mathewhe/aqua_rat huggingface dataset:
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 60 percent of those who attended the meeting were stockholders and 47 percent were employees, what percent were stockholders who were not employees?
(A)  34%
(B)  38%
(C)  45%
(D)  53%
(E)  62%
Rationale: Let M represent the number of meeting attendees. Then, since 60% of M or 0.60M
were stockholders and 47% of M or 0.47M were employees, it follows that 0.60M +
0.47M = 1.07M were either stockholders, employees, or both. Since 1.07M exceeds
M, the excess 1.07M − M = 0.07M must be the number of attendees who were both
stockholders and employees, leaving the rest 0.60M − 0.07M = 0.53M, or 53%, of
the meeting attendees to be stockholders but not employees.
The correct answer is D.
Answer: (D)  53%
Question: The average weight of 5 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
(A) 76 kg
(B) 77 kg
(C) 72.5 kg
(D) Data inadequate
(E) None of these
Rationale: total weight increases = 5 × 1.5 = 7.5 kg
so the weight of new person = 65 + 7.5 = 72.5 kg
Answer C
Answer: (C) 72.5 kg
Question: A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 5 people to travel x miles if he decides to give them a 50% discount?
(A) xr/40
(B) 3x/200r
(C) 3r/200x
(D) 3xr/200
(E) xr/600
Rationale: 1 person for x miles = xr cents
5 person for x miles = 5xr
After discount 50% = 5xr/2 cents
In dollars = 5xr/200= xr/40
Answer : A
Answer: (A) xr/40
Question: n a 1000m race, if A gives B a start of 40m, A wing by 19sec. But if A gives B start of 30sec, B wins by 40m.
Find the time taken by B to run 1000m race?
(A) 125
(B) 130
(C) 140
(D) 150
(E) 160
Rationale: then 960/B -1000/A = 19 => 24/B - 25/A = 19/40
and 1000/B - 960/A = 30 => 25/B - 24/A = 30/40
solving equation A speed =8 and B=20/3
for 1000m b will take 1000/20/3= 125 sec
A
Answer: (A) 125
Question: If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)?
(A) 85/365∗84/364
(B) 13/65∗13/64
(C) 1 - 85!/365!
(D) 1 - {365!}/{280!(365^8^5)}
(E) 1 - 85!/(365^8^5)
Rationale: Probability(At Least 2 share a bday) = 1 - Probability(All 85 have distinct birthdays)
total ways to pick 85 birthdays = 365^85
Ways to pick distinct 85 out of the 365 & distribute it to 85 people = C(365,85)*85!
Hence Probability = 1−365!/280!36585
ANswer is D
Answer: (D) 1 - {365!}/{280!(365^8^5)}
Question: The radius of a cylinder is 10 m, height 15 m. The volume of the cylinder is:
(A) 2200
(B) 5500
(C) 3300
(D) 1100
(E) 4714.3
Rationale: Cylinder volume = Ï€r(power2)h
= 22/7 Ã— 10 Ã— 10 Ã— 15
= 4714.3 m(power3)
Answer is E.
Answer: (E) 4714.3
Question: A doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage lesser than the typical dosage?
(A) 8%
(B) -25%
(C) 11%
(D) 12.5%
(E) 14.8%
Rationale: Typical dosage per 15 pound of the body weight = 2 c.c
Typical dosage per 120 pound of the body weight = 2 *(120/15)
= 2 * 8
= 16 c.c
Dosage prescribed by doctor for 120 pound patient = 12 c.c
% prescribed dosage greater than the typical dosage = (12-16/16) *100%
=(-4/16) *100%
= -25%
Answer B
Answer: (B) -25%
Question: If the simple interest on Rs.3100 amount to Rs. 632.40 in 2 Years, What is the rate percent?
(A) 11.2%
(B) 10.2%
(C) 12.2%
(D) 13.2%
(E) 18.2%
Rationale: $632.40 = (3100*2*R)/100
R = 10.2%
Answer: B
Answer: (B) 10.2%
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
(A) 22
(B) 27
(C) 20
(D) 288
(E) 21
Rationale: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
Answer: A
Answer: (A) 22
Question: There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar books in my bookshelf. The books are randomly arranged in the shelf and not at all in the order of their type. What is the least number of books that must be drawn from the shelf in order to get 6 books of a particular type?
(A) a)	20
(B) b)	23
(C) c)	25
(D) d)	28
(E) e)	None of these
Rationale: Indeed the answer is A. for the reason explained above
Answer: (A) a)	20
Question: A person purchased a TV set for Rs. 18000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 46000. What percentage of profit did he make?
