divelab/Sys2Bench huggingface dataset:
Question: 145 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
Options:
A)12 liters
B)32 liters
C)41 liters
D)50 liters
E)58 liters
Rationale: Milk = 3/5 * 145 = 87 liters
Water = 58 liters
87 : (58+P) = 3:4
174 + 3P = 348 => P = 58
58 liters of water are to be added for the ratio become 3:4.
Answer:E
Answer: E
Question: In a company 200 persons, working 6 hours per day complete 1/3 rd of the work in 7 days. Employee number of additional persons, working 4 hrs per day, required to complete the remaining work in 15 days is :
Options:
A)60
B)80
C)90
D)70
E)50
Rationale: Explanation :
Solution: Let the number of persons completing the work in 15 days be x.
Work done = 1/3, remaining work = (1-1/3) = 2/3.
less hours per day, more men required (IP)
more work, more men required (DP)
more days, less men required (IP)
hours per day 4 : 6
work 1/3 : 2/3 } : : 200 : x
days 15 : 7
.'. 4*1/3 * 15*x = 6 * 2/3 * 7 * 200
=> 60x = 16800
=> x = 16800/60 = 280.
Additional men required = (280-200) = 80.
Answer : B
Answer: B
Question: Which oif the following is a prime number?
Options:
A)45
B)39
C)27
D)33
E)31
Rationale: Clearly, 31 is a prime number. So choice E is correct.
Answer: E
Question: Find the odd man out. 24,36,52,72,96
Options:
A)52
B)72
C)36
D)24
E)96
Rationale: All except 52 are multiples of 6
Answer is A
Answer: A
Question: A village bank offers 5% compound interest calculated on half-yearly basis. A regular customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount the customer would have gained by the way of interest is:
Options:
A)121
B)130
C)125
D)135
E)140
Rationale: after 1 yr Rs 1600 at 5% at half yearly
P(1+(R/2)/100)^2T = 1600(1+(5/2)/100)^2*1 = 1600(1+1/40)^2--1
amt after 1/2 yr on Rs 1600 at 5%
==> 1600(1+(5/2)/100)^2*1/2 = 1600(1+1/40)--2
total amt after 1 yr from 1 and 2
1600(41/40)(81/40) = 41* 81 = 3321
Comp int = 3321- 3200 = Rs 121
ANSWER A
Answer: A
Question: The cost price of 12 articles is equal to the selling price of 8 articles. What is the profit percent?
Options:
A)40%
B)45%
C)50%
D)55%
E)60%
Rationale: 8*SP = 12*CP
SP = 1.5*CP
The profit percent is 50%.
The answer is C.
Answer: C
Question: A box contains 12 pairs of shoes (24 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
Options:
A)1/190
B)1/23
C)1/19
D)1/10
E)1/9
Rationale: The problem with your solution is that we don't choose 1 shoe from 24, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/23(as after taking one at random there are 23 shoes left and only one is the pair of the first one)=1/23
Answer: B
Answer: B
Question: In a group of ducks and cows, the total number of legs are 20 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)10
B)12
C)13
D)15
E)16
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 20
=> 2x = 20 => x = 10
A
Answer: A
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 5 cm, and the point of contact is 7 cm above the ground, what is the radius of the other ball?
Options:
A)10 cm
B)25/2 cm
C)35/3 cm
D)15 cm
E)none of the these
Rationale: similar triangle properties..
2/r+5 = 5/r-5
giving r = 35/3.
Answer: C
Answer: C
Question: In a factory, an average of 50 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 45 sets/day . The average production per day for day last 5days is ?
Options:
A)20
B)36
C)48
D)50
E)59
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 45 - 25 x 50
= 100
∴ Average for last 5 days = 100 / 5
= 20
A
Answer: A
Question: A machine is bought for Rs.4000/- and sold at a loss of 20% find its selling price?
Options:
A)s.4600/-
B)s.4560/-
C)s.4880/-
D)s.4800/-
E)s.4620/-
Rationale: 100 % ------> 600 (100 * 40 = 4000)
120 % ------> 4800 (120 * 40 = 4800)
Selling price = Rs.4800/-
Option 'D'
Answer: D
Question: Deepa bought a calculator at 30% discount on the listed price. Had she not got the discount, she would have paid 82.50 extra. At what price did she buy the calculator ?
