mathewhe/aqua_rat huggingface dataset:
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
(A) 2/113
(B) 2/115
(C) 1/108
(D) 1/119
(E) 2/117
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: (C) 1/108
Question: If 20,030 + x is a multiple of 3, which of the following could be the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: Sum of the digits of 20,030 is 2+0+0+3+0 = 5
Now 5 is not a multiple of 3, the next multiple of 3 close to 5 is 9, which is 4 added to 5.
So the least number to be added to 20,030 is 4
D
Answer: (D) 4
Question: Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 4 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
(A) 3 9/17
(B) 6
(C) 7
(D) 7 1/5
(E) 8 4/7
Rationale: rate of machine x = 1000/12
(1000/12 + y)4=1000
y=350/3
500/3 * t = 1000
t=6
B.
Answer: (B) 6
Question: Two trains travelling in the same direction at 70 and 35 kmph completely pass off another in 144 sec. If the length of the first train is 185 m, what is the length of the second train?
(A) 1387 m
(B) 1400 m
(C) 1215 m
(D) 1512 m
(E) 185 m
Rationale: RS =70 â€“ 35 = 35* 5/18 mps
T = 144 sec
D =35*5/18 * 144= 1400 m
185
--------
1215 m
Answer: C
Answer: (C) 1215 m
Question: Sixteen years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
(A) A)35
(B) B)34
(C) C)45
(D) D)25
(E) E)56
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Sixteen years ago, P was half of Q in age
=> 2(3x – 16) = (4x – 16)
=> 6x – 32 = 4x – 16
=> 2x = 16
=> x = 8
7x =7*8 = 56
Answer: Option E
Answer: (E) E)56
Question: If you throw two dice at a same time.
Can you find the probability of getting sum as 10 of the two numbers shown ?
(A) 1/16
(B) 2/14
(C) 1/12
(D) 1/19
(E) 1/17
Rationale: C
1/12
All possible cases can be 36 (6*6)
Case we need : [(4,6), (5,5), (6,4)] = 3
probability => 3/36 = 1/12
Answer: (C) 1/12
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
(A) 6 hrs 21 min
(B) 6 hrs 71 min
(C) 6 hrs 28 min
(D) 6 hrs 21 min
(E) 2 hrs 21 min
Rationale: Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer: A
Answer: (A) 6 hrs 21 min
Question: Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 40% of the previous term. What is the value range of the five numbers?
(A) 9,375
(B) 9,744
(C) 9,975
(D) 9,984
(E) 10,736
Rationale: 1st number= 10,000
2nd number = 40% of 10,000= 4000
3rd number= 40% of 4000= 1600
4th number = 40% of 1600= 640
5th number= 40% of 640= 256
Range = 10,000-256= 9744
B is the answer
Answer: (B) 9,744
Question: Josh spends a total of $6.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?
(A) 99
(B) 100
(C) 121
(D) 109
(E) 140
Rationale: Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=6.5 ---> x+10y=130 ...(1)
Also, x+y=N ...(2)
Solving 1 and 2 , we get, N = 130-9y ---> only value satisfied is when y = 1---> N = 130-9=121. C is the correct answer. Other options are not equal to multiples of 9 removed from 130.
Answer: (C) 121
Question: hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
(A) 720
(B) 900
(C) 1200
(D) 1800
(E) 2100
Rationale: 2(15 + 12) x h = 2(15 x 12)
h =	180/27m =	20/3	m.
Volume = 15 x 12 x	20/3	m3
Answer: Option C
Answer: (C) 1200
Question: When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction?
(A) 5/4
(B) 4/7
(C) 5/6
(D) 6/7
(E) None of these
Rationale: Let the fraction be x/y.
When the numerator decreased by 25% and the denominator decreased by 20%.
(x * 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5
ANSWER:E
Answer: (E) None of these
Question: What is the probability that two siblings, ages 6 and 8, will have the same birthday, assuming neither was born in a leap year?
(A) 1/133225
(B) 1/365
(C) 1/48
(D) 1/14
(E) 1/2
Rationale: Since we have to account for the FULL YEAR though, we would need to consider all 365 options. You don't really need to write them all out though, since you know that each is the same product. This gives us...
(365)(1/365)(1/365)
The first two parentheses 'cancel out', leaving us with....
