: Option C
Answer: (C) Rs. 1920
Question: The reciprocal of the hcf and lcm of two are 1/13 and 1/312 .if one of the number is 24 then other no. is
(A) 126
(B) 136
(C) 146
(D) 156
(E) 169
Rationale: reciprocal of the hcf and lcm of two are 1/13 and 1/312
so, HCF = 13 , LCM = 312
LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a
so, other = 13*312 / 24 = 169
ANSWER:E
Answer: (E) 169
Question: Of the 170 people at a party, 70 were women, and 30 women tried the appetizer. If 60 people did not try the appetizer, what is the total number of men who tried the appetizer?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Total people at party=170
Women=70
so Men 170-70=100
No. of pple who tried appetizer=170-60 (given info)=110
No of women who tried appetizer=30
So Remaining ppl(men) who tried the appetizer =110-30=80
Correct Option E
Answer: (E) 80
Question: Priya covers journey from kavali to nellore by car at average speed of 70 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey?
(A) 50 Km/hr
(B) 50.90 Km/hr
(C) 50.95 Km/hr
(D) 52 Km/hr
(E) 53 km/hr
Rationale: Explanation:
Average speed = 2 xy/x+y
= 2*70*40/110
= 50.90 Km/hr
Answer: Option B
Answer: (B) 50.90 Km/hr
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
(A) 12/15
(B) 37 1/2
(C) 3/7
(D) 4/9
(E) 5/2
Rationale: Explanation :
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
ANSWER:B
Answer: (B) 37 1/2
Question: In a games hour 4 different types of players came to the ground? cricket 15, hokey 12, football 13, softball 15. How many players are present in the ground?
(A) 70
(B) 52
(C) 55
(D) 49
(E) 50
Rationale: total number of players= 15+12+13+15= 55
Answer is C
Answer: (C) 55
Question: Bucket P has thrice the capacity as Bucket Q. It takes 60 turns for Bucket P to fill the empty drum. How many turns it will take for both the buckets P&Q, having each turn together to fill the empty drum?
(A) 45
(B) 53
(C) 54
(D) 46
(E) 63
Rationale: If caoacity of Q is x units, then capacity of P is 3x and capacity of drum is 60*3x = 180 x.
It will take 180x/4x = 45 turns it will take for both the buckets P&Q, having each turn together to fill the empty drum.
ANSWER:A
Answer: (A) 45
Question: Find the lowest positive integer that can be divided by all the even numbers between 14 and 21.
(A) 4581
(B) 5040
(C) 3682
(D) 1231
(E) 1563
Rationale: The even numbers between 14 and 21 are 14,16,18,20.
Find the LCM of these numbers
LCM=2^4*7*3^2*5
The answer is B)
Answer: (B) 5040
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 101
(B) 209
(C) 301
(D) 405
(E) 91
Rationale: Required number of ways = 6C1*4C3 + 6C2*4C2 + 6C6*4C1 + 6C4
= 24+90+80+15
= 209
Answer is B
Answer: (B) 209
Question: In a recent election, Geoff received 15 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,571 more votes to win the election, what is the value of x ?
(A)  74.5
(B)  54
(C)  56
(D)  60
(E)  63
Rationale: Word problems are tricky in somehow more than other problem because you have the additional step to translate.
Breaking the problem: Geoff how many votes he receives ?? 900 votes
he needs 3571 more votes so : 900+3571= 4471
Now what's the problem wants ?? a x %........4471 is what % of total votes 6000........translating: 4471 = x/100 * 6000 ---
x= 74.5 %..........A
Answer: (A)  74.5
Question: How many positive integers less than 6,000 are there in which the sum of the digits equals 5?
(A) 65
(B) 62
(C) 61
(D) 56
(E) 58
Rationale: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.
Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).
So, for example:
XX|X|X|X = 2111
||XXX|XX = 0032
etc.
There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.
D
Answer: (D) 56
Question: An old priest fell on a bottom of the well of a church.