Options:
A)192.5
B)275
C)117.85
D)Cannot be determined
E)None of these
Rationale: List price of calculator
82.50/30×100= 275
Deepa bought calculator in
275 × 0.70 = 192.50
Answer A
Answer: A
Question: If (n+2)!/n!=182, n=?
Options:
A)2/131
B)9
C)10
D)11
E)12
Rationale: (n+2)!/n!= 182
Rewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132
Cancel out terms: (n+2)(n+1) = 132
From here, we might just TEST the answer choices.
Since (14)(13) = 182, we can see that n = 12
E
Answer: E
Question: If the sum of the interior angles of a regular polygon measures up to 720 degrees, then how many sides does the polygon have?
Options:
A)10
B)6
C)12
D)11
E)14
Rationale: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=720
180n - 360 = 720
180n = 1080
n = 1080/180 = 6
ANSWER:B
Answer: B
Question: A train covers a distance in 50 min, if it runs at a speed of 48 kmph on an average. The speed at which the train must run to reduce the time of journey to 40 min will be.
Options:
A)60 kmph
B)45 kmph
C)50 kmph
D)55 kmph
E)70 kmph
Rationale: Time = 50/60 = 5/6 hr
dist = S * T = 48*5/6 = 40 km
Time = 50/60 => new speed = 40*3/2 = 60 kmph
ANSWER A
Answer: A
Question: On a map, 2.5 inches represent 25 miles. How many miles approximately is the distance if you measured 55 centimeters assuming that 1-inch is 2.54 centimeters?
Options:
A)212.5
B)213.5
C)214.5
D)215.5
E)216.5
Rationale: 1 inch = 2.54 cm
2.5 inch = 2.54 * 2.5 cm
6.35 cm = 25 miles
55 cms = 25/6.35*55 = 216.5 miles
Answer : E
Answer: E
Question: The workforce of Company X is 60% female. The company hired 26 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
Options:
A)160
B)220
C)312
D)360
E)420
Rationale: Let's xx be total quantity of employees
0.6x=females before adding men
0.55(x+26)=females after adding men
as quantity of women doesn't change we can make an equation:
0.6x=0.55(x+26)
0.05x=14.3
x=286 - this is quantity of employees before adding 26 men
So after adding it will be 312
Answer is C
Answer: C
Question: If Jack walked 7 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?
Options:
A) 4
B) 4.5
C) 5.6
D) 6.25
E) 15
Rationale: Distance walked in 1 hour and 15 mins = 7 miles
Speed per hour = Distance/Time = 7/(5/4) = 5.6 miles per hour
Answer C
Answer: C
Question: A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used
Options:
A)12 months
B)10 months
C)14 months
D)16 months
E)None of these
Rationale: Explanation :
B received 2/3 of the profit
=> A : B = 1 : 2
Let the total capital = x
Then A's capital = x/4
B's capital = x – x/4 = 3x/4
Assume B's money was used for b months
Then A:B = (x/4)*15 : (3x/4)*b = 1 : 2
=> 15/4 : 3b/4 = 1 : 2
=> 15 : 3b = 1 : 2
=> 5 : b = 1 : 2
=> 5/b = 1/ 2
=> b = 5*2 = 10. Answer : Option B
Answer: B
Question: Sachin borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends money to Rahul at 25/4% p.a. for 2 years. Find the gain of one year by Sachin.
Options:
A)110.5
B)111.5
C)112.5
D)113.5
E)None of these
Rationale: Explanation:
Two things need to give attention in this question, First we need to calculate gain for 1 year only.
Second, where we take money at some interest and lends at other, then we use to subtract each other to get result in this type of question. Lets solve this Simple Interest question now.
Gain in 2 year = [(5000×25/4×2/100)−(5000×4×2/100)]
=(625−400)=225
So gain for 1 year = 225/2=112.50
Option C
Answer: C
Question: How many real solutions does the equation x5 + 2x3 + 8x2 + 16 = 0 have?
Options:
A)0
B)1
C)2
D)3
E)5
Rationale: Note that x5+2x3+8x2+16 = (x3+8)(x2+2) = (x+2)(x2-2x+4)(x2+2).
