mathewhe/aqua_rat huggingface dataset:
Question: The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B ?
(A) 29/12
(B) 59/10
(C) 65/8
(D) 48/5
(E) 29/3
Rationale: Ratio in A: 4/5 so total students in A = 9x
Ratio in B: 3/17 so total students in B = 20y
(4x+3y)/(5x+17y) = 5/7
solving, x/y = 64/3
required ratio = 9x/20y = (64*9)/(3*20) = 48/5
ANSWER:D
Answer: (D) 48/5
Question: Ahmed, Babu, Chitra, David and Eesha each choose a large different number. Ahmed says, “ My number is not the largest and not the smallest”. Babu says, “My number is not the largest and not the smallest”. Chitra says, “My number is the largest”. David says, “ My number is the smallest”. Eesha says, “ My number is not the smallest”. Exactly one of the five children is lying. The others are telling the truth. Who has the largest number?
(A) Eesha
(B) David
(C) Chitra
(D) Babu
(E) EEEW
Rationale: Largest ->	A	B	C	D	E
A	F	T/F	T/F	T/F	T/F
B	T/F	F	T/F	T/F	T/F
C	F	F	T	F	F
D	T/F	T/F	T/F	F	T/F
E	T/F	T/F	T/F	T/F	T
Ans: A
Answer: (A) Eesha
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, x
(A) 23
(B) 26
(C) 36
(D) 35
(E) 45
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 30 + 5 = 35.
Answer: (D) 35
Question: Meera purchased two three items from a shop. Total price for three items is Rs.6000/- She have given Rs. 10000/- What is the balance amount meera got?
(A) 6000
(B) 3500
(C) 5000
(D) 4000
(E) 7500
Rationale: Total cost of Items : 6000/-
amount Paid : 10000/-
Balance receivable : 10000- 6000= 4000/-
Answer is D
Answer: (D) 4000
Question: Ifaequals the sum of the even integers from 2 to 40, inclusive, andbequals the sum of the odd integers from 1 to 39, inclusive, what is the value of a - b ?
(A) 1
(B) 10
(C) 19
(D) 20
(E) 21
Rationale: This is a solution from Beatthegmat:
even numbers:
(40-2)/2 + 1 = 20 even integers.
(40+2)/2 = 21 is the average of the even set.
sum = avg*(#of elements) = 21*20 =420 = a
odd numbers:
(39-1)/2 + 1 = 20 odd integers.
(39+1)/2 = 20 is the average of the odd set.
sum = avg*(#of elements) = 20*20 = 400 = b
a-b = 420 - 400 = 20.
Answer : D
Answer: (D) 20
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 48 now, the son age 5 years back was
(A) 14
(B) 17
(C) 11
(D) 19
(E) 99
Rationale: Let the son's present age be x years .Then, (48 - x) = x x= 24.
Son's age 5 years back = (24 - 5) = 19 years
Answer: D
Answer: (D) 19
Question: Mr.Jones gave 40% of the money he had to his wife. he also gave 20% of the remaining amount to his 3 sons. half of the amount now left was spent on miscellaneous items and the remaining amount of Rs.12000 was deposited in the bank. how much money did Mr.Jones have initially?
(A) 100
(B) 1000000
(C) 1000
(D) 1
(E) 10000
Rationale: Let the initial amount with Mr.Jones be Rs.x
Then, (1/2)[100-(3*20)]% of x=12000
 (1/2)*(40/100)*(60/100)*x=12000
x=((12000*25)/3)=100000
ANSWER B
Answer: (B) 1000000
Question: What number has a 5:1 ratio to the number 10?
(A) 42
(B) 50
(C) 55
(D) 62
(E) 65
Rationale: Explanation:
5:1 = x: 10
x = 50
ANSWER IS B
Answer: (B) 50
Question: An analyst will recommend a combination of 4 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 8 stocks are possible?
--
(A) 12
(B) 19
(C) 90
(D) 180
(E) 720
Rationale: 5C4 * 4C2 * 3C2 = 5*6*3 = 90.
Answer: C.
Answer: (C) 90
Question: 3-3*6+2=
(A) 2
(B) -13
(C) -18
(D) -17
(E) none of the above
Rationale: It is easy and you have to follow BODMAS..
3-3*6+2 = 5-18 = -13...
Your OA -17 would be if the equation is 3-(3*6+2)....
so the answer is -13.
