MU-NLPC/Calc-aqua_rat huggingface dataset:
P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 140 days, in how many days can R alone complete the remaining work? Answers: A) 50 days B) 102.7 days C) 100 days D) 150 days E) 80 days

Solution: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days   Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days   P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 390 days   P works for 60 days--> 60/200 work done => 30%   Q works for 140 days--> 140/250 work done => 56%   260% work left ... R alone will take 26% * 395 = 102.7 days   Answer is (102.7 days)
Answer: B
Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of b - a ?
Choices.
A) -10
B) 10
C) -19
D) 20
E) 21

Solution: Yes! there is really a faster way to solve it.   Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2   Here -10 = sum of even ints from 2 to 20, inclusive   number of even ints = 10,   first int + last int = 2+20= 
2+20 = 22
22   -10= 10*22 / 2= 
10*22 / 2 = 110
110   B= sum of odd ints from 1 to 19, inclusive   number of odd ints = 10,   first int + last int = 1+19= 
1+19 = 20
20   -10= 10*20 / 2= 
10*20 / 2 = 100
100   B - -10= 100 - 110 = -10   -10ns :-10
Answer: A
A goods train runs at the speed of 72 km/hr and crosses a 300 m long platform in 26 sec. What is the length of the goods train?  Choose the correct choice from the following options:
A) 382
B) 782
C) 278
D) 270
E) 220

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 300)/26 = 20   x = 220 m.   Answer: 220
Answer: E
The successive discounts 20% and 15% are equal to a single discount of?
Choose the most appropriate option:
A) 22
B) 27
C) 32
D) 997
E) 232

Solution: Let the CP of an article be Rs. 100   Given that successive discounts are 20% and 15%.   SP = 85% of 80% of 100 = (85/100)(80/100)(100)   => SP = Rs. 68   32learly, single discount is 32%.Answer: 32
Answer: C
Find the mean proportional between 25 & 36? Pick.
A) A)59
B) B)30
C) C)63
D) D)65
E) E)67

Solution: Formula = √a×b   A = 25 and 30 = 36   √25×36 = 5 × 6 = 30   30
Answer: B
The simple interest on Rs. 26 for 6 months at the rate of 7 paise per rupeeper month is
Choose the correct option:
A) 1.2
B) 10.92
C) 12.98
D) 12.38
E) None

Solution: Sol.   S.I. = Rs. [26 * 7/100 * 6] = Rs. 10.92   Answer 10.92
Answer: B
1*2+ 2*2^2+ 3*2^3+ 4*2^4……………………+2012*2^2012 Options
A) 8100312  B) 8100313  C) 8100412  D) 8200312  E) 8300312

Solution: take 2 outside as common   we get 2(1+2*1^2+3*1^3+.........2012*1^2012)   then 2(1+2+.....2012)   we get 8100312   8100312NSWER:8100312
Answer: A
Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Choose the correct choice from the following answers:
A) 338 B) 187 C) 120 D) 882 E) 272

Solution: 4x 5x 6x   100 50 25   400x + 350x + 150x = 16000   x = 20   6x = 120   Answer: 120
Answer: C
There are 20 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?	Choose the correct choice from the following options.
A) 10
B) 30
C) 190
D) 60
E) 90

Solution: 20 players are there.   two players play one game with one another.   so 201902=20*19/2= 
20*19/2 = 190
190   SO OPTION 190 is correct
Answer: C
In a sequence, each term is obtained by adding 7 to the preceding one. If the sum of the first 30 terms is equal to 705, what is the result of the addition of the first 40 terms? Pick one.
A) 2000
B) 2250
C) 2340
D) 2400
E) 2440

Solution: a is first term and d = 7 since the preceding number is always greater than the previous one..   Now 30th term is a+29(7).   Sum of n terms is n/2(first term + last term)and here we have to get sum of 30 terms , we get 30/2 ( a + a+203) = 705 ( given sum of 30 terms is 705)   => 15(2a+203) = 705   => 2a+203 = 47   => 2a=-156   => a = -78   Now to get sum of first 40 terms , we need to get 40th term value i.e. -78+39(7) = 195.   Sum of first 40 terms = 40/2( -78 + 195) =2340 .   Hence option 2340 is correct answer..
Answer: C
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 4 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] Choose the most appropriate option
A) 0.22
B) 0.44
C) 0.55
D) 22
E) 55

Solution: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;   A half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene.   How many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/12*33= 
8/12*33 = 22
22 cents.   Answer: 22.
Answer: D
A cube of side two meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Options:  A) 2878  B) 2778  C) 1000  D) 8000  E) 8900

