divelab/Sys2Bench huggingface dataset:
Question: Rahul went to a shop and bought things worth Rs. 29, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)Rs 15
B)Rs 12.10
C)Rs 23.70
D)Rs 26.80
E)None of these
Rationale: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 29 - 5 - 0.30
=23.70
Answer : C
Answer: C
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 5 years ago?
Options:
A) 9
B) 10
C) 12
D) 14
E) 16
Rationale: Let's say
Age of Richard isR
Age of David isD
Age of Scott isS
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 5 years ago?
i.e. D-5 = 14-5 = 9 years
Answer: Option
A
Answer: A
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
Options:
A)15 m,17 m
B)85 m,10 m
C)15 m,80 m
D)15 m,10 m
E)15 m,14 m
Rationale: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer:D
Answer: D
Question: A can do a piece of work in 12 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Options:
A)15 1/3
B)16 1/3
C)17 1/3
D)18 1/3
E)25 1/3
Rationale: 2/12 + 4/15 + x/20 = 1
x = 46/3 = 15 1/3
ANSWER:A
Answer: A
Question: If q and r are both odd numbers, which of the following must also be odd?
Options:
A)q – r
B)(q + r)^2
C)q(q + r)
D)(qr)^2
E)q/r
Rationale: Since q and r are odd numbers we can put q and r as q=2*Q+1 and r=2*R+1, for some integers Q, R.
A. q-r=(2*Q+1)-(2*R+1)=2*(Q-R) ---> must be an even number.
B. (q + r)^2 =(2Q+2R+2)^2= 4*(Q+R+1)^2 ---> must be an even number.
C. q(q+r) = (2Q+1)(2Q+2R+2)= 2*(2Q+1)(Q+R+1) ---> must be an even number.
D. (qr)^2 = ((2Q+1)(2R+1))^2 = (4QR +2Q +2R +1)^2
by putting 2QR+Q+R = T we have (2T+1)^2= 4T^2 + 4T +1=2(2T^2 +2T)+1 ---> must be an odd number.
E. q/r cannot be an integer
The answer is, therefore, (D)
Answer: D
Question: Find out the wrong term in the series 2, 3, 4, 4, 6, 8, 9, 12, 16
Options:
A)9
B)8
C)7
D)6
E)2
Rationale: Explanation:
The given sequence is a combination of three series:
i)1st, 4th, 7th terms i.e, 2, 4, 9
ii)2nd, 5th, 8th terms i.e, 3, 6, 12
iii)3rd, 6th, 9th terms i.e, 4, 8, 16
In each one of i, ii, iii, each term is twice the preceding term.
So, 9 is wrong and must be replaced by (4*2) = 8
Answer: A) 9
Answer: A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Options:
A)1/455
B)1/429
C)1/408
D)1/421
E)1/420
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue
= ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Answer: A
Question: If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 1/4 then b= ?
Options:
A)-1/2
B)1/2
C)2
D)-2
E)8
Rationale: f(a) = -1/2 = -1/a, and thus a = 2
f(ab) = 1/4, and thus ab = -4
2b = -4
b = -2
The answer is D.
Answer: D
Question: Find the ones digit of 73^340
Options:
A)3
B)5
C)6
D)7
E)9
Rationale: Cyclicity of 3 is 3,9,7,1after 4 multiplication again the cycle repeats.
So divide 340 by 4 and we get 87 as quotient and 2 as remainder. So cycle will run for 87 times and then 2 times more. So pick up the 2nd item from the cycle.
Hence Answer A.
Answer: A
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 35 degrees?
Options:
A)π
B)3π/2
C)2π
D)5π/2
E)7π/9
Rationale: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 35 degrees. 35/360 = 7/72.
Therefore length of arc = 7/72 * 8π = 7π/9 - Answer choice E.
Answer: E
Question: The perimeter of a triangle is 35 cm and the inradius of the triangle is 4.5 cm. What is the area of the triangle?