(A) 100%
(B) 90%
(C) 140%
(D) 115%
(E) 120%
Rationale: The total CP = Rs. 18000 + Rs. 5000
= Rs. 2300 and SP
= Rs. 46000
Profit(%)
= (46000 - 23000)/23000 * 100
= 100%
Answer:A
Answer: (A) 100%
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
(A) 23.99 cm
(B) 18.98 cm
(C) 16.98 cm
(D) 17.87 cm
(E) 23.57 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer: E
Answer: (E) 23.57 cm
Question: The smallest number which when diminished by 5, is divisible by 12, 16, 18, 21 and 28 is
(A) 1008
(B) 1013
(C) 1022
(D) 1032
(E) 1043
Rationale: Required Number = (L.C.M of 12, 16, 18,21,28)+5
= 1008 + 5
= 1013
Answer: B
Answer: (B) 1013
Question: A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?
(A) m:27.50 w:22.22
(B) m:27.50 w:22.50
(C) m:27.50 w:22.20
(D) m:23.50 w:22.50
(E) m:27.50 w:21.50
Rationale: Explanation:
Let the daily wage of a man be Rs. x.
Then, daily wage of a woman = Rs. (x - 5).
Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50.
Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50
Answer: B
Answer: (B) m:27.50 w:22.50
Question: How much time will take for an amount of Rs. 75 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 22
(B) 19
(C) 15
(D) 30
(E) 24
Rationale: Time = (100 * 81) / (75 * 4.5) = 24 years'
Answer:E
Answer: (E) 24
Question: In how many ways can 10 different gifts be divided among four children such that each child receives exactly two gifts?
(A) 16^4
(B) (4!)^4
(C) 10!/(2!)^4
(D) 16!/4!
(E) 4^16
Rationale: Total 10 different Gifts, and 4 children.
Thus any one child gets 10C2 gifts,
then the other child gets 8C2 gifts(10 total - 2 already given),
then the third one gets 6C2 gifts,
and the last child gets 4C2 gifts.
Since order in which each child gets the gift is not imp, thus, ans :
10C2 * 8C2 * 6C2 * 4C2 = 10! / (2!)^4
Ans : C.
Answer: (C) 10!/(2!)^4
Question: There are 11 software engineers and 7 civil engineers in a company. Theyare selecting member for row. In how many ways can they be seated in a row so that no two of the civil engineers will sit together?
(A) 10!×11!/5!
(B) 9!×11!/4!
(C) 11!×12!/5!
(D) 9!×5!/4!
(E) 5!×6!/7!
Rationale: 11 software engineers can be arranged in 11! ways. ...(A)
Now we need to arrange civil engineers such that no two civil engineers can be seated together. i.e., we can arrange 7 civil engineers in any of the 12 (=11+1) positions marked as * below.
* 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 *
(where 1, 2… 11 represent software engineers)
This can be done in 12P7 ways. ...(B)
From (A) and (B),
required number of ways
= 11! × 12P7
=11!×12!/5!
C
Answer: (C) 11!×12!/5!
Question: If Albert’s monthly earnings rise by 20%, he would earn $560. If, instead, his earnings rise by only 21%, how much (in $) would he earn this month?
(A) 643
(B) 652
(C) 660
(D) 564
(E) 693
Rationale: =560/1.2∗1.21
=564=564
Answer is D
Answer: (D) 564
Question: If x is a positive integer, and two sides of a certain triangle have lengths x+2 and x+2 respectively, which of the following could be the length of the third side of the triangle?
I. x + 1
II. x + 5
III. 2x + 1
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II and III
Rationale: Let the third side of triangle be AB.
Triangle rule states that:
Difference of other 2 sides < any side < sum of other two sides
So x+2 - (x+2) < AB < x+2 + (x+2)
i.e. 0 < AB < 2x + 4
Let's take x =1 :
So 0 < AB < 6
Check if any of the answers are between 0 and 4.
I: x+1 = 2 ; could be a possible value.
II: x+5 = 6 ; could not be a possible value.
III: 2x+1 = 3; could be a possible value.
I, II and III could not be a possible value.
Answer: D
Answer: (D) I and III only
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 972 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 9
(D) Cannot be determined
(E) None of these
Rationale: let rate = R% and time = R years
Then ( 1200 x R x R /100) = 972
=> 12R2= 972
=> R2= 81
=> R= 9
Answer C
Answer: (C) 9
Question: The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 80 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?