Solution: Along one edge, the number of small cubes that can be cut   =200/10= 
200/10 = 20
20   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 20 * 20 * 20= 
20 * 20 * 20 = 8_000
8000   Answer: 8000
Answer: D
Evaluate 926 + 9.026 + 0.926 + 9.0026	Choose the correct choice:
A) 944.9755
B) 944.9655
C) 944.9565
D) 946.9565
E) 944.9546

Solution: 926 + 9.026 + 0.926 + 9.0026= 
926 + 9.026 + 0.926 + 9.0026 = 944.9546
944.9546   Option 944.9546
Answer: E
If x is a whole number, then x²(x² - 1) is always divisible by  Choose one.
A) multiple of 12 B) 24 C) 12 - x D) 12 E) none

Solution: Solution   Putting x = 12,we get 2²(2² - 1)	= 12.   So, x²(x² - 1) is always divisible by 12.   Answer 12
Answer: D
For how many positive integers is the number of positive divisors equal to the number itself ?  Options
A) none
B) one
C) two
D) three
E) cannot be determined

Solution: The factors of 1: {1}. 1 factor. WORKS!   The factors of 2: {1,2}, 2 factors. WORKS!   The factors of 3: {1,3}, 2 factors. Doesn't work   The factors of 4: {1,2,4}, 3 factors. Doesn't work   As we can see, if an integer n has n factors, then the factors of n must be: {1, 2, 3,....., n)   So, we can quickly see that the only positive integers that meet this criterion are 1 and 2   Answer:one
Answer: B
If the average (arithmetic mean) of x^2, 2x^2, and 3x^2 is 200, what is the value of x?
Select:
A) 10
B) 12
C) 15
D) 20
E) 25

Solution: 10M of x^2, 2x^2 and 3x^2 = x^2 + 2x^2 + 3x^2 / 3 = 6x^2/3   Given that 2x^2 = 200   x^2 = 100   x = 10   10nswer is 10
Answer: A
The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 3 terms of the sequence?  Choose the correct choice from the following choices
A) 201/100
B) 99/100
C) 100/101
D) 1/10000
E) 3/4

Solution: 3/4asy task and accomplish   X1=1-1/2   x2=1/2-1/3   x3=1/3-1/4   sum=X1+X2+X3=1-1/2+1/2-1/3+1/3-1/4= 3/4   3/4 is the answer
Answer: E
Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?  Answers
A) 7/125  B) 4/125  C) 4/25  D) 3/25  E) 2/25

Solution: The number of ways to select w, x, and y is:   5*5*5= 
  5*5*5 = 125
125   The number of ways to choose three different numbers from the set is 5C3=10.   There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.   P(w < x < y) = 10/125 = 2/25   The answer is 2/25.
Answer: E
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is	Answers.
A) 5/5  B) 5/9  C) 5/21  D) 5/98  E) 5/1

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 = 5/9.   Answer:5/9
Answer: B
Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in.
Choose the correct choice from the following answers.
A) 40 min  B) 25 min  C) 54 min  D) 65 min  E) 58 min

Solution: Distance = Speed * time     3*20/3= 
  3*20/3 = 20
20km   New Speed= 18 kmph   Therefore time = 20/18 = 10/9= 54min   Answer : 54 min.
Answer: C
The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?
Choose the correct choice from the following options:
A) 6 B) 8 C) 10 D) 12 E) 14

Solution: For any given day, only the guards patrolling on the previous day won't be available. So, 2 guards who patrolled on Friday won't be available. We are thus left with 5 guards.   To choose 2 out of 5, we will have 5C2 = 10 different pairs.   The answer is 10.
Answer: C
If 20 liters of chemical X are added to 80 liters of a mixture that is 30% chemical X and 70% chemical Y, then what percentage of the resulting mixture is chemical X?  Choose the correct choice from the following options:
A) 32%	B) 35%	C) 38%	D) 41%	E) 44%

Solution: The amount of chemical X in the solution is 20 +0.3(80) = 44 liters.   44 liters / 100 liters = 44%   The answer is 44%.
Answer: E
Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
Choose the correct choice from the following answers
A) 3/7 B) 4/9 C) 4/7 D) 5/11 E) 6/11

Solution: Let A be the event ‘the number on the card drawn is even’ and B be the   event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).   Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}   Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}   and A n B = {4, 6, 8, 10}   Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10   Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7   4/7)
Answer: C
It takes Jake 15 minutes to do one oil change, and it takes Bob 10 minutes. If Jake and Bob both begin doing oil changes at exactly 10:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously? Choose the correct choice.
A) 10:00 a.m. B) 10:15 a.m. C) 10:30 a.m. D) 10:45 a.m. E) 11:00 a.m.