Since the quadratic equations x2 - 2x + 4 = 0 and x2 + 2 = 0 have no real solutions, the
original equation has just one real solution, x = -2.
correct answer B
Answer: B
Question: A mixture of 125 gallons of wine and water contains 20% water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?
Options:
A)10 glas
B)8.5 gals
C)8 gals
D)6.66 gals
E)8.33 gals
Rationale: In 125 gallons of the solution there are 0.2∗125=250 gallons of water. We want to add ww gallons of water to 125 gallons of solution so that 25+w gallons of water to be 25% of new solution:
25+w=0.25(125+w) --> w=25/3≈8.33
Answer: E.
Answer: E
Question: The bankers discount and the true discount of a sum at 20% per annum simple interest for the same time are Rs.80 and Rs.40 respectively. What is the sum and the time?
Options:
A)Sum = Rs.80 and Time = 5 years
B)Sum = Rs.100and Time = 5 years
C)Sum = Rs.60 and Time = 5 years
D)Sum = Rs.120 and Time = 5 years
E)None of these
Rationale: Explanation :
BD = Rs.80
TD = Rs.40
R = 10%
F = BD ×TD/(BD – TD)=80×40/(80–40)=80×40/40=Rs. 80
BD = Simple Interest on the face value of the bill for unexpired time =FTR/100
⇒80= (80×T×20)/100
⇒80 = 8 × T × 2 ⇒10= 2 × T
⇒ T = 10/2 = 5 years Answer : Option A
Answer: A
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, x
Options:
A)29
B)31
C)23
D)35
E)38
Rationale: The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 35 + 3 = 38.
E
Answer: E
Question: The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 55 terms of set X?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 55*4 + 54*40 + 53*400 = 220 + 2160 + 21200 = 23580
The hundreds digit is 5.
The answer is C.
Answer: C
Question: In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?
Options:
A)90
B)105
C)168
D)420
E)2520
Rationale: You need to choose 4 groups of 2 from 8 people: That's 8/!2!2!2!2!, then divided by 4!, since any ordering of these 4 groups is the same.
Total = 8/2!2!2!2!4!=8!/8∗2∗4!=7!/2∗4!=7∗6∗5∗4∗3∗2/4∗3∗2∗2=7∗6∗5/2=35∗3=105.
Answer: B
Answer: B
Question: During one month at a particular restaurant, 1/6 of the burgers sold were veggie burgers and 1/6 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?
Options:
A)x/8
B)x/2
C)2x/3
D)3x/4
E)6x/5
Rationale: T/6 - Veggi
(1/6)[T - (T/6)] = double meat = x = 5T/36
=> Veggie = T/6 = 6x/5
Answer is E.
Answer: E
Question: The sum t of prime numbers that are greater than 60 but less than 70 is
Options:
A) 67
B) 128
C) 191
D) 197
E) 260
Rationale: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum t of 61 and 67 is 128.
Answer B.
Answer: B
Question: John took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If he paid Rs. 540 as interest at the end of loan period, what was the rate of interest?
Options:
A)2 %
B)3 %
C)4 %
D)6 %
E)None of these
Rationale: Explanation:
Simple interest is same as the rate of interest.
Hence,
Rate of interest = R% and Time = R years
Simple Interest =	(P × R × T)/100
60 =	(1500 × R2)/100
15R2 = 540
R2 = 36
R=6 %
Rate of Interest = 6 %
ANSWER IS D
Answer: D
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
Options:
A)3888
B)2988
C)2777
D)8925
E)288
Rationale: Principal = (100 * 4016.25) / (9 * 5) = Rs. 8925.Answer: D
Answer: D
Question: A person travels from K to L a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?
Options:
A)55 kmph
B)58 kmph
C)60 kmph
D)66 kmph
E)70 kmph
Rationale: Explanation:
Speed on return trip = 150% of 50 = 75 km/hr.
Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.
ANSWER IS C
Answer: C
Question: How many plants will be there in a circular bed whose outer edge measure 34 cms, allowing 4 cm2 for each plant ?
Options:
A)18
B)750
C)23
D)120
E)None of these
Rationale: Circumference of circular bed = 34 cm
Area of circular bed = (34)2â„4Ï€
Space for each plant = 4 cm2
âˆ´ Required number of plants
= (34)2â„4Ï€ Ã· 4 = 22.98 = 23(approx)
Answer C
Answer: C
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,260 ?
