mathewhe/aqua_rat huggingface dataset:
Question: Set Q includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: First, reach to the point of getting the equation Q: x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D
Answer: (D) 3
Question: In how many ways a committee, Consisting of 4 men and 5 women can be formed from 8 men and 10 women?
(A) 2660
(B) 3360
(C) 11760
(D) 17640
(E) 17200
Rationale: To choose Required number of ways to form a committee:
Select 4 men out of 8 men and 5 women out of 10 women.
That is 8C4 * 10C5.
8C4=8!/4!*4!=70
10C5=10!/5!*5!=252
The Required number of ways=70*252=17640
D
Answer: (D) 17640
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour
of the stream. The ratio of the speed of the boat in still water and stream is
(A) 3:1
(B) 1:3
(C) 2:4
(D) 4:2
(E) None of these
Rationale: Explanation:
Let speed downstream = x kmph
Then Speed upstream = 2x kmph
So ratio will be,
(2x+x)/2 : (2x-x)/2
=> 3x/2 : x/2 => 3:1
Answer: A
Answer: (A) 3:1
Question: 24 people can write 48 book in 6 days working 8 hour a day.then in how many day 192 can be written by 50 people?
(A) 223/26
(B) 288/27
(C) 309/22
(D) 288/26
(E) 288/25
Rationale: work per day epr hour per person= 48/(6*8*24) // eq-1
people= 50; let suppose day=p; per day work for 8 hours
acc. to condition
work per day epr hour per person= 192/(p*8*50) // eq-2
eq-1==eq-2;
p= 288/25
ANSWER:E
Answer: (E) 288/25
Question: Eight kilograms of rice costing Rs. 16 per kg is mixed with four kilograms of rice costing Rs. 22 per kg. What is the average price of the mixture?
(A) 20
(B) 18
(C) 16
(D) 19
(E) 17
Rationale: P1 = Rs.16 per kg, p2 = Rs. 22 per kg, q1 = 8 kg, q2 = 4 kg
Now , p = (p1q1+p2q2)/(q1+q2)
Average price of the mixture = 8*16+4*22/12
= 128+88/12
= 216 /12 = 18
ANSWER:B
Answer: (B) 18
Question: If x and y are nonzero integers and 450x = 120y then which of the following must be an integer?
I. xy/60
II. 15x/4y
III. 4x/15y
(A) I only
(B) II only
(C) I and III
(D) I and II
(E) I, II, and III
Rationale: 450x=120y reduce by 30 --> 15x=4y --> x is a multiple of 4 (y=15x/4 so x must be multiple of 4 for y to be an integer) and y is a multiple of 15 (x=4y/15y must be multiple of 15 for x to be an integer).
I. xy/60 --> always true, as xy will be multiple of 4*15=60;
II. 15x/4y --> as 4y=15x then 15x/4y=15x/15x=1=integer so this option is also always true;
III. 4x/15y --> as x=4y/15 then 4x/15y=16/225≠integer, so this option is never true.
Answer: I and II (only).
ANSWER:D
Answer: (D) I and II
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 33,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
(A) Rs. 4000
(B) Rs. 4008
(C) Rs. 4002
(D) Rs. 4003
(E) Rs. 4001
Rationale: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 33,000 = Rs. 11,000
Salary of A = Rs. (15000 – 11000) = Rs. 4000
ANSWER: A
Answer: (A) Rs. 4000
Question: How many even integers from 1 to 50 (both inclusive) have even number of factors?
(A) 3
(B) 14
(C) 5
(D) 6
(E) 7
Rationale: Integers having even number of factors will be perfect squares. even numbers will have even perfect squares. Thus, the possible values for the perfect squares are :
4,16,36 and the corresponding integers are 2,4,6 (more than 2). Thus A is the correct answer .
Answer: (A) 3
Question: Two cars start at the same time from opposite ends of a highway that is 60 miles long. One car is riding at 13 mph and the second car is riding at 17 mph. How long after they begin will they meet?
(A) 0.75
(B) 1
(C) 1.25
(D) 1.5
(E) 2.0
Rationale: As cars are moving in opposite directions their speeds will be added. So their relative speeds: 17+13 = 30 mph
Total distance to be covered = 60 miles.