1/365
Final Answer:B
Answer: (B) 1/365
Question: When 40 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
(A) 40
(B) 44
(C) 96
(D) 98
(E) 95
Rationale: Explanation:
Let the number be x. Then,
x - 40 = 7x/12 => x - 7x/12 = 40
5x/12 = 40 => x = 96
Answer: Option C
Answer: (C) 96
Question: The reflex angle between the hands of a clock at 10:25 is?
(A) 180°
(B) 192 1⁄2°
(C) 195°
(D) 197 1⁄2°
(E) None of these
Rationale: Angle traced by hour hand in 125⁄12 hrs.
(360/12×125/12)∘=312 1/2∘
Angle traced by minute hand in 25 min.
= (360/12×25)∘=150∘
∴ Reflex angle = 360 - (312 1/2−150)∘=312 1/2∘
Answer D
Answer: (D) 197 1⁄2°
Question: In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 45, what is the greatest possible value of B x A?
(A) 0
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: I also was confused when I was looking forabove number:D
As far as I understood, 45 is a factor of AB. In other words, the values of B (units digits can be 5 or 0. Better to have option for 5 in this case to havebigger result). Now let's try 45x1 (A=4, B=5 respectively we have =20). This is the greatest possible value of B x A.
IMO E.
Answer: (E) 20
Question: 2,600 has how many positive divisors?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 48
Rationale: By factorization, you can write 2600 as 2600=2^3*5^2*13^1.
Number of factors = (3+1)(2+1)(1+1)=24
ANSWER:E
Answer: (E) 48
Question: if x^2+4y^2=4xy,then x:y=?
(A) 2:1
(B) 1:2
(C) 1:1
(D) 1:4
(E) none of these
Rationale: x^2+4y^2-4xy=0
(x-2y)^2=0, x-2y=0,x/y=2
x:y=2:1
answer A
Answer: (A) 2:1
Question: An Italian sausage is 8 inches long. How many pieces of sausage can be cut from the 8-inch piece of sausage if each piece is to be 2/3 of an inch ?
(A) 12
(B) 32
(C) 22
(D) 15
(E) 20
Rationale: Number of pieces=Italian sausage÷2/3 of an inch
=8 ÷ 2/3
=8/1 ÷ 2/3
=8/1*3/2 = 24/2
=12.
Answer is A.
Answer: (A) 12
Question: Two persons start running simultaneously around a circular track of length 250 m from the same point at speeds of 20 kmph and 40 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
(A) 144
(B) 15
(C) 18
(D) 32
(E) 38
Rationale: Time taken to meet the first time = length of track/relative speed
= 250/ (20 +40) (5/18)
= 250/60 *(18/5) = 15 sec.
Answer : B
Answer: (B) 15
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 625 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140
(B) 99
(C) 100
(D) 72
(E) 12
Rationale: Given that the area of the square = 625 sq.units
=> Side of square = √625 = 25 units
The radius of the circle = side of the square = 25 units Length of the rectangle = 2/5 * 25 = 10 units
Given that breadth = 10 units
Area of the rectangle = lb = 10 * 10 = 100 sq.units
Answer: C
Answer: (C) 100
Question: Anintegratedteam consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 5 members and the design team has 4 members, how manyintegratedteam formations are possible?
(A)  36
(B)  60
(C)  76
(D)  90
(E)  112
Rationale: 2 out of 5 times 2 out of 4 => 5*4/2*1 * 4*3/2*1 = 60
B
Answer: (B)  60
Question: If Jan 1, 2006 was a Saturday, What was the day of the week Jan 1, 2010?
(A) Friday
(B) Thursday
(C) Tuesday
(D) Saturday
(E) None of these
Rationale: Explanation :
Given that Jan 1 2006 was a Saturday
Number of odd days in the period 2006-2009
= 3 normal years + 1 leap year
= 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)
Hence Jan 1 2010 = (Saturday + 5 odd days) = Thursday.. Answer : Option B
Answer: (B) Thursday
Question: A school has 30% students from Maharashtra .Out of these 20% are Bombey students. Find the total percentage of Bombay?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: If total no of students is 100.
