mathewhe/aqua_rat huggingface dataset:
Question: On a certain day, Tim invested $600 at 10 percent annual interest, compounded annually, and Lana invested 1,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
(A) $5.5
(B) $15.5
(C) $23.5
(D) $100
(E) $105
Rationale: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
600(1.10)^2 = 600(1.21) = 726
and Lana would have
1,000(1.05)^2 = 1,000(1.1025) = 1102.5
Thus, Tim earned 126 dollars, while Lana earned 102.5 dollars
The difference is $23.5 and the answer is C.
Answer: (C) $23.5
Question: Pipe A can fill a tank in 20 hours, pipe B in 20 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 2.5
(C) 7
(D) 7.5
(E) None
Rationale: Sol.
Part filled by (A + B + C) in 1 hour = (1/20 + 1/20 + 1/30) = 2/15.
âˆ´ All the three pipes together will fill the tank in 7.5 hours.
Answer D
Answer: (D) 7.5
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 16 = f(x – 6) ?
(A) 1
(B) 4
(C) 6
(D) 7
(E) 13
Rationale: 2(3x-5)-16 = 3(x-6) - 5
3x = 3
x = 1
The answer is A.
Answer: (A) 1
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) s.575
(B) s.595
(C) s.590
(D) s.580
(E) s.585
Rationale: 80 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
ANSWER:E
Answer: (E) s.585
Question: How many positive integers less than 100 have a remainder of 11 when divided by 13?
(A) 11
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: We have to include 11 also.As 13*0 + 11=11
If somebody says to divide 11 by 13 ,we will be telling we have 0 quotient and remainder as 11.
Answer is A
Answer: (A) 11
Question: For which of the following functions does f(−q)=−f(q) for all real number values of x?
(A) q^8−q^4
(B) q^2−q^6
(C) q^5/q^7
(D) q^9/(q^5+1)
(E) q^5/(q^2+1)
Rationale: q^5/(q^2+1)
E
Answer: (E) q^5/(q^2+1)
Question: If the perimeter of square region E and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of E
(A) 25:16
(B) 24:25
(C) 5:6
(D) 4:5
(E) 4:9
Rationale: We know Perimeter of a square (Pe) = 4*side
Perimeter of a rectangle (Pr) = 2(length+breath)
Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)
Therefore,
Pe = Pr = 40
Area of the square = 100 sq. units
We know 2(length+breadth) = 40
i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)
Therefore length = 8, breath = 12
Area of the rectangle = 8*12 = 96 sq. units
Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25=B
Answer: (B) 24:25
Question: In a certain accounting class of 90 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 60%, and the students on the make-up date had an average score of 70%, what was the average score for the entire class?
(A) 63%
(B) 64%
(C) 65%
(D) 66%
(E) 67%
Rationale: 70% of the class scored 60% and 30% of the class scored 70%.
The difference between 60% and 70% is 10%.
The average will be 60% + 0.3(10%) = 63%.
The answer is A.
Answer: (A) 63%
Question: If the product of the integers j, k, l and m is 770, and if 1 < j< k< l< m, what is the value of j+ m?
(A) 10
(B) 13
(C) 16
(D) 18
(E) 21
Rationale: 770 = 2 * 5 * 7 * 11
So j= 2, k= 5, l= 7, m= 11
j+ m= 2 + 11 = 13
Answer - B
Answer: (B) 13
Question: For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Let’s test the first prime number greater than 3, which is 5.
5^3 = 125
125/12 = 10 remainder 5
Answer: D
Answer: (D) 5
Question: It costs $2 for the first 1/4 hour to use the bathroom. After the first ¼ hour it costs $8 per hour. If a certain customer uses the bathroom for 1 hour, how much will it cost him?
(A) $8
(B) $3
(C) $26
(D) $7
(E) $2.99
Rationale: 1 hour = 60 minutes
First 15 min ------> $2
Time left is 45 min...
Now, 60 min costs $ 8
1 min costs $ 8/60
45 min costs $ 8/60*45 => $ 6
So, Total cost will be $6 + $2 => $ 8
The answer will be (A) $ 8
Answer: (A) $8
Question: A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 9:5
(B) 2:3
(C) 4:7
(D) 5:6
(E) None of these
Rationale: Explanation:
Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5.
Answer: A
Answer: (A) 9:5
Question: Each day, Jane swims a certain number of lengths. On day 1, she swims 8 lengths. Each day, she swims 8 more lengths than the day before. What is the average number of lengths she swims each day in the first week?