(A) 75%
(B) 80%
(C) 100%
(D) 150%
(E) 159.2%
Rationale: Let length of each side of square A be 10
Area of A = 10^2 = 100
Since , length of each side of square A is increased by 100 percent to make square B
length of each side of square B = 2*10 = 20
Area of B = 20^2 = 400
Since , length of the side of square B is increased by 80 percent to make square C
length of each side of square C= 1.8*20 = 36
Area of C= 36^2 = 1296
Difference in areas of C and cummulative areas of A and B = 1296 -(400+100) = 796
percent is the area of square C greater than the sum of the areas of squares A and B = (796/500) * 100 % = 159.2%
Answer E
Answer: (E) 159.2%
Question: The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 86, and the average of the female students’ grades was 92, how many female students took the test?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 16
Rationale: Total Marks of male = M
Total Marks of female = F
Number of males = 8
Number of females = f
Given: (M+F)/(8+f) = 90 -------------1
Also given, M/8 = 86 Thus M = 688--------2
Also, F/f = 92 thus F = 92 F - --------3
Put 2 and 3 in 1: we get
(688+92f)/(8+f) = 90
solving this we get f = 16
Ans: E
Answer: (E) 16
Question: Mike's age is 40 years. If he is 4 more than four times the age of his son, find the age of his son.
(A) 20 years
(B) 12 years
(C) 16 years
(D) 9 years
(E) 14 years
Rationale: Let Mike's son age be x.
4+ 4 x = 40
x = 9
Hence Mike's son age is 9 years
Answer : D
Answer: (D) 9 years
Question: Alex has to take a quiz, which has ten true false-type question each carry 1 mark. What is the probability that Alex's can score more than 8 mark in the quiz. Given that he decides to guess randomly on the quiz.
(A) 12/1024
(B) 11/1024
(C) 11/256
(D) 12/256
(E) 14/256
Rationale: Each question has 2 options (True or false). Total number of ways of answering all 10 questions = (2)10(2)10
More than 8 correct means either 9 correct or all correct.
Number of ways such that 9 correct = 10! / 9! = 10
Number of ways of All correct = 1
Therefore, probability of more than 8 correct = 11/(2)1011/(2)10 = 11/1024
ANSWER:B
Answer: (B) 11/1024
Question: A shopkeeper forced to sell at cost price, uses a 950 grams weight for a kilogram. What is his gain percent?
(A) 10%
(B) 9%
(C) 11.11%
(D) 5.26 %
(E) None of these
Rationale: Shopkeeper sells 950g instead of 1000g.
So, his gain = 1000 - 950 = 50g.
Thus, %Gain = (50 *100)/950 = 5.26%.
answer : OPTION D
Answer: (D) 5.26 %
Question: If the ratio of a to b is 2 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?
(A) 4/15
(B) 1/3
(C) 2/15
(D) 4/5
(E) 7/6
Rationale: a:b = 2:3 -- 1
b:c = 1:5
=>b:c = 3 :15 --2
From 1 and 2 , we get
a:c = 2:15
Answer C
Answer: (C) 2/15
Question: The area of a square field is 1600 km2. How long will it take for a horse to run around at the speed of 16 km/h ?
(A) 12 h
(B) 10 h
(C) 8 h
(D) 6 h
(E) None of these
Rationale: Explanation Area of field =1600 km2. Then, each side of field = √1600=40km Distance covered by the horse = Perimeter of square field = 40 × 4 = 160 km ∴ Time taken by horse = distances/peed=160/16=10h Answer B
Answer: (B) 10 h
Question: The speed of a train is 120 kmph. What is the distance covered by it in 8 minutes?
(A) 15 kmph
(B) 11 kmph
(C) 16 kmph
(D) 18 kmph
(E) 12 kmph
Rationale: 120 * 8/60
= 16 kmph
Answer:C
Answer: (C) 16 kmph
Question: A wheel rotates 20 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in one hour?
(A) 4 metre
(B) 12 metre
(C) 240 metre
(D) 2400 metre
(E) 130 metre
Rationale: Number of times wheel moves in 1 hour = 20 * 60 = 1200
:. Distance moves = (1200*20) cms = 24000 cms
In metres = 240 metre
ANSWER:C
Answer: (C) 240 metre
Question: The value of a mobile depreciates at the rate of 5% every year. It was purchased 2 years ago. If its present value is Rs.9025 , its purchase price was
(A) 7500
(B) 8000
(C) 9000
(D) 9500
(E) 10000
Rationale: Explanation:
= Rs.10000
Answer: E
Answer: (E) 10000
Question: Daniel’s only source of income comes from his job as a question writer. In this capacity, Daniel earns a flat salary of $200 per week plus a fee of $7 for every question that he writes. Every year, Daniel takes exactly two weeks of unpaid vacation to visit his uncle, a monk in Tibet, and get inspired for the next year. If a regular year consists of 52 weeks and the number of questions that Daniel wrote in each of the past 5 years was an odd number greater than 20, which of the following could be Daniel’s median annual income over the past 5 years?
