RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In b is a positive integer smaller than 200 and (14b)/60 is an integer, then b has how many different positive prime factors?
A.2
B.3
C.5
D.6
Answer: B.3
Explanation: 7b/30 tells us that b is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
Answer: B
Question: What is the sum of three consecutive numbers if the product of the numbers can be expressed as 3079+3080+3081?
A.62
B.63
C.61
D.65
Answer: B.63
Explanation: Addition of any 3 consecutive numbers is always divisible by 3
that rules out options a, c, d and e
20, 21, 22 (Matches fine)
Answer =B
Question: A and B are two fixed points 5 cm apart and C is a point on AB such that AC is 3cm. if the length of AC is increased by 6%, the length of CB is decreased by
A.6%
B.7%
C.8%
D.9%
Answer: D.9%
Explanation: Solution: As A and B are fixed, C is any point on AB, so if AC is increases then CB decreases.
A________3 cm_________ C _____2 cm____B
Then, solution can be visualized as,
Increase in AC 6% = (106*3)/100=3.18 cm.
Decrease in CB = 0.18 cm
% decrease = (0.18/2)*100 = 9%.
Alternatively,
AC = 3 Cm.
BC = 2 Cm.
Increase in AC by 6%, then
New, AC = 3 + 6% of 3 = 3 + 0.18 = 3.18 cm.
0.18 cm increase in AC means 0.18 cm decrease in BC as already mentioned AB as the fixed point.
So, % decrease in BC,
= (Actual Decrease in BC /Original BC)*100
= (0.18/2) *100 = 9%.
Answer: Option D
Question: If y = 2 + 2K and y≠0y≠0, then 2/y + 2/y + 1/y + 1/y = ?
A.1/(8+8k)
B.3/(1+k)
C.1/(8+k)
D.4/(8+k)
Answer: B.3/(1+k)
Explanation: 2/Y + 2/Y + 1/Y + 1/Y
= 6/Y
= 6/(2 + 2K)
= 3/(1 + K)
ANSWER:B
Question: A bowl has only 3 apples and 3 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
A.1/10
B.1/5
C.2/9
D.2/5
Answer: B.1/5
Explanation: 3/6 * 2/5
=1/5
B. 1/5
Question: The cross section of a canal is trapezium in shape. The canal is 12m wide at the top and 8m wide at the bottom. If the area of the cross section is 840 sq.m, the depth of the canal is:
A.42m
B.84m
C.63m
D.8.75m
Answer: B.84m
Explanation: ½ (12+8)d=840 or d=84m
ANSWER:B
Question: A gardener increased the length of a rectangle-shaped garden by 30 percent and decreased its width by 20 percent. The area of the new garden
A.has increased by 4 percent
B.has increased by 8 percent
C.has increased by 12 percent
D.is exactly the same as the old area
Answer: A.has increased by 4 percent
Explanation: Let L be the original length and let W be the original width.
The original area was L*W.
The new area is 0.8W*1.3L = (0.8)(1.3)L*W = 1.04L*W
The answer is A.
Question: Arjun buys a toy at Rs 100 and sells it at Rs 120. Amin buys the same toy at Rs 120 but sells it at Rs 100. What are the respective profit/loss per cent for the two persons?