The well is 20 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
(A) 15-days
(B) 16-days
(C) 17-days
(D) 18-days
(E) 19-days
Rationale: Solution:
16-days
In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well
Answer B
Answer: (B) 16-days
Question: A merchant purchased a jacket for $42 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A)  $0
(B)  $3
(C)  $6
(D)  $12
(E)  $15
Rationale: Actual Cost = $42
SP = Actual Cost + Mark up
= Actual Cost + 30% SP
= 42*100/70
on sale SP = 80/100(42*100/70) = 48
Gross profit = $6
Answer is C
Answer: (C)  $6
Question: What is the greater of the two numbers whose product is 2560, given that the sum of the two numbers exceeds their difference by 32?
(A) A)90
(B) B)100
(C) C)160
(D) D)70
(E) of these
Rationale: Let the greater and the smaller number be g and s respectively.
gs = 2560
g + s exceeds g - s by 32 i.e., g + s - (g - s) = 32
i.e., 2s = 32 => s = 16
g = 2560/s = 160.
ANSWER:C
Answer: (C) C)160
Question: A team scored a total of 84 points. If each player on the team scored at least 14 points, then what is the greatest possible number of players on the team?
(A) A)6
(B) B)7
(C) C)8
(D) D)9
(E) E)10
Rationale: 84/14=6 plus remainder.
The answer is A.
Answer: (A) A)6
Question: If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
(A) 4 days
(B) 5 days
(C) 6 days
(D) 7 days
(E) 9 days
Rationale: Explanation:
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, 6x + 8y =	1/10and 26x + 48y =	1/2
Solving these two equations, we get : x =	1/100 and y =	1/200
(15 men + 20 boy)'s 1 day's work =15/100 + 20/200 = 1/4
15 men and 20 boys can do the work in 4 days.
ANSWER IS A
Answer: (A) 4 days
Question: A wildlife preserve is being planned for 5,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population?
(A)  340
(B)  560
(C)  320
(D)  310
(E)  300
Rationale: Number of rhinos = 5000
Watering area = 10,000 acres
Number of rhino to increase by 10 percent ,then number of rhino = 5500
Grazing area for a rhino = 100
Total grazing area for 5500 rhinos= 5500 * 100 = 5,50,000
Total area required for the wildlife preserve = 5,50,000 + 10,000 = 5,60,000 = 560 * 1000
Answer B
Answer: (B)  560
Question: Average expenditure of a person for the first 3 days of a week is Rs. 340 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
(A) 350
(B) 370
(C) 380
(D) 430
(E) None
Rationale: Explanation:
Assumed mean = Rs. 340
Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 340 + Rs. 40 = Rs. 380
Correct Option: C
Answer: (C) 380
Question: Two cars cover the same distance at the speed of 50 and 45 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?
(A) 278
(B) 277
(C) 960
(D) 600
(E) 261
Rationale: 50(x + 1) = 45 x
X = 10
60 * 10 = 600 km
Answer:D
Answer: (D) 600
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is ?
(A) 1/8
(B) 1/7
(C) 1/0
(D) 1/2
(E) 1/3
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:B
Answer: (B) 1/7
Question: In a queue, Shankar is ninth from the rear end. Althaf's place is eighth from the front. Nitu is standing between the two. What could be the minimum numbers of boys standing in the queue ?
(A) 18
(B) 14
(C) 22
(D) 24
(E) 26
Rationale: Explanation:
1 2 3 4 5 6(Shankar) 7(Nitu) 8(Althaf) 9 10 11 12 13 14
Here, Althaf is 8th from front, Shankar is 9th from rear end and Nitu is between them
So minimum no. of boys standing in the queue = 14
Answer IS B
Answer: (B) 14
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 20% 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) 74.2
(E) 62.9
Rationale: CP = 47.50
SP = 47.50*(125/100)
= 59.375
MP*(80/100)
= 59.375
MP = 74.2
Answer:D
Answer: (D) 74.2
Question: In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?