Time taken would be: 60 miles/30 mph = 2.0 hours
E is the answer.
Answer: (E) 2.0
Question: How many Q ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting next to one of the aisles?
(A) 120
(B) 240
(C) 360
(D) 540
(E) 720
Rationale: Jason can select his seat in 2 Ways (two aisles)
His 1st of 4 friends have 5 seats to select =>
His 2nd of remaining 3 friends will have 4 seat to chose from...and so on
Total ways Q=> 2*5*4*3*2*1 = 240.B
Answer: (B) 240
Question: Solve for x and check: - 200x = 1600
(A) 2000
(B) 2573
(C) 1600
(D) 2950
(E) None of these
Rationale: Solution : Dividing each side by -200, we obtain
(-200x/-200)=(1600/-200)
Therefore : x=-8
Check :
-200x=1600
(-200*-8)=1600
1600=1600
ANSWER : C
Answer: (C) 1600
Question: Albert invested amount of 16000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit
(A) Rs. 17640
(B) Rs. 8620
(C) Rs. 8730
(D) Rs. 8820
(E) None of these
Rationale: Explanation:
=>(16000×(1+5/100)2)
=>16000×21/20×21/20
=>17640
Option A
Answer: (A) Rs. 17640
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. y + z is odd
II. (x+z)/y is an integer
III. xz is not an integer
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: consecutive odds are:
2x+1, 2x+3, 2x+5
I. 2x+3+2x+5=4x+8=4(x+1), so divisible by 2 and even - NOT TRUE
II. 2x+1+2x+5=4x+6/2x+3=2(2x+3)/2x+3=2, so integer - TRUE
III. (2x+1)*(2x+5)=4x^2+10x+2x+5=4x^2+12x+5=(2x(x+6)+5)/2 is not integer, so TRUE
ANSWER: D
Answer: (D) II and III only
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 8 sec
(B) 6 sec
(C) 3 sec
(D) 2 sec
(E) 9 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man
=[110 * 3/55] sec =6 sec
Answer: B
Answer: (B) 6 sec
Question: Set A: {1, 3, 4, 6, 9, 12, 15,18}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?
(A) 3/14
(B) 2/7
(C) 5/14
(D) 5/7
(E) 11/14
Rationale: using probability you can solve: 6/8*5/7*4/6=5/14
Ans C
Answer: (C) 5/14
Question: A train running at 25 km/hr takes 30 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
(A) a) 200/3m175/3m
(B) b) 60m130m
(C) c) 50m45m
(D) d) 100/3 m200/3
(E) e) none of these
Rationale: Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m
lets solve it
To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.
The man covered the distance during 12sec is 5*5/30*12=10m so the train covered a distance in 12 sec= 25*5/30*12=50
so the length of the train(Lt) is 10+50=60m
Now crossing the platform means length of train+length of platform(Lt+p)= 30*25*5/30=125m Now the length of platform (Lp) is= 125-60=65m
So answer is 60m and 65m Must beBeven though its mentioned 60m and 130m thinking so typo mistake...........
Answer: (B) b) 60m130m
Question: The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
(A) 8 years
(B) 9 years
(C) 2 years
(D) 6 years
(E) 3 years
Rationale: 100 ---- 300 --- 3
900 --- 3
----
6 years
Answer: D
Answer: (D) 6 years
Question: If (m-8) is a factor of m^2-pm-24, then p=
(A) 3
(B) 5
(C) 6
(D) 11
(E) 16
Rationale: (m-8)(m-a)=m^2-pm-24
A=-3
p=8+a=5=B
Answer: (B) 5
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12 m
(B) 111.18 m
(C) 111.82 m
(D) 121.12 m
(E) 111.11m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer: A
Answer: (A) 111.12 m
Question: The number of people who moved to live in a small town per 200 persons is 10.5. if the number of person who leave the town per 200 persons is 5.5 how long will it take for the population of 1000 people to double.