A.20%, 20%
B.20%, 16.7%
C.16.7%, 16.7%
D.16.7%, 10%
Answer: B.20%, 16.7%
Explanation: Percentage profit = [(120 - 100) / 100] x 100 = 20%
Percentage loss = [(120 - 100) / 120] x 100 = 16.7 %
ANSWER:B
Question: The compound interest on a sum for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound and simple interest for 3 years will be
A.Rs. 48
B.Rs. 98.56
C.Rs. 66.56
D.Rs. 66.58
Answer: B.Rs. 98.56
Explanation: Explanation:
Given that simple interest for 2 years is Rs.800
i.e., Simple interest for 1st year is Rs.400
and simple interest for 2nd year is also Rs.400
Compound interest for 1st year will be 400
and Compound interest for 2nd year will be 832 - 400 = 432
you can see that compound interest for 2nd year is more than simple interest for 2nd year by 432 - 400 = Rs.32
i.e, Rs. 32 is the interest obtained for Rs.400 for 1 year
Rate, R = 100 × SI/PT = (100×32)/(400 × 1) = 8%
Difference between compound and simple interest for the 3rd year
= Simple Interest obtained for Rs.832
= PRT/100 = (832 × 8 × 1)/100 = Rs. 66.56
Total difference between the compound and simple interest for 3 years
= 32 + 66.56 = Rs.98.56
Answer: Option B
Question: $500 will become $1000 in 7 years find the rate of interest?
A.A)10%
B.B)20%
C.C)14.29%
D.D)30%
Answer: C.C)14.29%
Explanation: SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*7 =14.29%
Answer is C
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
A.$1
B.$1.84
C.$1.92
D.$2.13
Answer: B.$1.84
Explanation: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 15% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 10%. If Ron imported a $15,000 imported car and ended up paying $1800 in taxes, what is the first tier's price level?
A.$7000
B.$6500
C.$6050
D.$6000
Answer: D.$6000
Explanation: Let T be the tier price, P be total price = 15000
Per the given conditions:
0.15T + 0.10(P-T) = 1800
0.15T+0.10*15000-0.10T =1800
0.05T +1500 = 1800
0.05T = 1800-1500 = 300
T = 300/0.05 =6000
Answer D
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
A.16cm
B.18cm
C.24cm
D.Data inadequate
Answer: B.18cm
Explanation: Explanation:
2(l+b)/b=5/1
2l + 2b = 5b
3b = 2l
b = 2/3 l
Then, Area = 216 cm2
l x b = 216
l x (2/3)l = 216
l2 = 324.
l = 18 cm.
Answer: B
Question: In Town X, 120 percent of the population are employed, and 80 percent of the population are employed males. What percent of the employed people in Town X are females?
A.16%
B.25%
C.33%
D.40%
Answer: C.33%
Explanation: Total employed people 12%, out of which 80 are employed males, hence 40% are employed females.
(employed females)/(total employed people)=40/120=1/3=33%
Answer: C.
Question: A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 9 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?
A.3
B.4
C.18/5
D.9
Answer: C.18/5
Explanation: yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:
A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 9 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?
So for a job to be done in 2 hours R = 1/2
R_a(Rate of Machine R) = 1/36
R_s(Rate of Machine S) = 1/9
Lets say x machines are used to attain the desired rate, thus
x/36+x/9 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)
(x+4x)/36 = 1/2
5x/36 = 1/2
x = 18/5.
QA = 18/5 (ANSWER C)
Question: Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?
A.1/16
B.5/42
C.1/8
D.3/16
Answer: C.1/8
Explanation: 210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=1/8.
Answer: C.
Question: At a company, the average wage of male employees is $5 per hour, and the average wage of female employees is $8 per hour. If the average wage of all employees is $7 per hour, what is the ratio of the number of male employees to the number of female employees?
A.1 to 2
B.2 to 3
C.3 to 2
D.5 to 3
Answer: A.1 to 2
Explanation: Average hourly wage of male employees = 5 $
Average hourly wage of female employees = 8 $
Average hourly wage of all employees = 7 $
Let number of male employees = m
number of female employees = f
7= (5m + 8f ) / m+f
=>7m + 7f = 5m + 8f
=> 2m = 1f
=> m/f = 1/2
Answer A
Question: In order to complete a reading assignment on time, Terry planned to read 120 pages per day. However, she read only 60 pages per day at first, leaving 840 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
A.4
B.6
C.8
D.10
Answer: C.8
Explanation: D=120*X - according to the plan, assignment to be completed on time reading 120 pages per day for next X days. But, Terry's plans changed so she read as follow:
60 pages for first Y days and 780 pages for last 6 days, we get these equations:
60*Y+840=120*X
X-Y=6 --------->>X planned number of days, Y - actually used reading 60 pages per day and 6 leftover days used to complete a lump 780 pages
From above we find that X=Y+6 and 60Y+840=120Y+720 or 60Y=120 --->>>>> Y=2, hence X=8
Answer : C
Question: Together, Andrea and Brian weigh p pounds; Brian weighs 12 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds?
