mathewhe/aqua_rat huggingface dataset:
Question: Twenty times a positive integer is more than its square by 96, then the positive integer is
(A) 13
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: Explanation:
Let the number be x. Then,
20x = x2 + 96
=> x2 - 20x + 96 = 0
=>(x - 12)(x - 8) = 0
=> x = 8 or 12
Answer: Option D
Answer: (D) 12
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an odd number.
2. Y^(X + Y) is not an integer.
3. X^Y is a positive number.
(A) 1 and 2 only.
(B) 3 only.
(C) 1 and 3 only.
(D) 2 and 3 only.
(E) 1, 2 and 3.
Rationale: Statement I is TRUE
Statement II is TRUE
Statement III is not TRUE
Answer : A
Answer: (A) 1 and 2 only.
Question: 1/0.02 is equal to
(A) 50
(B) 2.5
(C) 25
(D) .25
(E) None of these
Rationale: Explanation:
1/0.02 = (1 * 100)/2 = 100/2 = 50
Option A
Answer: (A) 50
Question: Eighteen years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
(A) 120
(B) 76
(C) 108
(D) 105
(E) 86
Rationale: Let the present ages of the father and son be 2x and x years respectively.
then,(2x-18)=3 (x-18)
x=36.
Required sum =(2x+x)=3x=108 years.
Answer is C
Answer: (C) 108
Question: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount E in 1996 as they paid in 1995?
(A) 33 1⁄3%
(B) 40%
(C) 50%
(D) 66 2⁄3%
(E) 100%
Rationale: water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount E in 1996 as they paid in 1995, water use should decrease in the same ratio
150-> 100 means 1/3 rd= 33(1/3) %.A
Answer: (A) 33 1⁄3%
Question: At Parkin's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
(A) 700
(B) 1000
(C) 1300
(D) 1600
(E) 2000
Rationale: At Parkin's firm's annual revenue grows twice as fast as its costs. First solve for how much revenue is increasing each year:
R2008= R2007*(1+x)
R2009= R2007*(1+x)^2=1.44*R2007
(1+x)^2 = 1.44
1+x=1.2
x=0.2 aka revenue increases 20% each year and cost increases 10% annually
Next solve for R2007and C2007:
R2007= C2007- 1000
1.2*R2007- 1.1*C2007= 0
1.2*[C2007- 1000] - 1.1*C2007= 0
0.1*C2007= 1,200
C2007= 12,000
R2007= 11,000
Finally find 2009 profits:
Profit2009= 1.44*11,000 - 1.21*12,000
Profit2009= 15,840 - 14,520
Profit2009= 1320
Answer: C
Answer: (C) 1300
Question: if a person cover 3/5 part of his journey by train,7/20 part of his journey by bus and rest 6.5 km. by walk.what is total distance of his journey?
(A) 65 km
(B) 100 km
(C) 120 km
(D) 130 km
(E) 75 km
Rationale: let total distance be=x km.then,
3x/5+7x/20+6.5=x;12x+7x+130=20x;x=130
hence total distance=130 km.
answer D
Answer: (D) 130 km
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: F2, __, D8, C16, B32, ... What number should fill the blank?
(A) C6
(B) F3
(C) B5
(D) A1
(E) E4
Rationale: E
E4
The letters decrease by 1; the numbers are multiplied by 2.
Answer: (E) E4
Question: Johnie went up a certain hill at the rate of one and a half kilometers per hour and came down at the rate of four and a half kilometers per hour, so that it took just four hours to make the double journey. How far was it to the top of the hill ?
(A) 3 km
(B) 6 km
(C) 4.5 km
(D) km
(E) none of the above
Rationale: Assume the distance to the top of the hill (1 way) as: x
Now, speed=distance/time => time=distance/speed
So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5.
For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5
Now, the total time for the trip is given as 4 hrs.
Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km
So, the distance one side is = 4.5 km.
The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km
Can someone assist me in understanding where am I wrong here?
