mathewhe/aqua_rat huggingface dataset:
Question: If the given two numbers are respectively 7% and 14% of a third number, then what percentage is the first of the second ?
(A) 20%
(B) 25%
(C) 18%
(D) 50%
(E) none of these
Rationale: Here, l = 7 and m = 14
Therefore, first number = l/m x 100% of second number = 7/14 x 100% of second number = 50% of second number
ANSWER:D
Answer: (D) 50%
Question: At a local supermarket, a box of cereal usually costs 10 dollars. This week, the supermarket sells the box of cereal for 2 dollars. How much money will you save if you buy this cereal at this supermarket?
(A) 5 dollars
(B) 3 dollars
(C) 4 dollars
(D) 2 dollars
(E) 8 dollar
Rationale: Solution:
In this situation, there is a decrease in the price.
Saving = 10 - 2 = 8 dollars
Option E
Answer: (E) 8 dollar
Question: A milk seller has certain quantity of milk to sell. In what ratio, should he mix water to gain 5% by selling the mixture at the cost price ?
(A) 1:10
(B) 1:5
(C) 1:20
(D) 1:15
(E) None of these
Rationale: Let Cost price of 100 g milk was Rs. 100.
x +5% of x = 100
x + 0.05x = 100
1.05x = 100
x = 100/1.05 = 95.23
Water = 100 - 95.23 = 4.76
Ratio of water and Milk = 4.76 /95.23 = 1/20 = 1 : 20.
ANSWER : C
Answer: (C) 1:20
Question: Find the odd man out. 15, 20, 25, 32, 30, 45
(A) 15
(B) 20
(C) 30
(D) 32
(E) 25
Rationale: All numbers except 32 are multiples of 5
Answer is D
Answer: (D) 32
Question: In a box of 8 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
(A) 2/10
(B) 3/11
(C) 4/13
(D) 5/14
(E) 6/17
Rationale: P(neither pen is defective) = 5/8*4/7 = 5/14
The answer is D.
Answer: (D) 5/14
Question: A five-digit number is formed by using digits 1, 2, 3, 4 and 5 without repetition. What is the probability that the number is divisible by 4?
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 6/5
Rationale: A number divisible by 4 formed using the digits 1, 2, 3, 4 and 5 has to have the last two digits 12 or 24 or 32 or 52.
In each of these cases, the five digits number can be formed using the remaining 3 digits in 3! = 6 ways.
A number divisible by 4 can be formed in 6 x 4 = 24 ways.
Total number that can be formed using the digits 1, 2, 3, 4 and 5 without repetition = 5! = 120.
Hence, the required probability would be 24/120 = 1/5.
ANSWER:A
Answer: (A) 1/5
Question: Dhoni weighs twice as much as Nameetha. Nameetha's weight is 65% of Bima's weight. Dravid weighs 40% of Leela's weight. Leela weighs 35% of Dhoni's weight. Who among these 5 persons weighs the least?
(A) Dhoni
(B) Bima
(C) Nameetha
(D) Leela
(E) Dravid
Rationale: if
Bima weight = x
we get
Nameetha's weight = 0.65x
Dhoni's weight = 1.3x
Leela's weight = 0.455x
and Dravid's weight = 0.182x
Answer : E
Answer: (E) Dravid
Question: In 1937, the ship of the great sailor SINBAD left an Egyptian port heading Ivory coast at W mile/month .
One month later another ship of the greatest pirate ever CHENG I SAO was 5000 miles due south of the same Egyptian port and heading due north at Y miles/month. Six months later after the leaving of Sinbad’s ship from Egyptian port, how far apart were the ships? [Ivory coast is in the west of Egypt]
(A) { (6W)^2 + (5000-5y)^2 }^1/2
(B) { (36x)^2 + (5000-7y)^2 }^1/2
(C) { (16x)^2 + (5000-7y)^2 }^1/2
(D) { (7x)^2 + (5200-7y)^2 }^1/2
(E) { (2x)^2 + (300-7y)^2 }^1/2
Rationale: The chinese ship sailed for 5 months i.e. 5Y miles @Y miles/month, therefore distance from Egyptian port is 5000-5Y. Since A is the only option with this value ...therefore A is the answer
Answer: (A) { (6W)^2 + (5000-5y)^2 }^1/2
Question: Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10% of its volume is occupied by mortar ?
(A) 720
(B) 600
(C) 660
(D) 6000
(E) NONE OF THESE
Rationale: Explanation:
Let the number of bricks be 'N'
10 x 4/100 x 6 x 90/100 = 25/100 x 15/100 x 8/100 x N
10 x 4 x 6 x 90 = 15 x 2 x N => N = 720.