(A) 200
(B) 210
(C) 230
(D) 56
(E) 270
Rationale: 8p2 = 8 X 7 = 56
D)
Answer: (D) 56
Question: Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
(A) 56
(B) 28
(C) 20
(D) 72
(E) 27
Rationale: 1/x + 1/(x + 10) = 1/12
x = 20
Answer: C
Answer: (C) 20
Question: A Train usually travels at a speed of 72 kmph crossing a pole in 7 sec, what would be the length of the train?
(A) 140 m
(B) 142 m
(C) 146 m
(D) 152 m
(E) 158 m
Rationale: Explanation:
D = 72 * 5/18 * 7 = 140 m
Answer: Option A
Answer: (A) 140 m
Question: A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?
(A) 553 mph.
(B) 353 mph.
(C) 273 mph.
(D) 153 mph.
(E) 253 mph.
Rationale: The speed of the plane in still air = x miles/hour
The speed of the wind is 23 mph
Speed with the wind = (x + 23) mph
Speed against the wind = (x – 23) mph
Time = Distance/ Speed
According to the problem,
420/(x + 23) = 350/(x – 23)
420(x – 23) = 350(x + 23)
420x – 9660 = 350x + 805
420x – 350x = 8050 + 9660
70x = 17710
x = 17710/70
x = 253
Therefore, the speed of the plane in still air = 253 mph.
correct answer E
Answer: (E) 253 mph.
Question: A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: 60% is 20%-points above 40% and 20%-points below 80%.
Thus the ratio of "the first 30 games" to "remaining games" is 1:1.
So the team played a total of 30+30 = 60 games.
The answer is B.
Answer: (B) 60
Question: $500 will become $1000 in 3 years find the rate of interest?
(A) A)10%
(B) B)20%
(C) C)25%
(D) D)33.33%
(E) E)50%
Rationale: SI = simple interest = A-P = 1000-500 = $300
R = 100SI/PT = 100*500/500*3 =33.33%
Answer is D
Answer: (D) D)33.33%
Question: If M is the mean of x,y,z ; then what is the mean of x+20,y+20 and z+20
(A) M
(B) 3M
(C) 10M
(D) M+20
(E) M-10
Rationale: If each number is shifted up by 20, the mean also shifts up by 20 since it stays in the middle. The whole set is shifted on the number line so mean will also shift by the same amount.
So new mean is M + 20.
Answer (D)
Answer: (D) M+20
Question: 5 times the side of a square resulted in a parameter of 20x. What is the parameter before it was timed by 5?
(A) 4x
(B) 5x
(C) 10x
(D) 40x
(E) 2x
Rationale: The new parameter is 5 times the old parameter. The old parameter is therefore 20x/5. This is 4x. Answer option A.
Answer: (A) 4x
Question: Mike and his friend are going on a road trip and hoping to miss traffic. If they are driving at a rate of 6 miles per minute, what is their speed in kilometers per hour? [1km = 0.6 miles]
(A) 60
(B) 30
(C) 300
(D) 600
(E) None of the above
Rationale: To calculate the equivalent of kilometres in a mile
6 miles = 6*(0.6)^-1 = 10 kilometres
In 1 hour there are 60 minutes
Speed in kmph = 10 * 60 = 600
Correct answer - D
Answer: (D) 600
Question: Find the smallest positive integer n such that 11n - 1 is divisible by 105.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: The last digit of 11n − 1 is 0, so 5 always divides 11n − 1. Also, checking the
remainders when the powers of 11 are divided by 3 and 7 we get that 3 divides 11n −1
exactly when n is even, and 7 divides 11n − 1 exactly when 3 divides n.
correct answer D
Answer: (D) 6
Question: A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?
(A) 22
(B) 28
(C) 15
(D) 18
(E) 11
Rationale: Explanation:
P(1 + R/100)5 = 2P => (1 + R/100)5 = 2
Let P(1 + R/100)n = 8P
=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3
=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.