A. p/2 - 10
B. 3p/4 - 6
C. 3p/2 - 5
D. 5p/4 - 10
Answer: B. 3p/4 - 6
Explanation: Together, Andrea and Brian weigh p pounds --> A + B = p.
Brian weighs 10 pounds more than Andrea --> B = A + 12 --> A + (A + 12) = p --> A = (p - 12)/2 = p/2 - 6.
Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 6) + p/4 = 3p/4 -6.
Answer: B.
Question: Set S consists of integers {1,2,3,4,5,6}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 9?
A.2/15
B.1/7
C.3/11
D.4/19
Answer: A.2/15
Explanation: Number of ways you can choose 2 from 6 = 6C2 = 15
E = event of getting the 2 numbers is more than 6 = (4,6),(5,6) = 2
probability = 2/15
Answer is A
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.35, the number of 25 paisa coins is?
A.35
B.31
C.32
D.34
Answer: A.35
Explanation: 5x 6x 2x
50 25 100
250x + 150x + 200x = 3500
600x = 3500
x = 5.83 => 6x = 35
ANSWER:A
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
A.200
B.255
C.265
D.270
Answer: B.255
Explanation: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Question: Which of the following is closest to (6!-5!)/(6!+5!)?
A.0.01
B.0.1
C.0.2
D.0.7
Answer: D.0.7
Explanation: (6!-5!)/(6!+5!)
5! (6-1)/5! (6+1)
5/7 =0.7 (approximately)
D is the answer
Question: Before the regime change, the National Museum regularly displayed only one third of the artifacts in its collection; the other two thirds were kept in storage. The National Museum’s curator estimates that one seventh to one fifth of the artifacts in the museum’s collection disappeared during the regime change. If the National Museum now wishes to display the same number of artifacts as it did before the regime change, and if none of the missing artifacts are recovered, then the museum will keep in storage:
A.4/5 to 6/7 of artifacts in collection
B.9/14 to 13/20
C.3/5 to 5/7
D.7/12 to 11/18
Answer: D.7/12 to 11/18
Explanation: let T be total number of artifacts initially.
stolen (1/7)T to (1/5)T
left (6/7)T to (4/5)T = new total
1/3 for display T/3
storage (6/7)T -T/3 to (4/5)- T/3
11/21 T to 7T/15
so storage to new total = (11T/21) / (6T/7) to (7T/15) / (4T/5)
i.e 11/18 to 7/12
Answer is D.
Question: A CAN FINISH A WORK IN 18 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
A.5
B.5 1/2
C.6
D.8
Answer: C.6
Explanation: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (18*1/3)=6 DAYS.
CORRECT OPTION:C
Question: Of a certain group of 100 people, 40 graduated from High School L, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School L, did not graduate from College Y, and do not live in City Z ?
A. 5
B. 15
C. 35
D. 65
Answer: C. 35
Explanation: 1. l+y+z+ly+yz+lz+lyz+ none=100. Fornoneto be maximum others have to be minimum
2. We know the underlined portions sum to 65 and that is the minimum value of others
3. Maximumnone= 100-65=35=C
Question: There are two shelves A and B.The number of books in shelf A is 50 more than in shelf B..Then 20 books are removed from each shelf..Then the number of books in shelf A is twice the number of books in shelf..what are the number of books in shelf A originally?