(A) 25
(B) 30
(C) 40
(D) 10
(E) 2
Rationale: Annual increase is (200 + 10.5 - 5.5)*5=1025
Hence every year there is an increase of 25
for the population to double we needs additional 1000
therefore 1000/25=40
correct option is C)
Answer: (C) 40
Question: If the number 892,132,26x is divisible by 11, what must be the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11
Given number: 892,132,24x
Sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x (i)
Sum of digits at even places = 9 + 1 + 2 + 6 = 18(ii)
(i) - (ii) = 15 + x - 18 = x - 3
Hence x should be = 3 to make this a multiple of 11 (0) Option C
Answer: (C) 3
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.50 per glass on the first day, what was the price per glass on the second day?
(A) $0.15
(B) $0.20
(C) $0.33
(D) $0.40
(E) $0.45
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.5=3*x --> x=$0.33.
Answer: C.
Answer: (C) $0.33
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Rationale: Given that, A + B =12+ B + C
⇒ A - C =12
Therefore, C is younger than A by 12 years
Answer is C.
Answer: (C) 12
Question: There are two inlets and one outlet to a cistern. One of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 8 hours
Rationale: The combined inflow rate of the two inlets is 1/4 + 1/8 = 3/8 cistern/hour. Thus, working together, it takes 8/3 hours (time is reciprocal of rate) to fill the cistern.
From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) =2*3/8 = 3/4 th of the cistern .
Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour.
Letting x to be the rate of the outlet, we would have: 3/8 - x = 1/4 --> x = 1/8 cistern/hour, which means that it takes 8 hours the outlet working alone to empty the cistern.
Answer: E.
Answer: (E) 8 hours
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)
(A) 30 years
(B) 76 years
(C) 20 years
(D) 15 years
(E) 19 years
Rationale: Present total age of the members
= 26(5) = 130 years.
Present age of the youngest member
= 10 years
Present total age of the remaining four members
= 130 -10 = 120 years
Their average age at the time of the birth of the youngest member
= [120 - (4 * 10)] / 4 = 30 - 10 = 20 years.
Answer: C
Answer: (C) 20 years
Question: The Lucknow-Indore Express without its rake can go 24 km an hour, and the speed is diminished by a quantity that varies as the square root of the number of wagon attached. If it is known that with four wagons its speed is 20 km/h, the greatest number of wagons with which the engine can just move is
(A) 144
(B) 140
(C) 143
(D) 124
(E) 142
Rationale: Solution: Speed = 24- k√n;
Putting the value, n = 4;
we get, k = 2.
Now the equation (as k = 2) become, S = 24-2√n;
Thus, it means when n = 144, speed will be zero. Hence, train can just move when 143 wagons are attached.
Answer: Option C
Answer: (C) 143
Question: A circular dashboard of radius 1.0 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?
(A) 1.0
(B) 0.75
(C) 0.25
(D) 0.5
(E) 1.25
Rationale: .25
because the area of the circle with half radius 'r/2' is 1/4th of the area of circle with radius r
ANSWER:C
Answer: (C) 0.25
Question: A high school has 360 students 1/2 attend the arithmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 3/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.
(A) 45
(B) 40
(C) 35
(D) 50
(E) 55
Rationale: Basically, this question is asking you to figure out how many students are being double-counted.
A-Club has 180 members (1/2 of 360)
B-Club has 225 members (5/8 of 360)
C-Club has 270 members (3/4 of 360)
We can create an equation to solve this:
180+225+270 = n + x + 2y
where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.
The question provides y for us (135).
180+225+270 = 360 + x + 270
x = 405-360 =45
A
Answer: (A) 45
Question: Calculate how long it will take a swimmer to swim a distance of 10km against the current of a river which flows at 3km/hr, given that he can swim in still water at 5km/h
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: swim in still water at = 5
speed of river= 3
US = 5 - 3= 2
Distance = 10
T = 10/2 = 5
Answer: C
Answer: (C) 5
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 50% ?
(A)  0
(B)  1.46
(C)  2
(D) 1.34
(E)  4
Rationale: Let x be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = x/10
Probability that the second contestant selected is also a male = x-1/9
Total probability = x(x-1)/ 90 < 1/50 (this probability is less than 50%)
Solving for x we get, x(x-1)< 9/5. This implies that the maximum value of x can be 1.34.
Answer D!