(A) 8
(B) 16
(C) 32
(D) 34
(E) 40
Rationale: =8 + 16 + 24 + ... + 56
=8(1+2 + 3 + ...+ 7)/7
=8(7(7+1))/(7*2)
=4(8)
=32
Option C
Answer: (C) 32
Question: How many 4-digit W numbers (ABCD) can be formed such that |A – D| = 2?
(A) 2,000
(B) 1,900
(C) 1,800
(D) 1,600
(E) 1,500
Rationale: 1) A=0 and D-8
2) A and D as 1 and 9..so 3*100= 300 extra ways ans 1800-300 = 1500.
we are looking for |A-D|=2 so any of the two can be bigger..
these two can have values (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14..
another arrangement could be A as 2 and D as 0... D as 2 and A as 0 is not possible as number will become 3 digits..
so the ways A and D can be placed = 14+1=15 ways..
B and C can be placed in 10*10 ways..
Total W= 15*10*10=1500.E
Answer: (E) 1,500
Question: A single discount equivalent to the discount series of 14%, 10% and 5% is?
(A) 26.47
(B) 36.97
(C) 31.67
(D) 31.47
(E) 26.17
Rationale: 100*(86/100)*(90/100)*(95/100) = 73.53
100 - 73.53 = 26.47
Answer: A
Answer: (A) 26.47
Question: What will be the remainder if 2^300 is divided by 4?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: D
4
Now if you go on calculating 2^300, you will lose so much time and it might not even be feasible to carry out so long of calculations. Thus we will make use of a trick here. We will calculate the remainder of each power of 2 till we come across a pattern.
2^1 divided by 4 leaves the remainder 2.
2^2 divided by 4 leaves the remainder 0.
2^3 divided by 4 leaves the remainder 0.
2^4 divided by 4 leaves the remainder 0.
You can see that all the following powers of two will be divisible by 4. Therefore the remainder when 2^300 is divided by 4 will be 0 only.
Answer: (D) 4
Question: If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
(A) 26 2/3 %
(B) 30 %
(C) 27 1/2%
(D) 40 %
(E) 50 %
Rationale: Explanation:
8 = (1*20*R)/100
R = 40%
ANSWER IS D
Answer: (D) 40 %
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 49 hours respectively. The ratio of their speeds is?
(A) 4:7
(B) 7:3
(C) 4:9
(D) 4:4
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš49 : âˆš9 = 7:3.Answer: B
Answer: (B) 7:3
Question: The radius of a wheel is 24.2 cm. What is the distance covered by the wheel in making 500 resolutions?
(A) 708 m
(B) 704 m
(C) 774 m
(D) 760.57 m
(E) 744 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 24.2 = 76057 cm
= 760.57 m
Answer:D
Answer: (D) 760.57 m
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 40 per square m?
(A) s.43000
(B) s.50000
(C) s.57000
(D) s.38000
(E) s.62000
Rationale: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 40 * 950
= Rs.38000
D
Answer: (D) s.38000
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
(A) 20 seconds
(B) 30 seconds
(C) 40 seconds
(D) 50 seconds
(E) None of these
Rationale: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500∗2/25=40seconds
Option C
Answer: (C) 40 seconds
Question: Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new
man. Then weight of the new man is
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: Explanation:
Total weight increased is 1.5 * 10 = 15.
So weight of new person is 45+15 = 60
Answer: Option C
Answer: (C) 60
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 50 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 5%
(B) 10%
(C) 75%
(D) 40%
(E) 55%
Rationale: The complete round trip consists of driving to the service center and then back home again.
So, once the technician drives to the service center he/she has already competed 50% of the entire trip.
Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%
so 0.5+0.5*0.5=0.75
Answer:
C
Answer: (C) 75%
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.170000, find the cost of a camel?
(A) 3278
(B) 2669
(C) 2770
(D) Rs.6800
(E) 2791
Rationale: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.170000
P = Rs.[(24 * 4 * 4 * 170000)/(10 * 16 * 6 * 10)]
P = Rs.(65280000/9600) => P = Rs.6800
Answer: D
Answer: (D) Rs.6800
Question: In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1500 employees, then the no. of female employees who are computer literate ?
(A) 630
(B) 674
(C) 672
(D) 960
(E) None
Rationale: Solution: Total employees,
= 1500
Female employees, 60% of 1500.
= (60 *1500) /100 = 900.
Then male employees,
= 600
50 % of male are computer literate,
= 300 male computer literate.
62 % of total employees are computer literate,
= (62 *1500) /100 = 930 computer literate.