ANSWER IS A
Answer: (A) 720
Question: A car finishes a journey in five hours at the speed of 100 km/hr. If the same distance is to be covered in two hours how much more speed does the car have to gain?
(A) 8 km/hr
(B) 10 km/hr
(C) 150 km/hr
(D) 16 km/hr
(E) None of these
Rationale: Distance covered by the car = 100 × 5 = 500 km
\ Speed = 500⁄2 = 250 km/hr
\ Speed gain = 250 – 100 = 150 km/hr
Answer C
Answer: (C) 150 km/hr
Question: Solve below question 2x + 1 = -13
(A) -8
(B) -9
(C) 9
(D) 8
(E) -7
Rationale: 2x + 1 = -13
x = -7
E
Answer: (E) -7
Question: Adding 25% of x to x is equivalent to multiplying x by which of the following?
(A) 12.5
(B) 1.05
(C) 1.15
(D) 1.2
(E) 1.25
Rationale: 125x/100= 1.25*x
ANSWER:E
Answer: (E) 1.25
Question: The ratio of speeds of a car, a train and a bus is 5:9:4. The average speed of the car, the bus and the train is 72 km/hr together. What is the average speed of the car and the train together ?
(A) 84 km/hr
(B) 74 km/hr
(C) 34 km/hr
(D) 64 km/hr
(E) 14 km/hr
Rationale: Let the speeds of the car, train and bus be 5x, 9x and 4x km/hr respectively.
Average speed = 5x + 9x + 4x/3 = 18x /3 = 6x km/hr.
Also, 6x = 72 => x = 12 km/hr
Therefore, the average speed of the car and train together is = = 7x = 7 x 12 = 84 km/hr.
Answer: A
Answer: (A) 84 km/hr
Question: A certain protective additive increases from 30 days to 45 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?
(A) 25%
(B) 33 1/3%
(C) 50%
(D) 66 2/3%
(E) 75%
Rationale: General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the time between maintenance checks increased by 45−30/30∗100=50
Answer: C.
Answer: (C) 50%
Question: In digging a hole 10 m * 10 m * 100 m the volumes of the sand extracted will be?
(A) 100 cu.m
(B) 1000 cu.m
(C) 10000 cu.m
(D) 2000 cu.m
(E) 4000 cu.m
Rationale: 10 * 10 * 100 = 10000
ANSWER:C
Answer: (C) 10000 cu.m
Question: Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 14 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 14 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 14-3 = 11. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer D
Answer: (D) 11
Question: Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 6 minutes more to walk to work than to ride his bike to work, then x equals?
(A) 4
(B) 7
(C) 9
(D) 15
(E) 20
Rationale: Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 360 (which is TIME in seconds.).
Thus the correct equation is : 60*x-20*x=360 ----> 40x=360--> x = 9.
option C
Answer: (C) 9
Question: What is greatest positive integer n such that 2^n is a factor of 12^13?
(A) a)10
(B) b)12
(C) c)16
(D) d)26
(E) e)60
Rationale: The given number is 12^13
=(2*2*3)^13
=(2^26)*(3^13)
So the greatest possible value for n such that 2^n can be factor of given number is 26.
Answer D
Answer: (D) d)26
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did C get in a profit of Rs.2490 ?
(A) s. 332
(B) s. 498
(C) s. 822
(D) s. 812
(E) s. 810
Rationale: Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
C's share in the profit of Rs. 2490 = 12 (2490/60) = Rs. 498.
Answer: B
Answer: (B) s. 498
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
(A) 9:39
(B) 9:31
(C) 9:36
(D) 9:32
(E) 9:34
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Answer: (B) 9:31
Question: Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 1H, which of the following represents the amount that Roberta paid?
(A) D + 40
(B) D + H – 1
(C) D + 2H
(D) 2.03H
(E) 1.21D
Rationale: before Discount price was: 1.4D+1.5H
After Discount: 1.4D +1.5H-.42D-.45H
substitute D=H
final value: 2.03H
Ans Is D :
Answer: (D) 2.03H
Question: Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 25, what is the measure of side XY?
(A) 10
(B) 4√2
(C) 8
(D) 8√2
(E) Cannot be determined from the information provided
Rationale: ans A ..10..