No of students from Maharashtra = 30
No of students from Bombay = 30*20/100 = 6
so 6% students are from Bombay
ANSWER:D
Answer: (D) 6%
Question: A dealer sells his goods at cost price 950gm weight for 1kg his gain percentage is
(A) 5 4/95% Loss
(B) 5 4/95% Loss
(C) 5 5/19% Loss
(D) 5 5/19% Gain
(E) None of these
Rationale: Explanation:
Cost price ---> 950
Selling price --->1000
= ( 1000 ~ 950 )/950 * 100 ==> 50/950 * 100 = 5 5/19% Gain
Answer: Option D
Answer: (D) 5 5/19% Gain
Question: In a two-digit number, the digit in the unit's place is more than twice the digit in ten's place by 1. If the digits in the unit's place and the ten's place are interchanged,difference between the newly formed number and the oiginal number is less than the original number by 1. What is the original number ?
(A) 36
(B) 38
(C) 48
(D) 47
(E) 37
Rationale: Let the ten's digit be x. Then, unit's digit = 2X + 1.
[10X + (2X + 1)] - [{10 (2X + 1) + X} - {10X + (2X + 1)}] = 1
<=> (12X + 1) - (9X + 9) = 1 <=> 3x = 9, X = 3.
So, ten's digit = 3 and unit's digit = 7. Hence, original number = 37.
ANSWER:E
Answer: (E) 37
Question: The sum of ages of 5 girls born at the intervals of 3 years each is 50 years. What is the age of the youngest girl?
(A) 4 years
(B) 5 years
(C) 6 years
(D) 8 years
(E) 9 years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
A)
Answer: (A) 4 years
Question: A group of workers had agreed on a very strange payment schedule. Each of
them would get $100 for every day that they had worked, but for every day they
did not work will have to return $25. After 30 days they realised they did not
earn any money. How many days the workers did not work?
(A) 15
(B) 24
(C) 30
(D) 20
(E) 10
Rationale: The workers earn 4 times more than they have to return
per day for not working. So the number of days they did not work is
4 times the number of days they worked. That means 24 days of not
working in 30 days.
correct answer B
Answer: (B) 24
Question: How many multiples of 2 are less than 2400, and also multiples of 8?
(A) 104
(B) 208
(C) 300
(D) 832
(E) 833
Rationale: The LCM of 2 and 8 is 8. Divide 2400/8 = 300.xxx. So C is your answer.
Answer: (C) 300
Question: How many positive integers less than 22 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
(A) 17
(B) 13
(C) 12
(D) 11
(E) 10
Rationale: The number = 2a + 3b < 20
When a = 1, b = 1, 2, 3, 4, 5, 6 -> 2a = 2; 3b = 3, 6, 9, 12, 15, 18 -> the number = 5, 8, 11, 14, 17, 20 --> 6 numbers
when a =2, b = 1,2,3,4,5, 6 -> ....--> 6 numbers
when a =3, b = 1,2,3,4, 5 --> ....--> 5 numbers
Total number is already 17. Look at the answer there is no number greater than 17 --> we dont need to try any more
Answer must be A
Answer: (A) 17
Question: What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
(A) Rs.64.17
(B) Rs.64.22
(C) Rs.64.12
(D) Rs.64.10
(E) Rs.64.16
Rationale: S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000]
= Rs. 464.10 Difference = (464.10 - 400)
= Rs. 64.10
Answer:D
Answer: (D) Rs.64.10
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the starting word is W and 3rd word is O?
(A) A)2!
(B) B)4!
(C) C)1!
(D) D)5!
(E) E)6!
Rationale: required word is - W _ O _ _ _ _
the remaining 5 places can be filled by 5!
D
Answer: (D) D)5!
Question: There are 9 person among whom 2 are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
(A) 4!*2!
(B) 7!*2!
(C) 6!*2!
(D) 2!*1!
(E) 5!*1!
Rationale: Total number of ways = 6!*2!.
C
Answer: (C) 6!*2!
Question: The salaries of A, B and C are of ratio 2:3:5. If the increments of 15%, 10% and 20% are done to their respective salaries, then find the new ratio of their salaries.
(A) 20:33:60
(B) 21:33:60
(C) 22:33:60
(D) 23:33:60
(E) 24:33:60
Rationale: Explanation:
Let A salary be 2k
B salary be 3k and C salary be 5k
A's new salary = 115/100∗2k
=2310k
B's new salary = 110/100∗3k
=3310k
C's new salary = 120/100∗5k
=6k
New ratio = 23k/10:33k/10:6k=23:33:60
ANSWER IS D
Answer: (D) 23:33:60
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings?