Solution: Since Jake will finish s oil changes after s × 15 minutes and Bob will finish c oil changes after c × 10 minutes, they both will finish doing an oil change at the same time when s × 15 = c × 10. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 15 and 10. The question asks for the first time they will finish a car simultaneously, so you must find the least common multiple. The least common multiple of 15 and 10 is 30, so in the context of the question, this would be 30 minutes. Therefore, the first time they will finish changing the oil of a car at the same time is 10:00 + 30 minutes, or 10:30 a.m. The answer is (10:30 a.m.).
Answer: C
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? Choose one:  A) 80 kg  B) 85 kg  C) 95 kg  D) 100 kg  E) 105 kg

Solution: Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (65 + 20)= 
(65 + 20) = 85
85 kg.   85 kg)
Answer: B
The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?	Choose the most appropriate option: A) 11 years B) 31 years C) 81 years D) 61 years E) 35 years

Solution: Total age seven persons = (28 * 7)years   Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.   Age of the person sitting in the middle of the row = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102= 
196 - 63 - 102 = 31
31 years.   Answer:31 years
Answer: B
With 630 ml mixture of milk & water in the ratio 7:2. How much water mustbe added to make the ratio 7:3?
Choose the correct choice from the following answers:	A) 60 ml	B) 80 ml	C) 70 ml	D) 90 ml	E) 92 ml

Solution: concentration of water in mixture1   =2/9 (since the ratio of milk and water = 7:2) ...(1)   concentration of water in pure water= 1 ...(2)   Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3   => concentration of water in mixture2   =3/10   By rule of alligation,   concentration of water in mixture1   (2/9) concentration of water in pure water (1)   Mean concentration   (3/10)   1−3/10=7/10   =1:19   => Quantity of water   =630×1/9=70 ml   70 ml
Answer: C
Molly's age in 18 years will be seven times her age six years ago. What is Molly's present age?	Choose the correct choice from the following answers.
A) 6 B) 8 C) 10 D) 12 E) 14

Solution: Let x be Molly's present age.   x + 18 = 7(x-6)   x = 10   The answer is 10.
Answer: C
How many words can be formed by using all letters of the word “BIHAR”  Answers:
A) 14	B) 20	C) 420	D) 120	E) 340

Solution: The word BIHAR contains 5 different letters.   Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120   Option 120
Answer: D
10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many days will a woman finish the work?	Choose one:
A) 125 days
B) 150 days
C) 90 days
D) 225 days
E) None of these

Solution: 15 women's work of a day = 1⁄6 - 1⁄10 ⇒ 1⁄15 part   ∴ for 1 whole part a woman will take   = 15 × 15 = 225 days.   Answer 225 days
Answer: D
In a sample of associates at a law firm, 30 percent are second-year associates, and 60 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?
Choose the correct choice from the following
A) 10 B) 20 C) C D) 40 E) 50

Solution: Let the sample be 100.   Given 60% are not first year i.e. there could be second year (x) and more than 2 years(y) possibility.   60% = (x) + y   Given 30% = second year (x)   club both , we get y = 30%.   Answer: option C is correct answer.
Answer: C
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 7.5 m x 6 m x 22.5 cm?  Choose the correct choice from the following choices:  A) 6000  B) 6410  C) 6440  D) 6500  E) 6800

Solution: Number of bricks = Volume of Wall/Volume of Bricks   =750x600x22.5/25x11.25x6= = 6000   answer :6000
Answer: A
what is next no. 11 23 47 83 131 191 ??? Choose the correct answer
A) 263	B) 181	C) 191	D) 201	E) 211

Solution: 11+12*1= 
11+12*1 = 23
23   23+12*2= 
23+12*2 = 47
47   47+12*3= 
47+12*3 = 83
83   83+12*4= 
83+12*4 = 131
131   131+12*5= 
131+12*5 = 191
191   191+ 12*6= 
191+ 12*6 = 263
263   263
Answer: A
The distance between 2 cities A and B is 1000km. A train starts from A at 8 a.m. and travels towards B at 100 km/hr. Another starts from B at 9 a.m. and travels towards A at 150 km/hr. At what time do they meet?  Choices:
A) 11am.	B) 12p.m.	C) 3pm.	D) 2p.m.	E) 1p.m.