Options:
A)22
B)75
C)78
D)54
E)23
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 4.5 * 35/2
= 78.75 cm2
Answer:C
Answer: C
Question: In a camp, there is a meal for 160 men or 220 children. If 160 children have taken the meal, how many men will be catered to with remaining meal?
Options:
A)20
B)43
C)50
D)10
E)40
Rationale: There is a meal for 220 children. 160 children have taken the meal.
Remaining meal is to be catered to 60 children.
Now, 220 children 160 men.
60 children (160/220)	* 60 = 43 men
Answer is B.
Answer: B
Question: A batsman played seven games and scored an average of 80 runs per game. If, in his first five games, he scored 75, 69, 81, 90, and 73 runs, what was the average (arithmetic mean) number of runs scored over the last two games?
Options:
A)65
B)81
C)82
D)86
E)Cannot be determined from the information given.
Rationale: The first thing to recognize is that to find the average, you take the sum and divide by the number of inputs (games, in this case) you have. Here were have 7 inputs, or games. Therefore, I approach this problem by first writing the following:
(A+B+C+D+E+F+G)/7 = 80
Plug in the sum of the first 5 games (388) for (A+B+C+D+E)
[(388+F+G)/7]= 80
Multiply both sides by 7
388+F+G = 560
Subtract 388 on both sides
F+G = 172
Since the answer asks for the average of the last two games, F and G, all you need to do is take 172 and divide it by 2, giving 86.
The answer is D.
Answer: D
Question: A math teacher has 32 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
Options:
A)9
B)10
C)11
D)12
E)15
Rationale: a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)
Among the 32 cards with have:
15 rectangles
10 rhombus
8 squares
Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 32 - 17 = 15
Answer (E)
Answer: E
Question: Lori deposits $10,000 in a savings account at 10% annual interest, compounded annually.
After 3 years, what is the balance on the account?
Options:
A)13310
B)13410
C)13510
D)13610
E)13710
Rationale: The deposit of $10,000 increases by 10% every year. So use the formula for amount in case of CI.
Amount = P*(1 + r/100)^n
Amount = 10,000 * (1 + 10/100)^3
Amount = 10,000*(1.1)^3
Amount = 13310
ANSWER:A
Answer: A
Question: A 600 meter long train crosses a signal post in 15 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)4 min
B)2 min
C)8 min
D)9 min
E)1.5 min
Rationale: S = 600/15 = 40 mps
S = 3600/40 = 90 sec = 1.5 min
Answer: E
Answer: E
Question: If cost of 15 eggs be 90 rupees, then find out the cost of 5 dozen eggs.
Options:
A)300
B)400
C)500
D)600
E)360
Rationale: Cost of 15 eggs = 90 rupees
Cost of 1 egg = 90/15 = 6 rupees,
Cost of 5 dozens, i.e. 6 x 12 = 72 x 5 = 360
Answer : E
Answer: E
Question: Attorneys are questioning 11 potential jurors about their ability to serve on a jury and decide a case fairly. Seven individuals will be selected to serve on the jury. If each potential juror has an equal chance of being selected, what is the probability that Tamara and Inga are chosen for the jury?
Options:
A)2/11
B)2/7
C)21/55
D)4/11
E)34/55
Rationale: First person to be chosen one of the two girls - 2/11
Second person to be chosen to be the other girl - 1/10
The probability to chose both girls - (2/11)*(1/10) = 1/55.
The two girls can be chosen anywhere in the list of the 7 jurors, therefore the final probability is (1/55)*7C2 = (1/55)*(7*6/2) = 21/55.
Combinatorial approach:
Total number of possibilities to choose the 7 jurors - 11C7 = 11*10*9*8/(2*3*4) = 11*10*3.
Number of possibilities to have the two girls among the final 7 jurors - 9C5 = 9*8*7*6/(2*3*4) = 9*2*7 (the two girls must be in, therefore we need to choose 5 more people from the remaining 9).
Required probability 9*2*7/(11*10*3) = 21/55.
(I prefer not to multiply before I express the final probability as a ratio, I always try to reduce a fraction whenever possible.)