Thus, Female computer literate = 930 - 300
= 630
Answer: Option A
Answer: (A) 630
Question: There are 192 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?
(A) 72
(B) 85
(C) 107
(D) 98
(E) 108
Rationale: You had the answer almost right. The x = 84 refers to ONLY set A.
However what's being asked is how many members are part of set A. This will include:
1. Only Set A
2. Set A and Set B
So the answer is Set A = 84+ Set AB = 84+23 = 17
C
Answer: (C) 107
Question: 5n - 3 > 12 and 7n - 5 < 44; n must be between which numbers?
(A) 1 and 8
(B) 2 and 6
(C) 0 and 9
(D) 3 and 7
(E) 2 and 9
Rationale: 5n-3 > 12
5n > 15
n > 3
7n-5 < 44
7n < 49
n < 7
So n must be between 3 and 7
3 < n < 7
correct answer D
Answer: (D) 3 and 7
Question: 4.036 divided by 0.04 gives :
(A) 100.8
(B) 100.2
(C) 100.5
(D) 100.9
(E) 100.7
Rationale: = 4.036/0.04
= 403.6/4
= 100.9
Answer is D.
Answer: (D) 100.9
Question: The positive difference between Sam and Lucy’s ages is a, and the sum of their ages is z. If Lucy is older than Sam, then which of the following represents Lucy’s age?
(A) (z - a)/2
(B) a - z/2
(C) 2a + z
(D) (z + a)/2
(E) (a - z)/2
Rationale: let Lucy's age be L and sam's age be S
as given,
L-S=a -- 1
L+S=z --2
adding both the equations 2L=a+z
L= (a+z)/2 answer is D
Answer: (D) (z + a)/2
Question: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $190. Find the original price of petrol?
(A) $11
(B) $5
(C) $45
(D) $400
(E) $4.2
Rationale: Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 190/45=$4.2
Answer: E.
Answer: (E) $4.2
Question: The sum of a 2digit no. & the no. obtained byreversing the order ofthe digit is 165. If the digits are differ by 3, find the original no.?
(A) 76
(B) 86
(C) 88
(D) 90
(E) 96
Rationale: Let unit digit = x
Ten’s digit = x + 3
Original number = 10(x + 3) +x
= 10x + 30 + x
Original number = 11x +30
Reversing the digits :
Unit digit = x +3
Ten’s digit = x
New number = 10x + x + 3
New number = 11x + 3
As the sum of original number and the new number = 165
11x + 30 + 11x + 3 = 165
22x + 33 = 165
22x = 132
X = 6
Original number = 11 x + 30 = 11(6) +30
= 66 + 30
= 96
E
Answer: (E) 96
Question: 12 + 13 + 14 + ... 61 + 62 + 63 = ?
(A) 1361
(B) 1362
(C) 1950
(D) 1364
(E) 1365
Rationale: Sum = 12 + 13 + 14 + ... 61 + 62 + 63
Sum of n consecutive positive integers starting from 1 is given as n(n+1)/2
Sum of first 63 positive integers = 63*64/2
Sum of first 11 positive integers = 11*12/2
Sum = 12 + 13 + 14 + ... 61 + 62 + 63 = 63*64/2 - 11*12/2 = 1950
Answer : C
Answer: (C) 1950
Question: A 3-letters code consists of three different letters. If the code contains at least 2 vowels, how many such codes are possible?
(A) 480
(B) 510
(C) 520
(D) 430
(E) 540
Rationale: 5 Vowels
21 Consonants
Remember that the letters have to different.
At least 2 = 2-Vowels + 3-Vowels
2-Vowels: 5*4*21 = 420
3-Vowels: 5*4*3 = 60
Total = 480
ANS:A
Answer: (A) 480
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 28000
(B) 29000
(C) 37000
(D) 38000
(E) 40000
Rationale: Option B
Explanation:
CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Option D
Answer: (D) 38000
Question: A sum of 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of 362.50 more is lent but at the rate twice the former. At the end of the year, 33.50 is earned as interest from both the loans. What was the original rate of interest?
(A) 3.6%
(B) 4.5%
(C) 5%
(D) 3.46%
(E) None of these
Rationale: Let the original rate be R%. Then, new rate = (2R)%
∴ (725×R×1/100)+(362.50×2R×1/100×3)=33.50
⇒ (2175 + 725)R = 33.50 × 100 × 3 = 10050
⇒ R = 10050⁄2900 = 3.46%
Answer D
Answer: (D) 3.46%
Question: 2 no's are respectively 40% & 60% more than 3rdnumber. Find the ration of two numbers ?