(A) 3600
(B) 3629
(C) 3619
(D) 3611
(E) 3612
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 18000 => x = 3600
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 3600.
Answer:A
Answer: (A) 3600
Question: A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job ?
(A) 19
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Ratio of time taken by A & B = 160:100 = 8:5 Suppose B alone takes x days to do the job. Then, 8:5::12:x = > 8x = 5*12 = > x = 15 days.
Answer: (B) 15
Question: If it takes a machine 2⁄5 minute to produce one item, how many items will it produce in 2 hours?
(A) 1⁄3
(B) 4⁄3
(C) 80
(D) 120
(E) 300
Rationale: 1 item takes 2/5 min so it takes 120 min to produce x
2x/5=120 the x=300
Answer:E
Answer: (E) 300
Question: The number 150 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A)  17
(B)  18
(C)  15
(D)  14
(E)  13
Rationale: 10^2 + 7^2 + 1^2 = 150 = = => sum of these 3 integers = 10 + 7 + 1 = 18
B
Answer: (B)  18
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 ?
(A) -1
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 = x2(x2 - 4x + 4)
= x2(x - 2)2
= (1 + √2)2(1 + √2 - 2)2
=(√2 + 1)2 (√2 - 1)2
=[(√2)2 - (1)2]2
=(2 - 1)2 =1
Correct Option: C
Answer: (C) 1
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 2
(B) 6
(C) 8
(D) 3
(E) 7
Rationale: Explanation:
9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
Answer:D
Answer: (D) 3
Question: Alex deposited x dollars into a new account that earned 6 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
(A) w/(1+1.08)
(B) w/(1.08+1.16)
(C) w/(1.16+1.24)
(D) w/(1.06+1.06^2)
(E) w/(1.08^2+1.08^2)
Rationale: Account at the end of the first year would be 1.06x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.06x+x) dollars. Account at the end of the second year would be (1.06x+x)*1.06=w --> x(1.06^2+1.06)=w --> x=w/(1.06+1.06^2).
Answer: D.
Answer: (D) w/(1.06+1.06^2)
Question: A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 400 bolts?
(A)  36
(B)  72
(C)  96
(D)  144
(E)  180
Rationale: Old Machine
100 bolts in 60 mins
so,
5/3 bolts in 1 min
New Machine
150 bolts in 60 mins
so,
5/2 bolts in 1 min
together,
5/3 + 5/2 =
25/6 bolts in 1 min
so, for 400 bolts
400 * 6 / 25 = 96 mins
Ans C
Answer: (C)  96
Question: If T = 5/9 * (K - 32), and if T = 20, then what is the value of K?
(A) 68
(B) 70
(C) 72
(D) 74
(E) 76
Rationale: K-32=9T/5
K=9T/5 + 32
K=9(20)/5 + 32 = 68
The answer is A.
Answer: (A) 68
Question: If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/16, then the reciprocal of n must be
(A) Less than -4
(B) Between -1 and -1/4
(C) Between -1/4 and 0
(D) Between 0 and 1/4
(E) Greater than 4
Rationale: n^2 < 1/16
abs(n) < 1/4
Since n<0, then 0 > n > -1/4
1/n < -4
The answer is A.
Answer: (A) Less than -4
Question: A certain company employs 8 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?
(A) 8
(B) 24
(C) 58
(D) 224
(E) 210
Rationale: Number of ways to select 3 senior officers from 8 of them = 8C3 = 56 ways
Next we can determine the number of ways to select 1 junior officer.
number of ways to select 1 junior officer from 4 of them = 4C1 = 4 ways
Thus the number of ways to select 3 senior officers and 1 junior officer is 56 x 4 = 224 ways.
Answer: D
Answer: (D) 224
Question: Find the middle 1 when The sum of three consecutive even numbers is 36?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: (B) 12
Question: A machine, working at a constant rate, manufactures 40 pencils in 30 minutes. How many pencils does it make in 1 hr 30 min?
(A) 120
(B) 125
(C) 110
(D) 115
(E) 121
Rationale: Change 1 hr 30 min to 90 min. For this, we need to set up a simple proportion of pensils per time
40/30 = S/90
The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. Instead, cancel before you multiply. For what we can and can’t cancel in a proportion, seethis post. We can cancel the factor of 10 in the 40 and 30.