(A) $22,474
(B) $25,673
(C) $27,318
(D) $28,513
(E) $31,227
Rationale: Okay u just need less than one min to answer this question. any odd number greater than 20 means that that last digit must be 1,3,5,7, or 9. 7$ per week for every question. So (odd)(odd) will give odd digit. A and C out. (50 weeks) (200) = 10,000. subtract this amount from option B, C and E and u will find that only option B is divisible by 7 (once 10,000 is subtracted from 25673) so its the right choice..B.
Answer: (B) $25,673
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 7 kmph
(B) 4 kmph
(C) 8 kmph
(D) 3 kmph
(E) 5 kmph
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: (B) 4 kmph
Question: If the average weights of three groups of 15,20,25 children respectively is 20,25,30 what is the average weights of all the children?
(A) 32.89
(B) 12.89
(C) 38.76
(D) 25.83
(E) 43.74
Rationale: Average weights of group 1 =20
children in group 1 = 15
Total weights of group 1 = 15*20
Average weights of group 2 = 25
children in group 2 = 20
Total weights of group 2 = 25*20
Average weights of group 3 = 30
children in group 3 = 25
Total weights of group 3 = 25*30
Total children = 15+20+ 25 = 60
Average weights of all the children
=((15*20)+(25×20)+(25×30))/60
=155/6
=25.83
Answer is D.
Answer: (D) 25.83
Question: A certain company consists of 6 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)
(A) 84
(B) 108
(C) 135
(D) 288
(E) 990
Rationale: Total # of teams of 3 possible is 14C3=364
# of teams with only managers or only non-managers is: 6C3+8C3=20+56=76;
# of teams of 3 with at least one manager or at least one non-manager is: 364-76=288.
ANSWER:D
Answer: (D) 288
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 7 family members in a row for the picture?
(A) 9!
(B) 9×8!
(C) 8×9!
(D) 10!/2!
(E) 5x6!
Rationale: In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, 5, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 6!*2! ways.
Total - Restriction =
= 7! - 6!*2! =
= 6!(7 - 2!) =
= 5*6!.
Answer: E.
Answer: (E) 5x6!
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
(A) 22
(B) 86
(C) 68
(D) 55
(E) 23
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86
Answer: B
Answer: (B) 86
Question: On a trip covering 250 km, a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip?
(A) 15.8
(B) 16.3
(C) 16.7
(D) 17.2
(E) 17.5
Rationale: time 1 = 100 / 20 = 5 hours
time 2 = 150 / 15 = 10 hours
total time = 15 hours
average speed = 250 / 15 = 16.7 km/hr
The answer is C.
Answer: (C) 16.7
Question: According to a survey, at least 60% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
(A) 15%
(B) 20%
(C) 25%
(D) 0%
(E) 35%
Rationale: It seems that something is wrong with your answer options.
1) minimum applesbananas:
[XXXXXXXXXXXXXX------] - apples
[-----XXXXXXXXXXXXXXX] - bananas
mimimum ab = 60 - (100-75) = 35%
2) minimum (applesbananas)cherries:
[XXXXXXXXX-----------] - applesbananas
[----XXXXXXXXXXXXXXXX] - cherries
mimimum ab = 35 - (100-80) =15%
A
Answer: (A) 15%
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) 12
(B) 50
(C) 87
(D) 26
(E) 12
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: If an amount of Rs 11,200 is divided equally among
35 students, approximately how much amount will
each student get?
(A) Rs 206
(B) Rs 360
(C) Rs 300
(D) Rs 320
(E) None
Rationale: Amount received by each student = 11,200/35 â‰ˆ Rs
320
Answer D
Answer: (D) Rs 320
Question: Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
(A) 15
(B) 16
(C) 12
(D) 14
(E) 18
Rationale: 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
ANSWER B
Answer: (B) 16
Question: A multi level marketing devised a training program by which a trainer could convince 40 persons every 60 minutes he conducts the program. And in the next 60 minutes those each of those 40 persons will convince 40 persons. If this process is repeated how many people can be trained/convinced by the company in 300 minutes?