Options:
A)$12
B)$14
C)$16
D)$17
E)$18
Rationale: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,260, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,260 --> (5+x)(20-x)=126 --> x=2 or x=13 --> price=10+$2*2=$14 or price=10+$2*13=$36.
Answer: B.
Answer: B
Question: The water level in a reservoir has been dropping at the rate of 14 inches per day. Exactly 5 days ago, the water level was at h inches. What will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same?
Options:
A)h − 12
B)h − 56
C)h − 14
D)h + 14
E)h - 126
Rationale: Drop=14 inches/day
5 Days ago=h, means now it's equal h-70 and in 4 days = h-70-56=h-126
Answer E
Answer: E
Question: The average of Suresh’s marks in English and History is 55. His average of marks in English and Science is 65. What is the difference between the marks which he obtained in History and Science?
Options:
A)40
B)60
C)20
D)Data inadequate
E)None of the above
Rationale: E + H = (55 × 2) = 110;
E + S = (65 × 2) = 130
∴ Reqd difference = 130 – 110 = 20
Answer C
Answer: C
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
Options:
A)27
B)29
C)31
D)32
E)37
Rationale: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
C
Answer: C
Question: Tim and Élan are 60 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
Options:
A)30 miles.
B)35 miles.
C)40 miles.
D)60 miles.
E)65 miles.
Rationale: Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.
Plugging in the answer choice Only Answer Choice C meet the 2:1(Tim:Elan=40:20) ratio of maintaining total distance traveled 60 miles
So Correct answer C
Answer: C
Question: James has 300 roses, and he decided to make booke with 50 flowers in each. After that he packed these bookes and wanted to sent some friends. He he decide to arrange the bookes in every possible combination and moved just one booke every 1/4 minute, how long would it taken by him ?
Options:
A)200 minutes
B)180 minutes
C)250 minutes
D)160 minutes
E)300 minutes
Rationale: Explanation:
No of bookes = 300/50 = 6
Clearly, number of ways of arranging 6 bookes = 6 ! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
So, total time taken = 720*1/4 minutes = 180 minutes
Answer: B
Answer: B
Question: The sum and the product of two numbers are 16 and 64 respectively, the difference of the number is?
Options:
A)0
B)6
C)7
D)8
E)2
Rationale: Explanation:
x + y = 16
xy = 64
(x- y)2 = (x + y)2 - 4xy
(x- y)2 = 256- 256 => (x - y) = 0
Answer: A
Answer: A
Question: A survey of n people in the town of badaville found that 50% of them prefer brand A. Another survey of 100 people in the town of chottaville found that 60% prefer brand A.In total 55% of all the people surveyed together prefer Brand A.What is the total number of people surveyed?
Options:
A)138
B)100
C)128
D)278
E)112
Rationale: 50% (n) + 60% (100 ) = 55% (n + 100)
Solving we get n = 100
Answer:B
Answer: B
Question: Which of the following is a factor of 18!+1?
Options:
A)15
B)17
C)19
D)33
E)38
Rationale: 18! and 18!+1 are consecutive integers and so they do not have any common factor except 1.
15, 17, 33 (=3*11), and 39 (=3*13) are factors of 18! and none of those can be a factor of 18!+1.
So, only 19 can be a factor of 18!+1
Answer:C
Answer: C
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $10.00 per hour and a standard tip rate of 40% of the cost of the orders she serves. If she worked four 16-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
Options:
A)280
B)300
C)1664
D)350
E)400
Rationale: Jill earns 10 dollars/hour and the hourly tip is (2/5)*40.
Jill thus earns 10*16+16*16 per day(or 10(16)+16(16)=26(16)=416).
Jill has worked for 4 days -> 416*4=1664.
This matches answer choice C.
Answer: C
Question: If 7 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
Options:
A)7 × 6 × 5 × 4 × 3 × 2 × 1
B)7 × 6 × 5 × 4 × 3 × 2 × 1
C)7 x 8
D)21
E)45
Rationale: 1st person will have 6 handshakes, 2nd will have 5, ....6th will have 1 and 7th will have 0
= 6+5+4+3+2+1 = 21
if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.