Answer: (C) 4.5 km
Question: A man sells a horse for Rs. 620 and loses something, if he had sold it for Rs.860 , his gain would have been double the former loss. Find the cost price of the horse?
(A) 27
(B) 98
(C) 27
(D) 80
(E) 71
Rationale: CP = SP + 1CP = SP - g
620 + x = 860 - 2x
3x = 240 => x = 80
Answer:D
Answer: (D) 80
Question: If 50% of 100 is greater than 20% of a number by 47, what is the number?
(A) 60
(B) 30
(C) 15
(D) 75
(E) 100
Rationale: Explanation:
50/100 * 100 - 20/100 * x = 47
50 - 20/100 * x = 47
3 = 20/100 * x
3 * 100 / 20 = x
15 = x
Answer: Option C
Answer: (C) 15
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
(A) 15 m,15 m
(B) 15 m,90 m
(C) 16 m,10 m
(D) 15 m,10 m
(E) 15 m,30 m
Rationale: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer:D
Answer: (D) 15 m,10 m
Question: P and Q are the only two applicants qualified for a short-term research project that pays 420 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?
(A) $3
(B) $5
(C) $7
(D) $9
(E) $11
Rationale: Let Q's hourly wage be x, then P's hourly wage is 1.5x
Let T be the number of hours that Q needs, then P needs T-10 hours to do the job.
Since they both are paid an equal total amount of $420:
x*T=1.5x*(T-10)
T = 30 hours and Q's hourly wage is 420/30 = $14
P's hourly wage is 420/(T-10) = $21 which is $7 per hour more.
The answer is C.
Answer: (C) $7
Question: Complete the series 20, 19, 17, ...., 10, 5
(A) 2
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 20 - 1 = 19
19 - 2 = 17
17 - 3 = 14
14 - 4 = 10
10 - 5 = 5
Answer is C.
Answer: (C) 5
Question: A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 50% have red flags, what percentage of children have flags of both the colors?
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) It can not be determined
Rationale: Solution: let the total number of flags be 100(even number)
let the total number of 'blue' flags alone be 'a'
let the total number of 'red' flags alone be 'b'
let the total number of 'both' flags be 'c'
We have given,
total number of blue flags = 60% = 60 = a+c
total number of red flags=50%=50=b+c
total number of flags = a+b+c=100 (since all the flags have been utilized)
So, substituting for c in the third equation, we have,
60-c+c+50-c=100
c=10
Option B.
Answer: (B) 10%
Question: A car is 15 minutes late by running at a speed of 4/5th of its actual speed. The actual time taken by the car to cover that distance is:
(A) 30 minutes
(B) 1 hour
(C) 2 hours
(D) 3 hours
(E) None of these
Rationale: Explanation :
New speed=4/5th of its actual speed
New time=5/4th of its actual time
=> 5/4t-t=15/60=1/4
=> 1/4t=1/4
=> t=1hour
Answer : B
Answer: (B) 1 hour
Question: Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $45,000 higher than Store B's revenues. In the second month, Store A's revenues were $8,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue?
(A)  $14,000
(B)  $15,000
(C)  $42,000
(D)  $47,000
(E)  $50,000
Rationale: Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +45 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +8 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T):
(45 + 8 + T)/3 = 2
53 + T = 6
T = -47
Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -47 represents a $47,000 advantage in favor of Store B. Choice (D) is correct.
Answer: (D)  $47,000
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is:
(A) 32 years
(B) 36 years
(C) 38 years
(D) 40 years
(E) 45 years
Rationale: Explanation:
Let Rajan's present age be x years.
Then, his age at the time of marriage = (x - 8) years.
x = 6/5 (x - 8)
5x = 6x - 48 => x = 48
Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.
Rajan's sister's present age = (30 + 8) = 38 years.
ANSWER IS C
Answer: (C) 38 years
Question: A train running at the speed of 20 m/s crosses a pole in 24 sec less than the time it requires to cross a platform thrice its length at the same speed. What is the length of the train?
(A) 150 m
(B) 200 m
(C) 180 m
(D) 160 m
(E) 170 m
Rationale: Let the length of the train be x m.