Answer C.
Answer: C
Question: List R contains five numbers that have an average value of 60. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?
Options:
A)25
B)28
C)31
D)34
E)37
Rationale: The middle number is 60.
Let the smallest number be x. Then the largest number is 2x+20.
To make x as small as possible, let's make the remaining numbers as large as possible.
So the second largest = the largest = 2x+20.
The second smallest should be equal to the median.
The numbers are x, 60, 60, 2x+20, 2x+20.
x + 60 + 60 + 2x + 20 + 2x + 20 = 5*60 = 300
5x = 140
x = 28
The answer is B.
Answer: B
Question: Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 1200 widgets?
Options:
A)2 hour and 20 minutes
B)2 hour and 24 minutes
C)2 hour and 30 minutes
D)2 hour and 36 minutes
E)2 hour and 00 minutes
Rationale: (350+250)t=1200
600t=1200
t=2
t=2 hour and 00 minutes
Answer: E
Answer: E
Question: The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 202 to 300 inclusive?
Options:
A)5,150
B)7,550
C)10,150
D)12,550
E)20,150
Rationale: 2 + 4 + 6 + 8 +...+ 100 = 2550
202 + 204 + ... + 300 = 50(200) + (2+4+...+100) = 10,000 + 2550 = 12,550
The answer is D.
Answer: D
Question: A tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Options:
A) 1.25%
B) 3.75%
C) 9.33%
D) 10.67%
E) 11.7%
Rationale: The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 700 gallons (7% of initial solution of 10,000 gallons) then sodium chloride is 700/7,500*100=~9.33% of the remaining solution of 7,500 gallons.
Answer: C.
Answer: C
Question: Barbata invests $2200 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
Options:
A)1100
B)3000
C)1000
D)3600
E)2400
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
2200+0.05*2200+x+0.08x = 2200+x+0.06(2200+x)
0.05*2200+0.08x = 0.06x+0.06*2200
0.02x = 2200(0.06-0.05)
x = 2200*0.01/0.02 = 1100
Ans: "A"
Answer: A
Question: The average age of the mother and her 6 children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
Options:
A)42 years
B)40 years
C)48 years
D)50 years
E)None of these
Rationale: Total age of the mother and six children = 12 × 7 = 84 years.
Total age of six children = 7 × 6 = 42 years. (since average is reduced by 5)
Mother is 42 years old.
ANSWER:A
Answer: A
Question: In a certain company, a third of the workers do not have a retirement plan. 40% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
Options:
A)80
B)95
C)105
D)120
E)137
Rationale: Set up equation:
x = total number of workers
120 = 0,4 * 2/3 * x + 0,6 * 1/3 * x
120 = 14/30 x
x = 257
257 - 120 = 137
Answer E
Answer: E
Question: When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is
Options:
A)2970
B)297
C)2997
D)300
E)30
Rationale: (1/10)*3000 - (1/10)%*3000 =
300 - (1/1000)*3000 =
300 - 3 = 297
The answer is B.
Answer: B
Question: A student is ranked 13th from right and 8th from left.how many are there?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: 13th from right means = x + 12
8th from left means = 7 + x
Total = 12+7+1 = 20
ANSWER:C
Answer: C
Question: John must arrange 3 different physics books and 5 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
Options:
A)6
B)9
C)36
D)120
E)720
Rationale: First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways
Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places
Second Place, Physics Book - in 3 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.
Total no of ways = 5*4*3*3*2*2*1*1 = 720 ways
E
Answer: E
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number?
Options:
A)1375
B)8451
C)1546
D)2375
E)3215
Rationale: Total five-digit numbers with two even leftmost digits and with three odd last digits: EEOOO - 4*5*5*5*5=4*5^4 (notice that we have only 4 choices for the first digit since we cannot use zero);
Total five-digit numbers with two 4's as leftmost digits and with three odd last digits: 44OOO - 5*5*5=5^3;
So, the answer is 4*5^4-5^3=5^3(4*5-1)=125*19=2375.