Ans.D)
Answer: D
Question: A man on tour travels first 100 km at 50 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 260 km of tour.
Options:
A)60.11 km/hr
B)61.11 km/hr
C)62.11 km/hr
D)65.00 km/hr
E)None of these
Rationale: Explanation:
We know Time = Distance/speed
So total time taken =
(100/50+160/80)=4hours
Time taken for 260 Km = 260/4=65km/hr
Option D
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)298
B)288
C)120
D)776
E)991
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer:C
Answer: C
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)33 1/8 %
B)33 7/3 %
C)33 1/3 %
D)38 1/3 %
E)33 3/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: C
Answer: C
Question: Simple interest on a certain sum of money for 4 years at 10% per annum is half the compound interest on Rs. 3000 for 3 years at 12% per annum. The sum placed on simple interest is
Options:
A)Rs.3000
B)Rs.607.39
C)Rs.1214.78
D)Rs.1518.48
E)None
Rationale: Solution
C.I.	=Rs[3000x(1+12/100)3-3000]
Rs.(3000x112/100x112/100x112/100-3000)	= Rs.1214.78.
Sum	=Rs. [607.39x100 /4x10]
= Rs.1518.48.
Answer D
Answer: D
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=20. What is the value of f(6)?
Options:
A)9
B)0
C)1
D)2
E)4
Rationale: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=20 then f(5)=20-5=15 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=15-6=9.
Answer: A.
Questions on funtions to practice:
Answer: A
Question: Bhuvnesh invests an amount for n years. If the rate of interest is 25% it becomes Rs. 5000. If the rate of interest is 5% it becomes Rs. 3000. For how long it is invested?
Options:
A)5
B)4
C)3
D)6
E)7
Rationale: Explanation :
n = ((p1-p2)/(p2r1-p1r2))*100
= ((5000-3000)/(3000*25-5000*5))*100
= (2000/50000)*100
= 4
Answer : B
Answer: B
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 12 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)40
B)44
C)66
D)52
E)None of these
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 12)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 12 = 4/9(T - 12)
10T = 1188 - 528 => T = 66.
ANSWER:C
Answer: C
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)7
B)9
C)21
D)3
E)None
Rationale: 1 woman's 1 day's work =	1/70
1 child's 1 day's work =	1/140
(5 women + 10 children)'s day's work =(5/70 + 10/140) = (	1/14 + 1/14) = 1/7
5 women and 10 children will complete the work in 7 days.
Answer: A
Answer: A
Question: The sum of the first 80 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?
Options:
A) 5,050
B) 7,500
C) 10,500
D) 15,000
E) 19,600
Rationale: 101+103+.......199
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 80 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 80 positive even integers = 2550
sum of 1st 100 odd numbers = 5050 - 2550 = 2500
so 101+103+.......199 = 80 * 100 + (1+3+5+7+......) = 8000 + 2500 =10500
C is the answer.
Answer: C
Question: An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time D will it take to fill the bucket to full capacity?
Options:
A)7/18
B)9/18
C)2
D)18/7
E)18/5
Rationale: Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank D= 60/7 - 6 = 18/7 mins. ANS D.
Answer: D
Question: A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be the member chosen to be the treasurer?
Options:
A) 1/10
B) 1/80
C) 1/20
D) 1/9
E) 1/5
Rationale: This question is much easier than it appears.
Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the treasurer is also 1/10.
Answer: A
Answer: A
Question: In a mixture 60 litres, the raƟo of milk and water 2 : 1. If the this raƟo is to be 1 : 2, then the quanity
of water to be further added is
Options:
A)20 liters
B)30 liters
C)50 liters
D)60 liters
E)None of these
Rationale: Explanation:
Quantity of Milk = 60*(2/3) = 40 liters
Quantity of water = 60-40 = 20 liters
Answer: D
Answer: D
Question: If 30% of a number is equal to one-fourth of another number, what is the ratio of first number to the second number?
Options:
A)4:7
B)6:5
C)1:2
D)2:3
E)5:6
Rationale: Let 30% of A = 1/4 B. Then,
30A/100 = 1B/4 => 3A/10 = 1B/4
A/B = (1/4 * 10/3) = 5/6
A:B = 5:6.
Answer: E
Answer: E