(A) 3:4
(B) 4:5
(C) 7:8
(D) 9:7
(E) 11:9
Rationale: Step 1: Let the third number is A
Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.
Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7:8.
C
Answer: (C) 7:8
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 29 Kmph
(B) 27 Kmph
(C) 68 Kmph
(D) 22 Kmph
(E) 12 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: C
Answer: (C) 68 Kmph
Question: A three-character password consists of one letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 4,680
(B) 18,720
(C) 26,000
(D) 37,440
(E) 52,000
Rationale: 4 character password: DLDD
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
This gives us 10*26*9ways
Now, the letter can also be DDLD so there will be another 10*9*26 ways
Total = 10*26*9*2 = 4680 ways A
Answer: (A) 4,680
Question: The diameter of a ball is 20 inches. If the surface area of the diameter is the same as the surface area of a cube, what does 1 side of the cube measure? Round to the nearest whole number.
(A) 10
(B) 5
(C) 8
(D) 4
(E) 3
Rationale: The surface area of a sphere is determined by squaring the radius, multiply by Pi and multiply by 4. The radius is half of the diameter of a circle. So the radius of the ball is 10 inches. Multiply 10 by Pi, then multiply the answer by 4 will calculate to 125.663 inches as the surface area of the ball. Since a cube has 6 evenly measured sides we can divide the surface are by 6. This comes to 20.943 inches as the surface area for each square side of the cube. To find out the measurement for each side of the cube you will need to find out the square root of 20.943 inches. This comes to 4.576 inches. Rounding to the nearest whole number, each side of the cube measures 5 inches. The correct answer is (B).
Answer: (B) 5
Question: The sum of the ages of mother and her daughter is 50years. Also 5 years ago, the mother's age was 7 times the age of the daughter. What is the age of the mother?
(A) 50years
(B) 60years
(C) 30years
(D) 25years
(E) 40years
Rationale: Let the age of the daughter be x years
The age of the mother is 50-x years
5 years ago 7(x-5) = 50-x-5
x = 10
Mother's age = 50-10= 40years
Answer is E
Answer: (E) 40years
Question: A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked at 4 miles per hour for 5 hours. How many miles in total did she walk?
(A) 24
(B) 44
(C) 58
(D) 60
(E) 62
Rationale: First day - 18 miles with 3 miles per hours then total - 6 hours for that day
Second day - 4 miles per hour and 5 hours - 20 miles
Third day - 4 miles per hour and 5 hours - 20 miles
Total 18+20+20 = 58
Answer: option C
Answer: (C) 58
Question: The ratio, by volume, of soap to alcohol to water in a certain solution is 4:40:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 200 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
(A) 1300
(B) 1500
(C) 1600
(D) 1700
(E) 1800
Rationale: soap:alcohol
Initial ratio soap:alcohol: water --> 4:40:90
Initial soap:alcohol = 4/40 =4:40
after doubled soap:alcohol =2* 4/40 = 8:40
Initial soap:water = 4/90=4:90
after halved soap:water: 1/2 * 4/90 = 2/90 = 2:90
After soap: alcohol:water --> 8:40:360-->1:5:45
given alcohol 200 cubic centimeter.
ratio is 40:200:1800(1:5:45)
For 200 cubic centimeter of Alcohol --- 1800cubic cm water is required.
Answer-E
Answer: (E) 1800
Question: Jerry, an electrician, worked 8 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 8? 12 months = 1 year
(A) 58.33%
(B) 66.67%
(C) 78.33%
(D) 88.33%
(E) 98.33%
Rationale: 1. Multiply the opposites
8 x 100 = 800
100=8/12
Divide by the remaining number
66.67% (rounded to hundredth)
correct answer B
Answer: (B) 66.67%
Question: A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
(A) 20:64:49
(B) 49:20:64
(C) 49:64:20
(D) 64:49:20
(E) 20:49:64
Rationale: Ratio in which A,B and C shared the profit =5:7:8
Assume that the ratio of their investments =a:b:c
⇒14a:8b:7c=5:7:8⋯(A)
From (A),
14a:8b=5:7
⇒14a×7=8b×5
⇒7a×7=4b×5
⇒b=49a/20⋯(1)
From (A),
14a:7c=5:8
⇒14a×8=7c×5
⇒2a×8=c×5
⇒c=16a/5⋯(2)
a:b:c=a:49a/20:16a/5
=1:49/20:16/5
=20:49:64
Answer is E.