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=25 or yz=5*\sqrt{2}..
therefore hyp=xy=10
Answer: (A) 10
Question: Series 3,15,35,__,99
(A) 43
(B) 53
(C) 63
(D) 73
(E) 83
Rationale: 1*3=3
3*5=15
5*7=35
7*9=63
9*11=99
ANSWER:C
Answer: (C) 63
Question: A sum of Rs. 125000 amounts to Rs. 16500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 8%
Rationale: S.I. = (16500 - 12500) = Rs. 4000\
Rate = (100 * 4000) / (12500 * 4) = 8%
ANSWER:E
Answer: (E) 8%
Question: The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
(A) 279
(B) 283
(C) 308
(D) 318
(E) 338
Rationale: Other number =	(11 x 7700)/275= 308. Answer : C
Answer: (C) 308
Question: 9/5 of 11/122 of 8% of 33550 = ?
(A) 432.2
(B) 433.4
(C) 435.6
(D) 436.8
(E) 456.7
Rationale: Explanation :
? = 9x11x8x33550/5x122x100 = 435.6
Answer : Option C
Answer: (C) 435.6
Question: 675.987 - ? + 56.84 =289.654
(A) A)443.173
(B) B)752.804
(C) C)714.642
(D) D)629.906
(E) of these
Rationale: Explanation:
443.173
Answer: Option A
Answer: (A) A)443.173
Question: A is 2 times as fast as B. A alone can do the work in 20 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed?
(A) 23
(B) 22
(C) 21
(D) 24
(E) 26
Rationale: A can finish 1 work in 20 days
B can finish 1/2 work in 20 days - since A is 2 faster than B
This means
B can finish 1 work in 20*2 days = 40 days
Now using the awesome GMAT formula when two machines work together they can finish the job in = AB/ (A+B) = 20*40/(20+40) = 13 days
Since they alternate on days, it will take them double this time so total time = 13 * 2 = 26 days
So answer is E
Answer: (E) 26
Question: A committee that includes 12 members is about to be divided into 4 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is Annie also a member?
(A) 34%
(B) 30%
(C) 26%
(D) 22%
(E) 18%
Rationale: Michael is a member of one of the subcommittees.
P(Annie is on the same subcommittee) = 2/11 which is about 18%.
The answer is E.
Answer: (E) 18%
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
(A) 81000
(B) 22887
(C) 26877
(D) 26771
(E) 17121
Rationale: 64000* 9/8 * 9/8 = 81000
Answer:A
Answer: (A) 81000
Question: The average of six numbers is X and the average of three of these is Y.If the average of the remaining three is Z, then
(A) x = y + z
(B) 2x = y + z
(C) x = 2y + 2z
(D) None of these
(E) Cannot be determined
Rationale: Solution
Clearly, we have	X =(3y+3z/6)
or
2x= y + z
Answer B
Answer: (B) 2x = y + z
Question: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If k and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of k and n?
(A) -200
(B) -130
(C) -104
(D) 51
(E) 305
Rationale: 2 standard deviations from the average is from mean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:
-51 < k < 151
-51 < n < 151
-102 < k+n < 302.
Only option D is in this range.
Answer: D.
Answer: (D) 51
Question: A certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 120 miles at 60 mph?
(A) 15%
(B) 20%
(C) 25%
(D) 27%
(E) 40%
Rationale: Total time for travelling 120 miles @ 60 mph = 120/60 = 2 hour = 120 minutes.
Given, the car uses 1 gallon for every 40 minutes of driving @ 60 mph. Thus in 120 minutes it will use = 3 gallons. Thus, full tank = 3+8 = 11 gallons --->3/11= 27% of the fuel used. D is the correct answer.
Answer: (D) 27%
Question: At what rate percent on simple interest will Rs.650 amount to Rs.950 in 5 years?
(A) 3.33%
(B) 5.93%
(C) 4.33%
(D) 5.33%
(E) 9.23%
Rationale: 300 = (650*5*R)/100
R = 9.23%
ANSWER:E
Answer: (E) 9.23%
Question: The sum of the non-prime numbers between 20 and 30, non-inclusive, is
(A) 173
(B) 185
(C) 197
(D) 209
(E) 221
Rationale: sum of consecutive integers from 21 to 29, inclusive ====> (A1 + An)/2 * # of terms = (21 + 29)/2 * 9 = 25 * 9 = 225
sum of non-prime numbers b/w 20 and 30, non inclusive ===> 225 - 52 (i.e., 23 + 29, being the prime #s in the range) =173
Answer: A
Answer: (A) 173
Question: Two cars are driving toward each other. The first car is traveling at a speed of 100 km/h, which is 20% slower than the second car's speed. If the distance between the cars is 1125 km, how many hours will it take until the two cars meet?
(A) 4
(B) 4.5
(C) 4.8
(D) 5
(E) 5.5
Rationale: The speed of the first car is 100 km/h.