So, the length of the platform = 3x m.
Time taken in crossing the platform = 4x/20sec
Time taken in crossing the pole = x/20 sec
â‡’x/20+24=4x/20
x = 160 m
Answer : D
Answer: (D) 160 m
Question: Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days.?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 22
Rationale: g= grass initially, r= rate at which grass grow/day, c= cow eat grass/day
g+24r=70*24c=1680c-----------1
g+60r=60*30c=1800c--------->g=1800c-60r----------------2
by solving this 2 equation we have relation c=(3/10)r-------------3
g+96r=96nc
=>96nc=1800c-60r+96r=1800c+36r=1800c+120c=1920c
=>n=20
ANSWER:D
Answer: (D) 20
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 14
To be divisible by three the sum of the digits must be divisible by 3. Highest number made by these digits is 75 that is divisible. We count down the selections from there and see what is feasible.
75-yes
72 -yes
69 and 66 -no
63 - yes
60 -no
57, 54, and 51 -yes
48 - no
45 and 42 - yes
39 - no
36 - yes
33 and 30 - no
27, 24, and 21 - yes
18 -no
15 and 12 yes
Correct answer is E.
Answer: (E) 14
Question: A store owner estimates that the average price of type A products will increase by 40% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
(A) $14,755
(B) $15,430
(C) $16,000
(D) $16,225
(E) $17,155
Rationale: cost of type A products next year = 1.40 * 4500 = 6300
cost of type B products next year = 1.1 * 8300 = 9130
total 6300 + 9130 = 15430 option B
Answer: (B) $15,430
Question: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
(A) 7
(B) 10
(C) 12
(D) 5
(E) 14
Rationale: B
Answer: (B) 10
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize o n atleast one ticket is?
(A) 0.5919
(B) P(E)=0.5904
(C) 0.5929
(D) 0.5928
(E) 0.594
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Answer: (B) P(E)=0.5904
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
(A) 1750
(B) 1900
(C) 8600
(D) 10300
(E) 1200
Rationale: Explanation:
65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
ANSWER IS B
Answer: (B) 1900
Question: What is the sum of the greatest common factor and the lowest common multiple of 12 and 48?
(A) 20
(B) 60
(C) 40
(D) 56
(E) 20
Rationale: Prime factorization of 12 = 2 x 2 x 3
Prime factorization of 48 = 2 x 2 x 2 x 2 x 3
GCF = 12
LCM = 48
Sum = 60
Ans: B
Answer: (B) 60
Question: The units digit of (35)^(7) + (93)^(45) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: any power of anything ending in 5 always has a units digit of 5. So the first term has a units digit of 5. Done.
The second term takes a little more work. We can ignore the tens digit, and just treat this base as 3. Here is the units digit patter for the powers of 3.
3^45 has a units digit of 3
Of course 5 + 3 = 8,
D
Answer: (D) 8
Question: The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.
(A) 8.04kg
(B) 8.14kg
(C) 8.24kg
(D) 9.04kg
(E) None of these
Rationale: Explanation:
Volume of the metal used in the box = External Volume - Internal Volume
= [(50 x 40 x 23) - (44 x 34 x 20)] cm3
= 16080 cm3
Weight of the metal =[(16080 x 0.5)/1000] kg = 8.04 kg.
Answer: A
Answer: (A) 8.04kg
Question: What is the average of first 21 multiples of 7 ?
(A) 67
(B) 69
(C) 77
(D) 79
(E) 81
Rationale: Required average = 7(1+2+....+21) / 21
(7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 77
C
Answer: (C) 77
Question: A room 14 m 21 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
(A) 22636
(B) 22640
(C) 22647
(D) 22533
(E) 22675
Rationale: Explanation:
Area of the room = (1421 x 777) cm2.
Size of largest square tile = H.C.F. of 1421 cm and 777 cm = 7 cm.
Area of 1 tile = (7 x 7) cm2.