Answer: (E) 20:49:64
Question: A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?
(A) 60 km/hr
(B) 100 km/hr
(C) 110 km/hr
(D) 120 km/hr
(E) None of these
Rationale: Explanation :
Number of gaps between 41 poles = 40So total distance between 41 poles = 40*50= 2000 meter = 2 kmIn 1 minute train is moving 2 km/minute.Speed in hour = 2*60 = 120 km/hour
Answer : D
Answer: (D) 120 km/hr
Question: Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 8 seconds.What is the length of the fast train?
(A) 23 m
(B) 23 2/9 m
(C) 47m
(D) 37 7/9m
(E) 44 4/9 m
Rationale: relative speed=20kmph=50/9m/sec
length of the train=50/9*8=44 4/9 m
ANSWER:E
Answer: (E) 44 4/9 m
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 8 : 4?
(A) 16
(B) 45
(C) 277
(D) 92
(E) 11
Rationale: Let the distances between city A to B and B to C be 8x km and 4x km respectively.
Total time taken to cover from A to C
= (8x)/40 + (4x)/60 = (4x + 8x)/120 = 32x/120 = 4x/15 Average speed = (8*x + 4x)/(4x/15) = 45 kmph.
Answer:B
Answer: (B) 45
Question: Rahul went to a shop and bought things worth Rs. 30, out of which 40 Paise went on sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?
(A) 17.6
(B) 24.6
(C) 21.6
(D) 18.6
(E) 20.6
Rationale: Total cost of the items he purchased = Rs.30
Given that out of this Rs.30, 40 Paise is given as tax
=> Total tax incurred = 40 Paise = Rs.40/100
Let the cost of the tax free items = x
Given that tax rate = 8%
∴ (30−40/100−x)8/100 = 40/100
⇒ 8(30 −0.4−x) = 40
⇒ (30− 0.4 − x) = 5
⇒ x = 30 − 0.4 − 5 = 24.6.
B)
Answer: (B) 24.6
Question: a dealer buys 4 varieties of wheat costing rs. 20,rs.25,rs.30 and rs.35 per kg in the ratio 6:4:3:1 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of wheat?
(A) 30.5
(B) 31.0
(C) 32.0
(D) 33.0
(E) 34.5
Rationale: CP = 20*6+25*4+30*3+35*1=345
SP = 1.4*345=483
Total no.of kgs=6+4+3+1=14
SP per kg=483/14 = 34.50
ANSWER:E
Answer: (E) 34.5
Question: If the quantity (p − 4) is 5 times the quantity (q − 5), then what is the relationship between p and q?
(A) p = 5q + 30
(B) p = 5q − 21
(C) 5p = q + 20
(D) p = 5q
(E) p = 5q − 20
Rationale: p-4=5(q-5)
p-4=5q-25
p=5q-21
option B
Answer: (B) p = 5q − 21
Question: Kyle, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/8, 1/4 and 3/5, respectively, what is the probability no one will solve the problem?
(A) 3/80
(B) 21/80
(C) 5/16
(D) 25/76
(E) 9/80
Rationale: P(Kyle will not solve)=1 - 1/8 = 7/8
P(David will not solve)= 1 - 1/4 = 3/4
P(Catherine will not solve) = 1- 3/5 = 2/5
P= (7/8)*(3/4)*(2/5) = 42/160 = 21/80
Answer:B
Answer: (B) 21/80
Question: What percent of a day is nine hours?
(A) 20.83%
(B) 16x1/2%
(C) 18x2/3%
(D) 37.5%
(E) None of these
Rationale: Explanation :
Required percentage = (9/24100)%
= 37.5%.
Answer : D
Answer: (D) 37.5%
Question: If 10 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a four-percent vinegar solution, what was the concentration of the original solution?
(A) 20%
(B) 24%
(C) 25%
(D) 28%
(E) 30%
Rationale: Let x be the concentration of the original solution.
10x = 0.04(60)
x = 0.24
The answer is B.
Answer: (B) 24%
Question: 1/x+1/y=1/z where x=12 and y,z positive integer how many possible value of y and z ?
(A) 4
(B) 7
(C) 12
(D) 15
(E) infinite
Rationale: 1/12 = 1/z - 1/y
y = 12 * z / ( 12 - z )
0 < z < 12
Only for z = 3 ,4 ,6 ,8 , 9 ,10 and 11 , y is intiger
Hence seven solutions
ANSWER:B
Answer: (B) 7