ANSWER:B
Answer: (B) -13
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 312 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
(A) 140
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(312-9-90*2)/3=140
Answer : A
Answer: (A) 140
Question: Find the average of all prime numbers between 12 and 24.
(A) 30
(B) 33.6
(C) 18
(D) 20
(E) None
Rationale: Sol.
There are five prime numbers between 12 and 24.
They are 13, 17, 19, 23
âˆ´ Required average = [13+ 17+ 19+ 23 / 4] = 72/ 4 = 18
Answer C
Answer: (C) 18
Question: A man can swim in still water at 5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.78
(B) 1.667
(C) 1.15
(D) 1.5
(E) 1.2
Rationale: M = 5
S = x
DS = 5 + x
US = 5 - x
5 + x = (5 - x)2
5 + x = 10 -2x
3x = 5
x = 1.667
Answer:B
Answer: (B) 1.667
Question: In the parking lot there are 28 vehicles, 18 of them are buses, and the rest are cars. The color of 14 vehicles is red, of which 11 are buses. How many cars can be found in the parking lot which are not colored red?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: The number of cars is 28-18 = 10.
The number of red cars is 14-11=3.
The number of cars which are not red is 10-3=7.
The answer is A.
Answer: (A) 7
Question: In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?
(A) A)160
(B) B)170
(C) C)190
(D) D)210
(E) E)120
Rationale: 6p2 = 6 × 5 x 4= 120
Option 'E'
Answer: (E) E)120
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 1245 m^2
(B) 1345 m^2
(C) 2520 m^2
(D) 2560 m^2
(E) 2678 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 m^2
Question: A train crosses a platform of 170 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) A)150m
(B) B)170m
(C) C)180m
(D) D)70m
(E) E)350m
Rationale: Length of the train be ‘X’
X + 170/15 = X + 250/20
4X + 680 = 3X + 750
X = 70m
Answer: D
Answer: (D) D)70m
Question: In how many different ways can the letters of the word 'EVE' be arranged?
(A) 3 ways
(B) 20 ways
(C) 30 ways
(D) 60 ways
(E) 40 ways
Rationale: Totally there are 3 letters on the word EVE. it contains 2E,1V.
The no of ways is 3!/2!=3 ways.
ANSWER:A
Answer: (A) 3 ways
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
(A) 7508
(B) 7500
(C) 7506
(D) 7566
(E) 7508
Rationale: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs.7500
Answer: B
Answer: (B) 7500
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 65520 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
(A) 130000
(B) 12500
(C) 14000
(D) 12000
(E) None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 65520.
(75/100 * 96/100 * 70/100 * x) = 65520.
=> x = (65520*100*100*100)/(75*96*70) = 130000
Answer : A
Answer: (A) 130000
Question: In how many different number of ways 4 boys and 4 girls can sit on a bench such that girls always sit together.
(A) A)720
(B) B)2000
(C) C)2880
(D) D)780
(E) E)790
Rationale: 2880
Option 'C'
Answer: (C) C)2880
Question: How many values of c in x^2 - 5x + c, result in rational roots which are integers?
(A) 23
(B) 27
(C) 25
(D) 12
(E) 82
Rationale: Explanation:
By the quadratic formula, the roots of x2−5x+c=0x2−5x+c=0 are −(−5)±−52−4(1)(c)−−−−−−−−−−−√2(1)−(−5)±−52−4(1)(c)2(1) = 5±25−4c−−−−−−√25±25−4c2
To get rational roots, 25−4c25−4c should be square of an odd number. Why? because 5 + odd only divided by 2 perfectly.
Now let 25 - 4c = 1, then c = 6
If 25 - 4c = 9, then c = 4
If 25 - 4c = 25, then c = 0 and so on...
So infinite values are possible.
Answer:C
Answer: (C) 25
Question: ? x 48 = 173 x 240
(A) 545
(B) 685
(C) 865
(D) 495
(E) 534
Rationale: Let y x 48 = 173 x 240
Then y = (173 x 240) / 48
=173 x 5
= 865 .
ANSWER :C
Answer: (C) 865
Question: What percent of a day is five hours?
(A) 20.83%
(B) 16x1/2%
(C) 18x2/3%
(D) 22x1/2%
(E) None of these
Rationale: Explanation :
Required percentage = (5/24100)%
= (125 / 6)%.
= 20.83%.