Answer: (D) 1.34
Question: A semicircle has a radius of 20. What is the approximate perimeter of the semicircle?
(A) 50
(B) 25
(C) 86
(D) 75
(E) 102
Rationale: circumference of a circle =2pi*r
perimeter of a semicircle = pi*r + 2r
aprox perimiter = 3.14*20 + 2*20 = 102.8 approximately 102
answer E
Answer: (E) 102
Question: The average of 10 consecutive integers is 16. Then, 9 is deducted from the first consecutive number, 8 is deducted from the second, 7 is deducted form the third, and so on until the last number which remains unchanged. What is the new average?
(A) 10.5
(B) 11
(C) 11.5
(D) 12
(E) 12.5
Rationale: The total subtracted is (9+8+...+1) = (9*10) / 2 = 45
On average, each number will be reduced by 45/10 = 4.5
Therefore, the overall average will be reduced by 4.5
The answer is C.
Answer: (C) 11.5
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1320 cm is?
(A) A)15
(B) B)10
(C) C)14
(D) D)12
(E) E)11
Rationale: 2 * 22/7 * 14 * x = 1320 => x = 15
ANSWER:A
Answer: (A) A)15
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed amount A, B and C
(A) 3:7:5
(B) 6:10:5
(C) 6:10:7
(D) 6:7:5
(E) None of these
Rationale: Explanation:
Let initial investment of A is 3x and B is 5x, then C investment is also 5x, but most important to note in this question is the time duration of investment
Like, A invested for 12 months, B invested for 12 months and C invested for 6 months.
A:B:C =(3x*12):(5x*12):(5x*6)
= 36:60:30
= 6:10:5
Option B
Answer: (B) 6:10:5
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 12 km
(B) 20 km
(C) 24 km
(D) 4 km
(E) None of these
Rationale: Explanation:
Distance = Relative Speed * Time
= (2 + 3) * 4 = 20 km
[ They are travelling in the opposite direction, relative speed = sum of the speeds].
ANSWER IS B
Answer: (B) 20 km
Question: A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
(A) 81 km/hr
(B) 80 km/hr
(C) 90 km/hr
(D) 99 km/hr
(E) 45 km/hr
Rationale: speed x and y
x/8.4 = (y-4.5)*5/18...1)
x/8.5=(y-5.4)*5/18----2)
dividing = y-4.5/y-5.4
8.4y-8.4*4.5=8.5y-8.5*5.4
=>y=81
ANSWER A
Answer: (A) 81 km/hr
Question: in a scheme, a pack of three soaps with mrp rs45 is available for rs42. if it still gives a profit of 5% to the shopkeeper,then the cost price of the pack is:
(A) rs40
(B) rs37
(C) rs41
(D) rs35
(E) rs45
Rationale: Price of the pack = 42
x*105/100=42 . 105=100(Price of soap pack) + 5(profit)
x=42*100/105=2*100/5=40
ANSWER:A
Answer: (A) rs40
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 11. What could be the ratio of Cats to dogs in the pet store?
(A) 1:3
(B) 1:4
(C) 1:5
(D) 44:55
(E) 4:6
Rationale: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.
We are told that ax - bx = 11 --> x(a - b) = 11. Since 11 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*11.
The above implies that either x = 1 and (a - b) = 11 or x = 11 and (a - b) = 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 11.
For the original question only option which fits is E, 4:5. Cats = 11*4 = 44 and dogs = 11*5 = 55.
Answer: D.
Answer: (D) 44:55
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 7 minutes, then the area of the park (in sq. m) is
(A) 153200
(B) 153400
(C) 153600
(D) 154000
(E) 117600
Rationale: Perimeter = Distance covered in 7 min. = 12000 x 7 m = 1400 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1400 or x = 140.
Length = 420 m and Breadth = 280 m.
Area = (420 x 280) m2 = 117600 m2.