Answer: C
Answer: (C) 15
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
(A) 299
(B) 297
(C) 261
(D) 280
(E) 172
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: (D) 280
Question: What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 3?
(A) 6
(B) 0.6
(C) n/6
(D) 6.2
(E) π
Rationale: Maximum distance straight line is diameter
d = 2r = 6..
ANS option A.
Answer: (A) 6
Question: Solve the given two equations and find the inequality of X and Y. (a) 225X^2-4 = 0 and (b) (225y)^(1/2) +2 = 0
(A) If x>y
(B) If x>=y
(C) If x<Y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X= +2/15 and -2/15
Y= 4/225
Comparing we get X>Y and X<y
Hence, no relationship can be established
E)
Answer: (E) x=y or relationship cannot be established
Question: A truck covers a distance of 288 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 90 km more than that travelled by the truck ?
(A) 6 hours
(B) 5 hours
(C) 7 hours
(D) 8 hours
(E) None
Rationale: Explanation :
Speed of the truck = Distance/time = 288/8 = 36 kmph
Now, speed of car = (speed of truck + 18) kmph = (36 + 18) = 54 kmph
Distance travelled by car = 288 + 90 = 378 km
Time taken by car = Distance/Speed = 378/54 = 7 hours.
Answer –C
Answer: (C) 7 hours
Question: A snail, climbing a 20 feet high wall, climbs up 8 feet on the first day but slides down 4 feet on the second. It climbs 8 feet on the third day and slides down again 4 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
(A) 7
(B) 16
(C) 17
(D) 20
(E) 21
Rationale: total transaction in two days = 8-4 = 4 feet
in 7 days it will climb 20 feet
thus reaching the top
therefore , total no of days required =7
A
Answer: (A) 7
Question: The average of 6 observations is 13. A new observation is included and the new average is decreased by 1. The seventh observation is?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: Let seventh observation = X.
Then, according to the question we have
=> (78 + X) / 7 = 12
=> X = 6.
Hence, the seventh observation is 6.
ANSWER:D
Answer: (D) 6
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 15 seconds. Find the length of the faster train?
(A) 270
(B) 277
(C) 187
(D) 257
(E) 150
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 15 sec = 15 * 10 = 150 m.
The length of the faster train = 150 m.
Answer: E
Answer: (E) 150
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is?
(A) 40m2
(B) 45m2
(C) 49m2
(D) 51m2
(E) 55m2
Rationale: 39/360 * 22/7 * 12 * 12
= 49m2
Answer:C
Answer: (C) 49m2
Question: The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
(A) 3:4
(B) 3:0
(C) 3:1
(D) 3:2
(E) 3:7
Rationale: Let the present ages of A and B be 5x and 3x years respectively.
Then, (5x - 4)/(3x + 4) = 1/1
2x = 8 => x = 4
Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1.Answer: C
Answer: (C) 3:1
Question: c can run a kilometer race in 4 1/2 min while d can run same race in 5 min. How many meters start can c give d in a kilometer race, so that the race mat end in a dead heat?
(A) m
(B) m
(C) m
(D) m
(E) m
Rationale: c can give d (5 min - 4 1/2 min) = 30 sec start.
The distance covered by d in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
c can give d 100m start.
ANSWER:D
Answer: (D) m
Question: A marketing firm determined that, of 200 households surveyed, 80 used neither Brand E nor Brand B soap, 60 used only Brand E soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?
(A)  15
(B)  20
(C)  30
(D)  40
(E)  45
Rationale: SOLUTION FOR SOAP E AND SOAP B
(D) 40
Answer: (D)  40
Question: A customer pays 40 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
(A) 50
(B) 40
(C) 70
(D) 60
(E) 20
Rationale: Let x be the original price.
x - 20 = 40
x - 20 + 20 = 40 + 20
x + 0 = 60
x = 60
Answer is D
Answer: (D) 60
Question: The speed of a train is 90 kmph. What is the distance covered by it in 20 minutes?