The speed of the second car is 100 / 0.8 = 125 km/h.
The two cars complete a total of 225 km each hour.
The time it takes the cars to meet is 1125 / 225 = 5 hours.
The answer is D.
Answer: (D) 5
Question: In an hour a boat goes 10 Km along the stream and 4 Km against the stream. The speed of the boat in still water (in Kmph) is:
(A) 7 Kmph
(B) 8 Kmph
(C) 10 Kmph
(D) 12 Kmph
(E) None of these
Rationale: Explanation:
Let the speed of stream = X Kmph
and the speed of water = 8 Kmph
X + Y = 10
X - Y = 4
X = 7, Y = 3
Speed of stream = 7 Kmph
Answer: Option A
Answer: (A) 7 Kmph
Question: Jim is now twice as old as Fred, who is eight years older than Sam. Four years ago, Jim was four times as old as Sam. How old is Jim now?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 52
Rationale: J = 2F = 2(S+8) = 2S+16
J-4 = 4*(S-4)
(2S+16)-4 = 4S-16
S = 14 and so J = 44
The answer is C.
Answer: (C) 44
Question: A firm of ready made garments makes both men’s and women’s shirts. Its average profit is 6% of the sales. Its profit in men’s shirts average 8% of the sales and women’s shirts comprise 60% of the output. The average profit per sale rupee in women shirts is
(A) 0.0466
(B) 0.0666
(C) 0.0166
(D) 0.0366
(E) None of these
Rationale: Women's shirt comprise 60% of the output.
∴ Men's shirts comprise (100 – 60) = 40% of the output.
∴ Average profit from men's shirt = 8% of 40 = 3.2 out of 40
Overall average profit = 6 out of 100
∴ Average profit from women's shirts = 2.8 out of 60
i.e. 0.0466 out of each shirt.
Answer A
Answer: (A) 0.0466
Question: In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows.
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 32 more than twice the number of heads
=> 2(d + 2c) = 32 + 2(c + d)
=> d + 2c = 16 + c + d
=> 2c = 16 + c
=> c = 16
i.e., total number of cows = 16
Answer is C.
Answer: (C) 16
Question: A man is 30 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
(A) 16
(B) 19
(C) 15
(D) 20
(E) 28
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 30) years.
(x + 30) + 2 = 2(x + 2)
x + 32 = 2x + 4
=> x = 28 .
Answer: E
Answer: (E) 28
Question: A man buys a scooter for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the scooter?
(A) Rs. 1240
(B) Rs. 1190
(C) Rs. 1090
(D) Rs. 1130
(E) Rs. 1330
Rationale: SP=1400×85/100=14×85=1190
Answer : Option B
Answer: (B) Rs. 1190
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 978
(B) 789
(C) 999
(D) 778
(E) 787
Rationale: a2 = 3136
=> a = 56
56 * 4 * 3
= 672 – 6
= 666 * 1.5
= 999
Answer: C
Answer: (C) 999
Question: Pipe A runs 10 liters of water per minute into a tank that has a total volume of 1,200 liters. Pipe B fills an half the tank in 1 hours.
Working together how long will it take both pipes to fill the tank ?
(A) 2 hours and 36 minutes
(B) 1.5 hours
(C) 9 hours and 12 minutes
(D) 15 hours
(E) 1 hour and 12 minutes.
Rationale: Pipe A has a rate of 10 liters per minute which equals a rate of 600 liters per hour.
Pipe B has a rate of 400 liters per hour.
400 + 600 (A+B) = Together they have a rate of 1000 liters per hour.
1200 (The tank ) / 1000 = 6/5 = 1 hour and 12 minutes
Answer -E
Answer: (E) 1 hour and 12 minutes.
Question: Nine family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
(A) 7080
(B) 8080
(C) 9080
(D) 10,080
(E) 11,080
Rationale: Let's consider Michael and Bobby as one unit.
There are 8! possible arrangements of 8 units.
Around a table, there would be repetitions of each arrangement, so we divide by 8.
Then there are 7! arrangements around a circular table.
For each arrangement, Michael and Bobby can switch places, so we multiply by 2.
The number of arrangements is 7!*2 = 10,080.
The answer is D.
Answer: (D) 10,080
Question: Of the integers between 100 and 999, inclusive, how many do not have digit 3 and 5?
(A)  310
(B)  320
(C)  448
(D)  428
(E)  528
Rationale: Options for the first digit 9-2(2 and 5)=7;
Options for the second digit 10-2=8;
Options for the third digit 10-2=8;
Total numbers possible 7*8*8=320.
Answer: C.