Number of tiles required =(1147×777)/(7×7)=22533
Answer: Option D
Answer: (D) 22533
Question: The ratio of male to female in a class is 4:6. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
(A) a)160 degree
(B) b) 168 degree
(C) c)191 degree
(D) d)192 degree
(E) e)204 degree
Rationale: here is my approach => males => 3x and females =7x => total =10x
now 10x=> 360
therefore 17x/3 => 204 degree .
P.S => 17x/3 is nothing but total number of students with the given preference
Answer E
Answer: (E) e)204 degree
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is
(A) 86
(B) 90
(C) 92
(D) 94
(E) 96
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86.
A
Answer: (A) 86
Question: The speed at which a girl can row a boat in still water is 30 kmph. If she rows downstream, where the speed of current is 6 kmph, what time will he take to cover 240 metres?
(A) 21
(B) 22
(C) 23
(D) 20
(E) 24
Rationale: Speed of the boat downstream = 30 + 6 = 36 kmph
= 36 * 5/18 = 10 m/s
Hence time taken to cover 240 m = 240/10 = 24 seconds.
Answer: E
Answer: (E) 24
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda spends 60% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?
(A) 1/2 m
(B) 1/3 m
(C) 1/4 m
(D) 1/5 m
(E) 1/6 m
Rationale: After the final transaction:
Angela received $(m-n) for t hours;
Linda received $(m+n) for 1.5t hours;
We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/4.
Answer: C
Answer: (C) 1/4 m
Question: Teja can do a piece of work in 15 days .Ravi is 20% is more efficient than sakshi. the number of days taken by Tanya to do the same piece of work is?
(A) 17 days
(B) 25 days
(C) 12 days
(D) 15 days
(E) 20 days
Rationale: The ratio of times taken by Teja and Ravi=120:100=6:5
suppose Teja takes x days to do the work.
6:5::20:x
x=(5*20)/6 work in 17 days
Answer(A)
Answer: (A) 17 days
Question: During a certain two-week period, 64 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
(A) 10A
(B) 12A
(C) 14A
(D) 16A
(E) 18A
Rationale: Total movies = 100.
Comedies = 64.
Action + Drama = 36. Since there were 5 times as many dramas as action movies, then Action + 5*Action = 36 --> Action = A = 6.
Comedies = 60 = 10A.
A
Answer: (A) 10A
Question: In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party
(A) 14
(B) 12
(C) 13
(D) 15
(E) 16
Rationale: Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by nC2.
Now, according to the question,
nC2 = 105;
Or, n!/[2!*(n-2)!] = 105;
Or, n*(n-1)/2 = 105;
Or, n2-n = 210;
Or, n2-n-210 = 0;
Or, n = 15, -14;
But, we cannot take negative value of n.
So, n = 15 i.e. number of persons in the party = 15.
ANSWER D
Answer: (D) 15
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
(A) 1245
(B) 1340
(C) 1349
(D) 1450
(E) 1540
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349
Question: The population of a town increased from 1,62,500 to 2,62,500 in a decade. The average percent increase of population per year is :
(A) 4.37%
(B) 5%
(C) 6.154%
(D) 8.75%
(E) None of these
Rationale: Solution
Increase in 10 year= (262500 - 162500) = 100000.
Increase% =( 100000/162500x 100 )% = 61.54%
âˆ´ Required average = ( 61.54/10 )% =6.154%
Answer C
Answer: (C) 6.154%
Question: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 4 ½ sec
(B) 7 ½ sec
(C) 9 ½ sec
(D) 8 ½ sec
(E) 2 ½ sec
Rationale: D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 ½ sec
Answer:D
Answer: (D) 8 ½ sec
Question: 469157 * 9999
(A) 1691100843
(B) 4591100843
(C) 4691100843
(D) 3691100843
(E) None of these
Rationale: Explanation:
469157 * (10000 - 1)
= 4691570000 - 469157
= 4691100843
Option C
Answer: (C) 4691100843
Question: A man goes 10 km against the current of the stream in 5 hr and goes 5 km along the stream in 1hour. How long will it take to go 5 km in stationary water?