Answer : A
Answer: (A) 20.83%
Question: A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
(A) 4 : 3
(B) 9:2
(C) 18:20
(D) 1:4
(E) 18:4
Rationale: A: B =24000 : 18000 = 8 : 6 = 4 : 3
ANSWER:A
Answer: (A) 4 : 3
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 3
(B) 7
(C) 5
(D) 9
(E) 6
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: (A) 3
Question: If a man lost 4% by selling oranges at the rate of 48 a rupee at how many a rupee must he sell them to gain 44%?
(A) 1
(B) 8
(C) 9
(D) 4
(E) 32
Rationale: 96% ---- 48
144% ---- ?
96/144 * 48= 32
Answer: E
Answer: (E) 32
Question: Train X and train Y pass one another traveling in opposite directions. Twelve minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?
(A) 28
(B) 40
(C) 53
(D) 72
(E) 80
Rationale: Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30
d=100 and t = 12 min i.e 12/60 hr
using RTD table, (2R+30) * 12/60 = 100 ==> R= 235 miles/hr
So the rate of train X is 265 miles/hr (since R+30)
The distance traveled by Train X in 12 min is R*T = 265 * 12/60 = 53 miles (C)
Answer: (C) 53
Question: The forth proportional to 5,8,15 is?
(A) 15
(B) 12
(C) 18
(D) 20
(E) 24
Rationale: Let the fourth proportional to 5,8,15 be x
then 5:8::15:x
5x = 8*15
x = 24
Answer is E
Answer: (E) 24
Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is?
(A) 200
(B) 400
(C) 450
(D) 500
(E) None
Rationale: Let the numbers be x and y.
Then, xy = 9375 and x = 15.
y
xy = 9375
(x/y) 15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.
Option is B
Answer: (B) 400
Question: On a trip, a cyclist averaged 12 miles per hour for the first 18 miles and 10 miles per hour for the remaining 18 miles. If the cyclist returned immediately via the same route and took a total of 7.3 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
(A) 8.4
(B) 8.6
(C) 8.8
(D) 9
(E) 9.2
Rationale: The time to go 36 miles was 18/12+18/10=1.5+1.8=3.3 hours.
The average speed for the return trip was 36 miles/4 hours= 9 mph.
The answer is D.
Answer: (D) 9
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are white,black, red, orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the nine socks?
(A) 12
(B) 15
(C) 21
(D) 36
(E) 72
Rationale: It's a question of permutation since order matters here ....
It can be deduced to-
9P2 = 9!/7! = 9*8 = 72 .........Answer is - E
Answer: (E) 72
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(A) Rs. 3700
(B) Rs. 3800
(C) Rs. 3900
(D) Rs. 4000
(E) Rs. 4900
Rationale: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5 x.
2
15x + 2y = 4000
15x + 2 x 5 x = 4000
2
20x = 4000
x = 200.
So, y = 5 x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
C)
Answer: (C) Rs. 3900
Question: Consider a Number 3.1n3
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
(A) 2
(B) 1
(C) 3
(D) 4
(E) 5
Rationale: In this ques we are given the thousandth digit as 3, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 3, the hundreth digit has to go up by 0, and correspondingly, the tenth digit should remain same.i.e 0-9.say 1
B
Answer: (B) 1
Question: Tomy started a software business by investing Rs.50,000. After 6months, Nanda joined her with a capital of $80,000. After 3years, they earned a profit of $24,500. What was Simran's share in the profit?
(A) $8,500
(B) $9,500
(C) 10,500 dollars
(D) $11,500
(E) $12,500
Rationale: Tomy : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Tomy 's share = $24500 x	3/7	= $10,500.
C
Answer: (C) 10,500 dollars
Question: If the radii of umbra and penumbra cast by an object on a wall are of the ratio 2:6, what is the area of the penumbra ring around the umbra of the latter’s radius is 40 cms?
(A) 40288.57 centimeter square
(B) 40388.57cm^2
(C) 40488.57cm^2
(D) 40588.57cm^2
(E) 40688.57cm^2
Rationale: et the radius of umbra and penumbra are 2k and 6k.
Then as given radius of umbra=40cm
so 2k=40
k=20
radius of penumbra=20*6=120
area of penumbra ring around the umbra= area of penumbra-area of umbra
22/7*[(120)^2-(40)^2]
=40288.57cm^2
ANSWER:A
Answer: (A) 40288.57 centimeter square
Question: A circle in the coordinate plane passes through points (-3, -2) and (1, -4). What is the smallest possible area of that circle?