4/3 = S/90
We can cancel the common factor of 3 in the two denominators.
4/1 = S/30.
Now that the fraction is entirely simplified, we can cross-multiply.
S = 4*30 = 120
The machine would be 120 pencils in 1 hr 30 min.
Answer: A
Answer: (A) 120
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
(A) 229
(B) 277
(C) 378
(D) 480
(E) 287
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
Answer:D
Answer: (D) 480
Question: Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?
(A) 5 hrs
(B) 8 hrs
(C) 9 hrs
(D) 36 hrs
(E) None
Rationale: Sol.
Part filled by ( A + B ) in 1 hour = [1/5 + 1/20] = 1/4.
So, A and B together can fill the tank in 4 hours.
Work done by the leak in 1 hour = (1/4 - 2/9) = 1/36.
∴ Leak will empty the tank in 36 hrs.
Answer D
Answer: (D) 36 hrs
Question: What number should replace the question mark?
105, 87, 70, 52, ?
(A) 49
(B) 35
(C) 70
(D) 55
(E) 83
Rationale: B
35
The sequence progresses -18, -17, -18, -17.
Answer: (B) 35
Question: If a van moving at the speed of x km/hr travels a distance of y km, which of the following cannot be equal to the distance traveled?
(A) x-y km
(B) y-x km
(C) (x-y)/2 km
(D) y/x km
(E) x/2 km
Rationale: This question can be solved by TESTing VALUES, but there's a particular pattern that you have to recognize to make the workeasy.
We're not really limited by anything in this question, so X and Y can be anything. Under normal circumstances, I won't TEST the number 1 in PS questions (as it often leads to duplicate answers), but here it's a great option (since we're looking to eliminate 4 answers, multiple TESTs are going to be likely anyway).
We're given information on speed (X km/hour) and distance (Y km). We're asked which of the 5 answer choices CANNOT be the distance traveled.
IF....
X = 2 and Y = 1
Answers A (2-1 = 1) and E (2/2 = 1) are POSSIBLE. Eliminate A and E.
IF....
X = 3 and Y = 1
Answer C ([3-1]/2 = 1) is POSSIBLE. Eliminate C.
IF....
X = 1 and Y = 1
Answer D (1/1 = 1) is POSSIBLE. Eliminate D.
Final Answer:
B
Answer: (B) y-x km
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 36 kmph. For how many minutes does the bus stop per hour?
(A) 20 min
(B) 8 min
(C) 9 min
(D) 10 min
(E) 11 min
Rationale: Due to stoppages, it covers 18 km less.
Time taken to cover 18 km =(18/54)x60 = 20 min
answer : A
Answer: (A) 20 min
Question: For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 960, what is the maximum possible sum of the length of x and the length of y?
(A) 10
(B) 16
(C) 12
(D) 14
(E) 19
Rationale: we know that : x > 1, y > 1, and x + 3y < 960,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 =1024 (it exceeds 960, so, x can't be 2^10)
so, max value that X can take is 2^9 , for which has length of integer is 9.
now, since x =512 ,x+3y<960
so, 3y<448
==> y<448/3
so, y can take any value which is less than 448/3. and to get the maximum no of factors of smallest integer, we can say y=2^7
for 2^7 has length of integer is 7.
SO, combined together : 9+7 = 16.
B
Answer: (B) 16
Question: Mike needs 30% to pass. If he scored 212 marks and falls short by 19 marks, what was the maximum marks he could have got?
(A) 543
(B) 677
(C) 770
(D) 867
(E) 832
Rationale: If Mike had scored 19 marks more, he could have scored 30%
Therefore, Mike required 212 + 19 = 231 marks
Let the maximum marks be m.
Then 30 % of m = 231
(30/100) × m = 231
m = (231 × 100)/30
m = 23100/30
m = 770
Answer:C
Answer: (C) 770
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 4
(B) 29
(C) 8
(D) 2
(E) 1
Rationale: 1250 = D(100/4)2
D = 2.Answer: B
Answer: (B) 29
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes S of the competition are possible?
(A) 18
(B) 20
(C) 54
(D) 84
(E) 120
Rationale: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total S=84 outcomes
D
Answer: (D) 84