A.100
B.120
C.140
D.160
Answer: B.120
Explanation: books in a=50+x and b=x when 20 are removed 50+x-20=2(x-20) therefore x=70 and no of buks in A initially=50+70=120
ANSWER:B
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 40 percent butterfat to obtain milk that is 20 percent butterfat?
A.6
B.12
C.14
D.16
Answer: D.16
Explanation: Equate the fat:
0.1x + 0.4*8 = 0.2(x + 8) --> x = 16.
Answer: D.
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
A.11
B.10
C.17
D.16
Answer: B.10
Explanation: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.Answer: B
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
A.27 7/7 m
B.27 9/7 m
C.27 6/9 m
D.27 7/9 m
Answer: D.27 7/9 m
Explanation: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train
= 50/9 * 5 = 250/9
= 27 7/9 m.
Answer:D
Question: At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
A.62
B.171
C.475
D.513
Answer: C.475
Explanation: Total automobile instalment credit = 57*3 = 171
Total consumer instalment credit =171∗100/36=475;Answer = C. 475
Question: 150 metres long yard, 11 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
A.10
B.15
C.14
D.16
Answer: B.15
Explanation: 11 trees have 10 gaps between them,
Required distance (150/10) = 15
B
Question: Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.
A.15
B.30
C.18
D.12
Answer: B.30
Explanation: Sol. Height of the triangle = [(13) 2- (12) 2](1/2) cm = (25)(1/2) cm = 5 cm.
Its area = (1/2)* Base * Height = ((1/2)*12 * 5) cm^2 = 30 cm^2.
Ans: B
Question: A man sold 20 articles for $50 and gained 20%. How many articles should he sell for $90 to incur a loss 20%?
A.45
B.36
C.40
D.54
Answer: D.54
Explanation: Production cost per article: $50*(100%-20%) / 20 = $2.0
Required production costs for a loss of 20%: $90*(100% + 20%) = $108
Number of articles to be sold for $108 to incur a 20% loss: $108 / $2.0 = 54
Thus, solution D is correct.
Question: When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
A.1
B.2
C.8
D.31
Answer: B.2
Explanation: Total outcome is 2^3 = 8
Favourable cases = H_ H
The second place can be occupied by either H or T
There are 2^1 =2 ways that can be done.
Hence, the correct option is B
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
A.299
B.2676
C.150
D.288
Answer: C.150
Explanation: 1/2 * 15 * 20 = 150
Answer:C
Question: T is 10% S. S is 5% of U. How are T and U related?
A.T is 50% of U
B.T and U are equal
C.T is 500% of U
D.T is 5% of U
Answer: C.T is 500% of U
Explanation: If...
T=.1S
S=.5U
Then...
T/.1=.5U
Multiply both sides by .1
T=5U
T is 500% of U
The answer is C
Question: In a board game, a stack of 42 cards, 8 of which have pictures of fruit, are shuffled and then placed face down. If the first 2 cards selected do not have pictures of fruit, what is the probability that the third card selected will have a picture of fruit?
A.1/8
B.1/5
C.1/4
D.4/21
Answer: B.1/5
Explanation: After 2 cards have been selected, there are 40 cards remaining.
P(third card has a picture of fruit) = 8/40 = 1/5
The answer is B.
Question: The price of 24 apples is equal to that of 28 oranges. The price of 45 apples and 60 oranges together is Rs.1350. The total price of 30 apples and 40 oranges is
A.Rs.920
B.Rs.940
C.Rs.880
D.Rs.900
Answer: D.Rs.900
Explanation: This can be done much easier.
Price of 45 apples and 60 oranges = Rs.1350
Price of 15 apples and 20 oranges = Rs.1350/3 = Rs.450 (∵ Divided LHS and RHS by 15)
Price of 30 apples and 40 oranges = Rs.450 × 2 = Rs.900 (∵ Multiplied LHS and RHS by 2)
ANSWER:D
Question: In how many ways can a cricket eleven be chosen out of a batch
of 15 players.