Answer: D.
Answer: D
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
Options:
A)15
B)10
C)20
D)25
E)30
Rationale: Dividend on rs 20 = (9/100*20) = 9/5
=>9/5 is an income on Rs (100/12 * 9/5) = 15
ANSWER A
Answer: A
Question: Find number which is 60% less than 80.
Options:
A)18
B)32
C)28
D)26
E)98
Rationale: Explanation:
60% less is 40% of the given number
Therefore, 40% of 80 is 32.
ANSWER: B
Answer: B
Question: The average weight of 6 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?
Options:
A)74 kg
B)77 kg
C)76.5 kg
D)Data inadequate
E)None of these
Rationale: total weight increases = 6 × 1.5 = 9 kg
so the weight of new person = 65 + 9 = 74 kg
Answer A
Answer: A
Question: The area of a rectangular plot is 360 square metres. If the length is 25% less than the breadth, what is the breadth of the plot?
Options:
A)32 m
B)12 m
C)20 m
D)22 m
E)25 m
Rationale: length =75% of breadth.
length×breadth =360 m2
⇒ 75% of breadth×breadth =360 m2
⇒ 75/100× breadth×breadth =360 m2
⇒ breadth×breadth =480 m2
⇒ breadth =22 m
ANSWER:D
Answer: D
Question: Missing number in the series
4 9 20 43 90 185 ?
Options:
A)376
B)185
C)190
D)195
E)180
Rationale: 4*2+1=9
9*2+2=20
20*2+3=43
43*2+4=90
90*2+5=185
185*2+6=376
ANSWER:A
Answer: A
Question: Several people are sitting around a round table playing a card game with a deck of 67 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?
Options:
A)4
B)5
C)7
D)11
E)13
Rationale: Let n be the number of people at the table.
If Martin gets the first and the last card, it means Martin got one more card than the others.
Thus 67/n has a remainder of 1 and so 67-1 = 66 is a multiple of n.
The answer is D.
Answer: D
Question: Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 8 days. In how many days Peter complete the work separately.
Options:
A)21
B)24
C)20
D)25
E)30
Rationale: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 8 days which means that the whole job(1) can be completed in X days.
X=8/(8/20)=20
C
Answer: C
Question: In how many ways can the letters in MATHEMATICS be arranged?
Options:
A)4989060
B)4999980
C)4989600
D)4989800
E)4998800
Rationale: There are 11 letters in the word "MATHEMATICS" of which two are M's, two are A's, two are T's and all other are distinct. Therefore require number of arrangements =11!/2!*2!*2! =4989600 Answer : C
Answer: C
Question: Which of the following is a prime number ?
Options:
A)33
B)81
C)93
D)97
E)None of these
Rationale: Explanation:
Clearly, 97 is a prime number.
ANSWER IS D
Answer: D
Question: A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?
Options:
A)9km/hr
B)7km/hr
C)12km/hr
D)15km/hr
E)18km/hr
Rationale: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr
Ans:E
Answer: E
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $22. What is the cost of the carpet, in dollars per square yard? (1 square yard = 8 square feet)
Options:
A)xy/297
B)11xy/3
C)176/(xy)
D)297/(xy)
E)297xy
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 8.
The price per square yard is 22/ (xy/8) = 176/(xy).
The answer is C.
Answer: C
Question: Given that 2x + 9 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
Options:
A)-4 and -1
B)-1 and 4
C)-4 and 1
D)-2 and 4
E)2 and 5
Rationale: 2x + 9 > 5
i.e 2x >5-9
i.e. 2x > -4
i.e. x > -2
Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4
i.e. -2 < x < 4
Answer: Option D
Answer: D
Question: At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows him from J's house on his bicycle at 8 kmph. When will J be 3 km behind P?
Options:
A)19.39
B)19.3
C)19.32
D)19.33
E)19.36
Rationale: By the time P starts J is 1.5 hr x 6 = 9 km away from his house.