(A) 13π
(B) 26π
(C) 262√π
(D) 5π
(E) 64π
Rationale: The distance between the two points is sqrt(20).
radius = sqrt(20)/2
Area= pi*(sqrt(20)/2)^2
D. 5π
Answer: (D) 5π
Question: A cube with volume of 125 cm^3 is dropped in a fish tank with dimensions 3 m x 1 m x 2 m. If the tank is full of water, how much water will remain after the cube is droppped?
(A) 5.9999999 m^3
(B) 5.725 m^3
(C) 5.650 m^3
(D) 5.999875 m^3
(E) 5999.725 m^3
Rationale: Volume of fish tank = 3m x 1m x 2m = 6 m^3
125 cm^3 x (1 m^3 / 1,000,000 cm^3) = 0.000125 m^3
6-.000125 = 5.999875 m^3
Answer is D
Answer: (D) 5.999875 m^3
Question: Two pipes can fill a tank in 20 minutes and 15 minutes. An outlet pipe can empty the tank in 10 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 36
(B) 42
(C) 48
(D) 54
(E) 60
Rationale: Let V be the volume of the tank.
The rate per minute at which the tank is filled is:
V/20 + V/15 - V/10 = V/60 per minute
The tank will be filled in 60 minutes.
The answer is E.
Answer: (E) 60
Question: The fourteen digits of a credit card are to be written in the boxes shown above. If the sum of every three consecutive digits is 18, then the value of x is :
(A) 1
(B) 3
(C) 8
(D) 7
(E) 9
Rationale: Sol : A
Explanation:
Let us assume right most two squares are a , b
Then Sum of all the squares = 18 x 4 + a + b .......... (1)
Also Sum of the squares before 7 = 18
Sum of the squares between 7, x = 18
and sum of the squares between x , 8 = 18
So Sum of the 14 squares = 18 + 7 + 18 + x + 18 + 8 + a + b (2)
Equating 1 and 2 we get x = 3
Answer:B
Answer: (B) 3
Question: f(x) = 1/(1-x) find(f(f(f(x)))
(A) 1
(B) x
(C) 2x
(D) 3x
(E) 0
Rationale: f(x) = 1/(1-x)
==>f(f(x)) = f(1/(1-x))
= 1/(1-(1/(1-x)))
= 1/((1-x-1)/(1-x))
= 1/(-x/(1-x))
= x-1/x
==> (f(f(f(x)))=f(x-1/x)
= 1/(1-(x-1/x))
= 1/((x-x+1)/x)
= 1/(1/x)
= x
ANSWER:B
Answer: (B) x
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.192 in 4 Years?
(A) 5%
(B) 6%
(C) 3%
(D) 9%
(E) 1%
Rationale: 192 = (800*4*R)/100
R = 6%
Answer: B
Answer: (B) 6%
Question: A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?
(A) 5
(B) 7
(C) 6
(D) 31
(E) 18
Rationale: Explanatory Answer
Step 1: Key data
1. Total value of all certificates sold = $93.
2. Certificates sold were in denominations of $3 and $5.
3. Both 'm' and 'n' are natural numbers.
Step 2: Approach
The value of all certificates sold, 93 is divisible by 3.
So, a maximum of 31 $3 certificates and no $5 certificates could have been sold.
However, the question states that both 'm' and 'n' are natural numbers.
Hence, at least 1 $5 certificate should have been sold.
Let us reduce the number of $3 certificates from theoretical maximum count of 31 by say 'x' and correspondingly increase $5 certificates by 'y'.
Evidently, 3x = 5y because the value of $3 certificates reduced should be the same as the value of $5 certificates increased.
It means that x has to be a multiple of 5 and y has to be a multiple of 3.
Or $3 certificates reduce in steps of 5 certificates.
Step 3: List down possibilities
The following combinations are possible
1. m = 26, n = 3
2. m = 21, n = 6
3. m = 16, n = 9
4. m = 11, n = 12
5. m = 6, n = 15
6. m = 1, n = 18
An alternative way to think of the same concept - Replacing five $3 certificates with three $5 certificates leads to no change in the overall value of certficates sold and gives us a new combination each time. We need to see how many such combinations are possible.
Answer C
Answer: (C) 6
Question: A pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 and 1/3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
(A) 5 hrs
(B) 7 hrs
(C) 12 hrs
(D) 14 hrs
(E) 16 hrs
Rationale: The rate of the pump + leak = 3/10
1/2 - leak's rate = 3/10
leak's rate = 1/5
The leak will empty the tank in 5 hours.
The answer is A.
Answer: (A) 5 hrs
Question: A man counted his animals, 80 heads and 250 legs (ducks and goats). how many goats are there?