(A) 1hr 30min
(B) 1hr 12min
(C) 2hr
(D) 2hr 15min
(E) 3hr
Rationale: Speed up stream = 10/5 = 2 km/hr
Speed down stream = 5/1 = 5 km/hr
Speed in still water = 1/2(2+5) = 7/2 = 3.5 km/hr
Time taken to travel 5 km in still water is = 5/7/2 = 10/7 = 1hr 12min
Answer is B
Answer: (B) 1hr 12min
Question: A rectangular floor is covered by a rug except for a strip X meters wide along each of the four edge. If the floor is L meters by B meters, what is the area of the rug in square meters?
(A) (L-2X)(B-2X)/2
(B) 2*(L-2X)(B-2X)
(C) (L-2X)(B-2X)/3
(D) (L-2X)(B-2X)
(E) (L-2X)(B-2X)/4
Rationale: A strip of X meters is covering the inner rectangular rug for all 4 sides.
Length of inner rug = L-(2X)
breadth of inner rug= B-(2X)
Area of Rug= (L-2X)(B-2X)
Ânswer: D
Answer: (D) (L-2X)(B-2X)
Question: How many multiples of 4 are there between 64 and 256 ?
(A) 47
(B) 49
(C) 42
(D) 41
(E) 40
Rationale: It should be mentioned whether 64 and 256 are inclusive.
If 64 and 256 are inclusive, then the answer is (256-64)/4+1=49.
If 64 and 256 are NOT inclusive, then the answer is (252-68)/4+1=47.
Since OA is A, then we have NOT inclusive case.
Answer: (A) 47
Question: Of the 1000 inhabitants of a town, 60 % are males of whom 120 % are literate. If, of all the inhabitants, 25% are literate, then what percent of the females of the town are literate ?
(A) 32.5 %
(B) 32.9 %
(C) 92.5 %
(D) 38.5 %
(E) 37.5 %
Rationale: Explanation:
Number of males = 60% of 1000 = 600. Number of females = (1000 - 600) = 400.
Number of literates = 25% of 1000 = 250.
Number of literate males = 20% of 600 = 120.
Number of literate females = (250 - 120) = 130.
Required pecentage = (130/400 * 100 ) % = 32.5 %.
Answer: A) 32.5 %
Answer: (A) 32.5 %
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 45
(B) 44
(C) 64
(D) 63
(E) 92
Rationale: Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: Option B
Answer: (B) 44
Question: a = 7^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: This is a tricky worded question and I think the answer is should be D not C...
Here is my reason :
The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime
Number has no factor grater than 1 and Itself .
On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )
AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is
An integer . so, X COULD Be ( not Must be) 5 , 31 ,or 2 !!! so , X could get 4 different values and answer is E....
Answer: (E) Four
Question: Find the principle on a certain sum of money at 5% per annum for 6 years if the amount being Rs.1120?
(A) 862
(B) 1067
(C) 1977
(D) 1056
(E) 1097
Rationale: 1120 = P [1 + (5*6)/100]
P= 862
Answer: A
Answer: (A) 862
Question: A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 4 months and 7 months respectively. What was the ratio of their investments?
(A) 10:12:14
(B) 12:24:28
(C) 20:22:12
(D) 10:49:32
(E) None of these
Rationale: Explanation :
Ratio in which A,B and C shared the profit = 5 : 7 : 8
Assume that the ratio of their investment = a:b:c
Then 14a : 4b : 7c = 5 : 7 : 8
Good to go, we got the equation. Now it's a matter of time to find a, b and c
14a/4b = 5/7
=> 98a = 20b
=> b = 98a/20 = 49a/10 ---(1)
14a/7c =5/8
=> 2a/c =5/8
=> 16a = 5c
=> c = 16a/5 ---(2)
a : b : c = a : 49a/10 : 16a/5 = 1 : 49/10 : 16/5 = 10 : 49 : 32. Answer : Option D
Answer: (D) 10:49:32