Answer: (C)  448
Question: If 3x=6y=z, what is x+y, in terms of z?
(A) z/2
(B) 2z
(C) z/3
(D) 3z/5
(E) z/9
Rationale: 3x=6y=z
x = z/3
and y = z/6
x+y = z/3 + z/6 = z/2
Answer is A
Answer: (A) z/2
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 12 ways
(B) 14 ways
(C) 30 ways
(D) 61 ways
(E) 51 ways
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= 4C2 * 5C1
= (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Answer: (C) 30 ways
Question: If the cost price of 8 articles is the same as the selling price of 10 articles. Find the gain or loss percentage?
(A) 20% gain
(B) 20% loss
(C) 30% gain
(D) 30% loss
(E) 40% loss
Rationale: Explanation:
Ex:-
2X = 3Y
X = 3
Y = 2
12 cp = 15 sp
Cost price CP = 15
Selling price SP = 12
Formula = (SP-CP)/CP * 100 = (12 - 15)/10 * 100 = 30 % Loss
Answer: Option D
Answer: (D) 30% loss
Question: If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years?
(A) (1+k/100)^n
(B) (1+k)^n
(C) (1+kn/100)
(D) (1+k/100)^4n
(E) (1+kn)
Rationale: Amount after 7n years will be = x ( 1 + k/100)^4n
Amount after 3n years will be = x ( 1 + k/100)^3n
So, required ratio will be -
{ x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n
Hence answer will be a. (1+k/100)^4n
D
Answer: (D) (1+k/100)^4n
Question: A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase Q in sales?
(A)  2%
(B)  17%
(C)  20%
(D)  65%
(E)  83%
Rationale: Last year's sales = $320 million;
This year's sales = $385 million;
Increase Q = $65 million.
Now, 20% of $320 million is $64 million, which is very close to actual increase of $65 million.
Answer: C.
Answer: (C)  20%
Question: How many seconds will a train 130 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 28 sec
(B) 23 sec
(C) 24 sec
(D) 25 sec
(E) 26 sec
Rationale: D = 130 + 150 = 280
S = 36 * 5/18 = 10 mps
T = 280/10 = 28 sec
A
Answer: (A) 28 sec
Question: The total cost of a vacation was divided among 4 people. If the total cost of the vacation had been divided equally among 5 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?
(A) $200
(B) $300
(C) $400
(D) $500
(E) $1000
Rationale: C for cost.
P price per person.
C= 4*P
C=5*P-250
Substituting the value of P from the first equation onto the second we get P = 250.
Plugging in the value of P in the first equation, we get C= 1000. Which leads us to answer choice E
Answer: (E) $1000
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) 2661
(B) 1651
(C) 1267
(D) 1627
(E) 1261
Rationale: Explanation:
A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer:E
Answer: (E) 1261
Question: Truck P and Truck Q drive on the highway in the same direction at respective rates of 72 kph and 80 kph. If Truck Q is 5 km behind Truck P, by how much does Truck P need to increase the speed to catch up with Truck P in 30 minutes?
(A) 2 kph
(B) 4 kph
(C) 6 kph
(D) 8 kph
(E) 10 kph
Rationale: Truck Q needs to gain 5 km in 30 minutes.
The relative speed difference needs to be 5 km / 30 minutes = 10 km/hour
Truck Q needs to increase up to 82 kph, thus an increase in 2 kph.
The answer is A.
Answer: (A) 2 kph
Question: If A and B are positive integers, A - 4 is divisible by 4 and B - 2 is divisible by 2, all of the following could be the value of A - B Except?
(A) 4
(B) 8
(C) 10
(D) 14
(E) 3
Rationale: A-4 = 4B
=> A = 4B + 4 = 4,8,12,16,20,24,28,32,36
B-2 = 2A
=> B = 2A + 2 = 2,4,6,8,10,12,14,16,18,20
4 = 8 - 4
8 = 12 - 4
10 = 16 - 6
14 = 32 - 18
So , we can see that all the answer choices are possible here except E
Answer: (E) 3
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 2 : 3?
(A) 16
(B) 50
(C) 277
(D) 92
(E) 11
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.
Answer:B
Answer: (B) 50
Question: Simple interest on a certain sum is 36 over 25 of the sum. Find the rate per cent and time, if both are equal.
(A) 8% and 8 years
(B) 6% and 6 years
(C) 10% and 10 years
(D) 12 % and 12 years
(E) None of these
Rationale: 36â„25P = PÃ—RÃ—R/100
â‡’ R^2 = 3600â„25 â‡’144=> R = 12%
Also, time = 12 years
Answer D
Answer: (D) 12 % and 12 years