A.1302
B.1365
C.1205
D.1064
Answer: B.1365
Explanation: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
ANSWER B 1365
Question: 2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill?
A.1/5
B.1/3
C.2/7
D.3/5
Answer: B.1/3
Explanation: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
B
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
A.10
B.76
C.88
D.55
Answer: A.10
Explanation: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.265 m
B.755 m
C.245 m
D.127 m
Answer: C.245 m
Explanation: Speed = (45 * 5/18) m/sec
= (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2
==> 2(130 + X) = 750
==> X
= 245 m.
Answer:C
Question: Find the L.C.M of 40,60,800
A.2600
B.1200
C.800
D.2400
Answer: D.2400
Explanation: 40=2^3*5 60=2^2*3*5 800=2^5*5^2
L.C.M=2^5*3*5^2=2400
Answer=(D)
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
A.7m
B.4m
C.9m
D.2m
Answer: D.2m
Explanation: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6
=2m.
Answer:D
Question: In 2010, Arman’s birthday was on a Thursday. What day of the week was it 68 days after his birthday?
A.Tuesday
B.Friday
C.Saturday
D.Sunday
Answer: A.Tuesday
Explanation: Day of week after 68 days after Arman's birthday = 7*9 + 5
Saturday as the period will have 9 weeks and 5 days .
The 5 days in the end will be Friday - Saturday - Sunday- Monday- Tuesday
Answer A
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400?
A.2000
B.1900
C.2888
D.2777
Answer: B.1900
Explanation: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74
=> 1900
Answer:B
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 86 minutes, then the slower pipe alone will be able to fill the tank in
A.81 min
B.108 min
C.144 min
D.192 min
Answer: C.144 min
Explanation: Solution
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipes will fill it in x/3 minutes.
Therefore, 1/x + 3/x	= 1/36
‹=› 4/x = 1/36
‹=› x= 144 min.
Answer C
Question: A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y 1(3/4) hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z 2(1/3) hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?
A.15 minutes
B.25 minutes
C.1 hour 15 minutes
D.1 hour 40 minutes
Answer: B.25 minutes
Explanation: Trains depart from X at 6/7/8/9 and reach Y at 7:45/8:45/9:45 etc
Trains depart from Y at 9/9:30/10/10:30 etc. This means a minimum wait of 15 mins is required at Y.
They arrive at Z at 11:20/11:50/12:20/12:50. They depart from Z at 8/8:45/9:30/10:15/11/11:45/12:30 and so on. Note that if she arrives at Z at 20 mins past the hour, she will need to wait for at least 10 mins for 12:30/3:30 etc train. If she arrives at 50 mins past the hour, again she needs to wait for at least 10 mins to take the 2 o clock train. So anyway 10 mins at Z is a given.
So minimum she will need to wait for 15+10 = 25 mins.
This works out if she takes 8 o clock train from X, reaches Y at 9:45, takes 10 o clock train from Y and reaches Z at 12:20 and takes 12:30 train from Z.
Answer (B)
Question: What is the greatest positive integer x such that 3^x is a factor of 9^8?
A.5
B.9
C.16
D.20
Answer: C.16
Explanation: What is the greatest positive integer x such that 3^x is a factor of 9^8?
9^8 = (3^2)^8 = 3^16
C. 16
Question: Two pipes C and D can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
A.A)1/8
B.B)1/3
C.C)1/9
D.D)1/2
Answer: B.B)1/3
Explanation: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer:B
Question: In the manufacture of a certain product, 6 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
A.0.125%
B.0.24%
C.0.8%
D.1.25%
Answer: B.0.24%
Explanation: Percent of defective produced = 6%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(6/100)*100%
= (24/10000)*100%
= (24/100)%
= .24 %
Answer B
Question: Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 36, what is the measure of side XY?
A.4
B.4√2
C.12
D.8√2
Answer: C.12
Explanation: ans C ..12..
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=36 or yz=3*\sqrt{2}..
therefore hyp=xy=12