(A) 2560000
(B) 102400000
(C) 64000
(D) 5120000
(E) 6120000
Rationale: in first 60 min convinced persons = 40
in next 60 min convinced persons = 40*40
similarly in next 3 intervals no of convinced persons = 40^3, 40^4, 40^5
so total persons convinced in last 60 min = 40^5 = 102400000
and total no of convinced persons = 40+1600+64000+2560000+102400000
= 105025640
ANSWER:B
Answer: (B) 102400000
Question: 75 60 50 45 30 50 15 ? ?
(A) 0 50
(B) 10 50
(C) 30 25
(D) 25 35
(E) 20 15
Rationale: 75-15=60
again 50
60-15=45
45-15=30
again 50
30-15=15
15-15=0
again 50
then answer is 0 ,50
ANSWER:A
Answer: (A) 0 50
Question: Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number Q is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+Q is odd?
(A)  1/2
(B)  2/3
(C)  3/4
(D)  4/7
(E)  5/8
Rationale: All primes except 2 are odd, thus N must be odd. For N + Q = odd + Q to be odd, Q must be even.
There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.
Therefore the probability that N + Q is odd is 4/7.
Answer: D.
Answer: (D)  4/7
Question: Adam borrowed some money at the rate of 6% p.a. for the first 2years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of $ 11400 at the end of 9years, how much money did he borrow?
(A) $12000
(B) $15000
(C) $14500
(D) $12900
(E) $13200
Rationale: Let the sum borrowed be x
(x*2*6/100)+(x*9*3/100)+(x*14*4/100) = 11400
(3x/25)+(27x/100)+(14x/25) = 11400
95x/100 = 11400
x = 12000
Answer is A
Answer: (A) $12000
Question: How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 31% iodine solution?
(A) 35
(B) 42
(C) 100
(D) 105
(E) 140
Rationale: Solution 1:
Assume the iodine solution to be mixed = x lts.
Iodine = 0.4x lts, Water = 0.6x lts.
Solution 2: 35 liters of a 20% iodine solution
Iodine = 7 lts, Water = 28 lts.
Total iodine = 0.4x + 7
Total water = 0.6x + 28
The resultant is a 35% idoine solution.
Hence (0.4x + 7) / (x + 35) = 31/100
40x + 700 = 31x + 1085
9x = 385
x = 42 lts
Correct Option: B
Answer: (B) 42
Question: If 6 men and 2 boys working together, can do five times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 2:5
(B) 2:3
(C) 2:8
(D) 3:1
(E) 3:2
Rationale: 6M + 2B = 5(1M + 1B)
6M + 2B = 5M + 5B
1M = 3B
The required ratio of work done by a man and a boy = 3:1
Answer:D
Answer: (D) 3:1
Question: Ages of two persons differ by 24 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
(A) 12,28
(B) 14,30
(C) 16,32
(D) 18,42
(E) 19,34
Rationale: Explanation:
Let the age of younger person is x,
Then elder person age is (x+24)
=> 3(x-6) = (x+24-6) [6 years before]
=> 3x-18 = x+18
=> x = 18.
So other person age is x + 24 = 42
Answer: Option D
Answer: (D) 18,42
Question: By investing Rs. 1800 in 9% stock, Syam earns Rs. 120. The stock is then quoted at
(A) Rs.135
(B) Rs. 96
(C) Rs. 85
(D) Rs. 122
(E) Rs. 142
Rationale: Explanation :
Assume that face value = Rs.100.
Dividend per share = Rs.9 (as it is a 9% stock)
By investing Rs. 1800, he earns Rs.120
Investment needed to earn Rs.9 = 1800×9/120 = Rs.135
ie, stock is then quoted (then market value) = Rs.135
Answer : Option A
Answer: (A) Rs.135
Question: If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is
(A) 40
(B) 44
(C) 80
(D) 88
(E) 48
Rationale: according to the given conditions x+y = 22
and x^2+y^2 = 404
now (x+y)^2 = x^2+y^2+2xy
so 22^2 = 404 + 2xy
so xy = 80/2 = 40
ANSWER:A
Answer: (A) 40
Question: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 24 seconds but himself in 8 seconds. Find the length of the train and its speed.
(A) 10 m/sec
(B) 15 m/sec
(C) 11.25 m/sec
(D) 19 m/sec
(E) 25 m/sec
Rationale: If length of train is l and speed of train is s, then
l/s = 8
(l+180)/s = 24
(l+180)/l = 24/8 =3
l+180 =3*l
2*l= 180
l=90 mtrs
s= l/8 = 90/8 = 11.25 m/sec
ANSWER:C
Answer: (C) 11.25 m/sec