(A) 15
(B) 66
(C) 77
(D) 30
(E) 42
Rationale: 90 * 20/60 = 30 kmph
Answer:D
Answer: (D) 30
Question: In a sequence of 42 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 281, what is the smallest term in the sequence?
(A) 2
(B) -2
(C) 0
(D) 8
(E) -6
Rationale: Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term.
An = 281 + (42 - 1)*(-7)
An = 281 - 287 = -6
E
Answer: (E) -6
Question: A tour group of 25 people paid a total of $735 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22
(B) $23.94
(C) $28
(D) $25.20
(E) $30
Rationale: Soln:-
735/25=x+0.05x
735/25=1.05x
x=28
ANSWER:C
Answer: (C) $28
Question: A boy can reach a certain place in 15 hours. If he reduces his speed by 1/30th, he goes 5 km less in that time. Find his speed.
(A) 4 km/hr.
(B) 6 km/hr
(C) 8 km/hr
(D) 10 km/hr
(E) None of these
Rationale: Explanation :
Solution: Let the speed be x km/hr. then,
15x - (15 * 29x/30) = 5
=> 30x-29x = 5*2
=> x =10 km/hr.
Answer : D
Answer: (D) 10 km/hr
Question: If |x| = 4x - 2, then x = ?
(A) 1
(B) 1/2
(C) 1 and 1/2
(D) -1/2
(E) 3
Rationale: Approach:
Substituted option A i.e x=3. Inequality satisfied.
E
Answer: (E) 3
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 3637
(C) 3630
(D) 3631
(E) 3635
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer: A
Answer: (A) 3630
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 2 2 8/2
(B) 2 2 1/9
(C) 2 9 1/2
(D) 2 2 1/2
(E) 2 2 4/2
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 1/2kmph
Answer:D
Answer: (D) 2 2 1/2
Question: A bag contains 6 white balls, 6 black balls, and 3 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
(A) 0.2
(B) 0.15
(C) 0.35
(D) 0.45
(E) 0.4
Rationale: Each ball has an equal probability of being the third ball drawn.
P(3rd ball is red) = 3/15 = 0.2
The answer is A.
Answer: (A) 0.2
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the children stand together?
(A) 12
(B) 24
(C) 50
(D) 48
(E) 120
Rationale: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C1 and C2 are always together.
Consider F and M to be one unit, then we would have total of four units: {F), {M}, {C1C2}, {D}. The number of arrangements of these four units is 4!, but C1 and C2 within their unit can be arranged in 2 ways: {c1c2} or {c2c1}, so total number of arrangements is 4!*2=48.
Answer: D.
Answer: (D) 48
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 57%
(B) 82%
(C) 52%
(D) 22%
(E) 58%
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
Answer:A
Answer: (A) 57%
Question: Express of the following as a fraction:
25%
(A) 1/4
(B) 1/8
(C) 2/9
(D) 3/6
(E) None of them
Rationale: 25% = 25/100= 1/4.
Answer is A.
Answer: (A) 1/4
Question: The larger interior angle of a parallelogram is 90° more than its smaller interior angle. What is the measure of the smaller interior angle of the parallelogram?
(A) 90°
(B) 75°
(C) 60°
(D) 45°
(E) 30°
Rationale: let smaller be x ,larger becomes x+90... total of all angles=360
so 4x+180=360 and x=45
ANSWER:D
Answer: (D) 45°
Question: A is twice as good a work man as B and together they finish the work in 6 days. In how many days A alone can finish the work?
(A) 3
(B) 9
(C) 7
(D) 2
(E) 6
Rationale: WC = 2:1
2x + x = 1/6 => x = 1/18
2x = 1/9
A can do the work in 9 days.
Answer: B
Answer: (B) 9
Question: In what time will Rs.4600 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 7 1/3
(B) 7 1/6
(C) 7 1/4
(D) 7 1/2
(E) 7 1/5
Rationale: (4600*3*R)/100 = (5000*5*4)/100
R = 7 1/4
Answer: C
Answer: (C) 7 1/4