(A) 30
(B) 40
(C) 50
(D) 45
(E) 70
Rationale: let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=250 and divide 2d+4g=250 by 2 we get d+2g=125 -----------> eq2
subtract eq1 from eq2
we get no of goats=45
ANSWER:D
Answer: (D) 45
Question: To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 8 hours a day?
(A) 40
(B) 36
(C) 42
(D) 44
(E) 46
Rationale: Man-hours required to asphalt 1 km road=30*12*8=2880
Man-hours required to asphalt 2 km road=2880*2=5760
Man-hours available per day=20*8=160
Therefore number of days=5760/240=36 days
Ans=B
Answer: (B) 36
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 2288
(C) 2777
(D) 2999
(E) 2711
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A
Answer: (A) 1000
Question: During the second quarter of 1984, a total of 4,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?
(A) 714,240
(B) 2,261,760
(C) 2,400,000
(D) 3,690,240
(E) 4,012,903
Rationale: Let number of cars sold in 1st quarter = x
Number of cars sold in 2nd quarter = 24% greater than the number sold during the first quarter = (1 + 24/100)x = 1.24 x
1.24 x = 4,976,000
=> x = 4,012,903
So, answer will be E
Answer: (E) 4,012,903
Question: One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey.
(A) 600/53km/h
(B) 1200/53 km/h
(C) 1800/53 km/h
(D) 1600/53 km/h
(E) None of these
Rationale: Solution: Let distance be 120 KM, hence 30 KM is covered by @ 25 kmph and 40 km covered by @ 30 kmph and rest 50 km has been covered@ 50 km.
Now, average = (120/total time taken);
= {120/[(30/25)+(40/30)+(50/50)}]
= 3600/106 = 1800/53 km/h.
Answer: Option C
Answer: (C) 1800/53 km/h
Question: I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last?
(A) 4 hours
(B) 2 hours
(C) 3 hours
(D) 2 hours 24 minutes
(E) None
Rationale: Explanatory Answer
The total time of journey = 5 hours.
Let 'x' hours be the time that I traveled at 40 kmph
Therefore, 5 - x hours would be time that I traveled at 60 kmph.
Hence, I would have covered x*40 + (5 - x)60 kms in the 5 hours = 240 kms.
Solving, for x in the equation 40x + (5 - x)*60 = 240, we get
40x + 300 - 60x = 240
=> 20x = 60 or x = 3 hours.
Answer C
Answer: (C) 3 hours
Question: A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7,8,9}. If no digit may be repeated and each password must be at least 8 digits long, how many passwords are possible?
(A) 8! + 9!
(B) 2 x 9!
(C) 8! x 9!
(D) 17!
(E) 18!
Rationale: If we choose the 9 different digits then they can be arranged in 9! ways.
The number of possible 8-digit passwords is 9*8*...*2 = 9!
The total number of passwords is 9! + 9! = 2*9!
The answer is B.
Answer: (B) 2 x 9!
Question: A woman sold 300 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 4 for 85 cents. How many were sold at the first rate?
(A) 45
(B) 21
(C) 9
(D) 16
(E) 13
Rationale: This can be solved like a classical mixture problem but numbers are awkward to deal with.
It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 4.
100 - 45 = 255 => not a multiple of 4 so exclude
100 - 21 = 279 => not a multiple of 4 so exclude
100 -9 = 291 => not a multiple of 4 so exclude
100 - 16 = 284 => a multiple of 4 so keep
100 - 13 = 287 => not a multiple of 4 so exclude
Hence, answer choice 16 is correct.
D
Answer: (D) 16
Question: The price of an item is discounted 5 percent on day 1 of a sale. On day 2, the item is discounted another 5 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 80%
(B) 82.5%
(C) 83%
(D) 84%
(E) 85.5%
Rationale: Let initial price be 100
Price in day 1 after 5% discount = 95
Price in day 2 after 5% discount = 90.25
Price in day 3 after 10% discount = 81.23
So, Price in day 3 as percentage of the sale price on day 1 will be = 81.23/95*100 => 85.5%
Answer will definitely be (E)
Answer: (E) 85.5%
Question: If 8 boys can color 48 m long cloth in 2 days, then 6 boys can color 36 m long cloth in
(A) day
(B) days
(C) days
(D) days
(E) days
Rationale: The length of cloth painted by one boy in one day = 96 / 8 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 boys = 36/ 6 × 6 = 1 day.
A)
Answer: (A) day