J is 3 km behind when P is 3 km ahead of him. ie., P has to cover 12 km. So he takes 12 / (8 - 6) = 6 hrs after 13.30. So the required time is 19.30Hrs
Answer:B
Answer: B
Question: A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Options:
A)80 km/hr
B)81 km/hr
C)85 km/hr
D)84 km/hr
E)83 km/hr
Rationale: Let x is the length of the train in meter and y is its speed in kmph
x/8.4 = (y-4.5)(10/36) ---(1)
x/8.5 = (y-5.4)(10/36) ---(2)
Dividing 1 by 2
8.5/8.4 = (y-4.5)/ (y-5.4)
=> 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4
.1y = 8.5×5.4 - 8.4×4.5
=> .1y = 45.9-37.8 = 8.1
=> y = 81 km/hr
Answer is B.
Answer: B
Question: Jackson has $313,194 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
Options:
A)$1
B)$2
C)$3
D)$4
E)$5
Rationale: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,194 = 21 and 18 is divisible by 9.
Hence we need to subtract 3 to this number for it to be divisible by 9
Correct Option: C
Answer: C
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)Rs. 650
B)Rs. 690
C)Rs. 698
D)Rs. 700
E)Rs. 718
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: C
Question: A and B can finish a work in 12 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
Options:
A)76 days
B)48 days
C)98 days
D)31 days
E)24 days
Rationale: B = 1/12 – 1/24 = 1/24 => 24 days
Answer: E
Answer: E
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
Options:
A)1778
B)1682
C)9178
D)1900
E)1782
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer: D
Answer: D
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 1/4 %, then the amount invested at 11% was?
Options:
A)12500
B)37500
C)29977
D)26777
E)19871
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 37/4 * 1/100)
(9x + 1100000 - 11x) = 37000/4 = 925000
x = 87500
Sum invested at 9% = Rs. 87500
Sum invested at 11% = Rs. (100000 - 87500) = Rs. 12500.
Answer: A
Answer: A
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 8 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
Options:
A)8/3 DAYS
B)3/8 DAYS
C)1/4 DAYS
D)4/1 DAYS
E)NONE OF THESE
Rationale: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/4, B'S 1 DAY'S WORK = 1/8
(A+B)'S 1 DAY'S WORK = (1/4+1/8)=3/8=8/3
SO, A AND B TOGETHER CAN FINISH THE WORK IN 8/3 DAYS.
CORRECT OPTION: A
Answer: A
Question: Natasha carries a paintbrush of length 1 and walks around the perimeter of a regular 2016-gon
with side length 1, painting all of the area outside the polygon that she can reach. What is the
area that Natasha paints?
Options:
A)2014+π
B)2015+π
C)2016+π
D)2013+π
E)2012+π
Rationale: If the curve is convex, Natasha will only be turning one way, and by the time she
returns to the origin she will have turned exactly 2π radians. Therefore, she will paint the area
of a circle as she turns corners, because she paints a sector of the unit circle each time until the
sum of the sector angles is 2π. On each of the 2016 straight edges, she paints a rectangle of
length 1 and width 1, because the 2016-gon has side length 1 and the paintbrush also has length
1. Thus the total area is 2016 *1 + π* 12 = 2016 + π
correct answer C
Answer: C
Question: When a 160 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ?
Options:
A)52
B)50
C)62
D)67
E)69
Rationale: Answer
No. of pieces = Total length / Length of each piece
= 160/3.2
= 50
Option: B
Answer: B
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)5
B)8
C)9
D)1
E)3
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Answer: B
Question: In a room there are 7 people. Each person shook hands with every other person. How many hand shakes were there?
Options:
A)19
B)20
C)21
D)22
E)23
Rationale: 7C2 = 21
The answer is C.
Answer: C
Question: Jaclyn buys $30 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter
Options:
A)712.5
B)1234
C)1289
D)1345
E)None of these
Rationale: Explanation:
I=(p x r x t)/100
= 30000*9.5/100*(18/12)^1/6 = 712.50
Answer: A
Answer: A