E
Answer: (E) 117600
Question: If 2/z = 2/(z + 1) + 2/(z + 49) which of these integers could be the value of z?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 7
Rationale: Solving for z algebraically in this problem would not be easy. Instead, we can follow the hint in the question (“which of these integers…”) and test each answer choice:
A. 2/0 = 2/1 +2/49 INCORRECT (Division by zero)
B. 2/1 = 2/2 +2/50 INCORRECT
C. 2/2 = 2/3 +2/51 INCORRECT
D. 2/3 = 2/4 +2/54 INCORRECT
E. 2/4 = 2/5 +2/56 CORRECT
The correct answer is E, because it contains the only value that makes the equation work. Notice how quickly this strategy worked in this case
Answer: (E) 7
Question: A man can row upstream at 4km/hr and down stream at 10km/hr find mans rate in still water ?
(A) 4km/hr
(B) 5km/hr
(C) 5.5km/hr
(D) 6km/hr
(E) 7km/hr
Rationale: given upstream(u) =4km/hr
down stream (v)= 10km/hr rate in still water =1/2(u+v)=1/2(4+10)=7km/hr Answer is (E):7
Answer: (E) 7km/hr
Question: If (x × 10^q) – (y × 10^r) = 10^r, where q, r, x, and y are positive integers and q > r, then what is the units digit of y?
(A) 0
(B) 1
(C) 5
(D) 7
(E) 9
Rationale: Group the 10^r terms on one side of the equal sign.
(x × 10^q) – (y × 10^r) = 10^r
x × 10^q = (y × 10^r) + (1 × 10^r)
x × 10^q = (y + 1) × 10^r
Now, solve for y.
x∗10 q=(y+1)∗10 rx∗10 q=(y+1)∗10r
x∗10q10r=y+1x∗10q10r=y+1
x∗10 q−r=y+1x∗10 q−r=y+1
x∗10q−r−1=yx∗10 q−r−1=y
Since q > r, the exponent on 10^(q-r) is positive. Since x is a positive integer, x*10^(q-r) is a multiple of 10 and therefore ends 0. Any multiple of 10 minus 1 yields an integer with a units digit of 9.
The correct answer is E.
Answer: (E) 9
Question: The present worth of a certain bill due sometime hence is Rs. 1296 and the true discount is Rs. 72. What is the banker's discount?
(A) Rs. 76
(B) Rs. 72
(C) Rs. 74
(D) Rs. 4
(E) None of these
Rationale: Explanation :
BG = (TD)2/PW=722/1296 = 72×72/1296 = 12 × 12/36=12/3= Rs. 4
BG = BD – TD
=> 4 = BD - 72
=> BD = 72 + 4 = Rs. 76 Answer : Option A
Answer: (A) Rs. 76
Question: If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
(A) 2.87
(B) 2.967
(C) 3.876
(D) 3.912
(E) 3.7
Rationale: Explanation:
log5 512
=	log 512 /log 5
=	log 29 /log (10/2)
=	9 log 2 /log 10 - log 2
=	(9 x 0.3010) /1 - 0.3010
= 2.709 /0.699
=	2709 /699
= 3.876
ANSWER IS C
Answer: (C) 3.876
Question: If P gets 25% more than Q, then by what percent does Q get less than P?
(A) 33 1/3%
(B) 30%
(C) 20%
(D) 16 2/3%
(E) None of these
Rationale: Let Q get 1 unit.
25% of 1 unit = 1/4 = 0.25
P gets (1 + 0.25) i.e., 1.25 units.
Difference = (1.25 - 1) = 0.25
Required percentage = 0.25/1.25 * 100 = 1/5 * 100 = 20%
ANSWER:C
Answer: (C) 20%
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 29 kmph
(B) 28 kmph
(C) 54 kmph
(D) 37 kmph
(E) 27 kmph
Rationale: S = 240/16 * 18/5
= 54 kmph
Answer: C
Answer: (C) 54 kmph
Question: When 28 is divided by the positive integer q, the remainder is 1. What is the sum of all the possible values of q for which this is true?
(A) 2
(B) 3
(C) 9
(D) 30
(E) 39
Rationale: The only possible values of the form 28=qp+1 are 3,9 or 27
The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
Answer: (E) 39
Question: 45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 30 meters deep by working for 6 hours?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: 45 workers * 8 hours / 30 meters = x * 6 / 30
x = 60 total workers
60 - 45 = 15 new workers
The answer is B.
Answer: (B) 15