Solution: Suppose they meet x hrs after 8 a.m.   Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000   100x + 150 (x-1) = 1000   x = 4.60 = 5 hrs   They meet at 8+5 = 1 p.m.   Answer is 1p.m.
Answer: E
Real-estate salesman Z is selling a house at a 30 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 30 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 30 percent discount. Salesman Y's final price is what fraction of salesman X's final price?  Choose the correct choice from the following answers:
A) 12/13	B) 11/15	C) 11/17	D) 11/14	E) 11/7

Solution: Let the retail price be = x   Selling price of Z = 0.70x   Selling price of X = 0.70*0.80= 
0.70*0.80 = 0.56
0.56x   Selling price of Y= ((0.70x + 0.56x)/2)*0.70 = 0.63x * 0.70 = 0.44x   0.44x = k * 0.56x   k = 0.44/0.56 = 44/56=11/14   Answer: 11/14
Answer: D
It takes John 25 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? Choose the correct answer
A) 5:40 a.m B) 7:50 a.m C) 6:55 a.m D) 8:00 a.m E) 4:25 a.m

Solution: The time it takes John to get to work: time to walk to car park + time to drive     25 + 45= 
  25 + 45 = 70
70 minutes= 1 hour and 10 minutes   John needs to get out of the house 1 hour and 10 minutes before 9:00 am at   9:00 - 1:10 = 7:50 a.m   correct answer 7:50 a.m
Answer: B
Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be multiple of 3?  Choose the correct choice from the following answers:	A) 3/14	B) 2/7	C) 1/3	D) 1/2	E) 2/21

Solution: M2/21THOD-1   Probability that the number on first die is multiple of 3 = 2/6   Probability that the number on Second die is multiple of 3 = 2/7   Probability that Both Dice result in odd numbers = (2/6)*(2/7) = 4/42 = 2/21   Answer: Option 2/21
Answer: E
A rectangular rug with side lengths of 3 feet and 6 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?  Choose one:
A) A.3/16
B) 1/4
C) C.1/2
D) 23/32
E) 7/8

Solution: Area of the rectangular rug = 3*6= 
3*6 = 18
18   Fraction not covered by the rug= (Total Area - Rug area) / Total Area   = (64 - 18)/64   = 23/32=23/32
Answer: D
What is the unit digit in {(6374)^1793 x (625)317 x (341^491)}? Select
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Unit digit in (6374)^1793 = Unit digit in (4)^1793   = Unit digit in [(4^2)^896 x 4]   = Unit digit in (6 x 4) = 4   Unit digit in (625)^317 = Unit digit in (5)^317 = 5   Unit digit in (341)^491 = Unit digit in (1)^491 = 1   Required digit = Unit digit in (4 x 5 x 1) = 0.   0)
Answer: A
Find the simple interest on $3200 for 3 years at 10% per annum?	Pick one:
A) $250	B) $300	C) $500	D) $600	E) $960

Solution: SI = PTR/100   = 3200*3*10/100= 
3200*3*10/100 = 960
$960   Answer is $960
Answer: E
Solution Y is 30 percent liquid W and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid W?	Options:
A) 30%  B) 33 1/3%  C) 37 1/2%  D) 40%  E) 50%

Solution: Answer:C   Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid W and 70% water, and then I was able to get the answer. That was a bit tricky and nice question=37 1/2%
Answer: C
Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 150 cookies, what percent of the cookies did Nell bake?	Choose the correct choice from the following answers.
A) 0.125%  B) 1.25%  C) 12.6%  D) 125%  E) 0.152%

Solution: 9.18x+5.17x+2.05x = 16.4x 9.18 +5.17 +2.05= 
9.18 +5.17 +2.05 = 16.4
16.4x= 150 cookies   x= 150/16.4 = 9.1 (approx)   So, Nell baked 9.1*2.05 cookies or 19 cookies (approx)   % share = 19/150 = 12.6 approx   Hence, answer is 12.6%.
Answer: C
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?  Choose the most appropriate option: A) 10- B) 99 C) 88 D) 62 E) 22

Solution: Speed of the boat in still water = (60+80)/2= 
(60+80)/2 = 70
70 kmph. Speed of the stream= (80-60)/2= 
(80-60)/2 = 10
10 kmph.10-nswer: 10-
Answer: A
What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?  Pick.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: (1056 / 23) gives remainder 21   21 + 2= 
21 + 2 = 23
23, So we need to add 2   2
Answer: B
A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube?	Pick one.
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: Given: positive integer n is a perfect square and a perfect cube --> n is of a form of n=x6 for some positive integer x --> 0<x^6<10^3 --=""> 0<x^2<10 --=""> x can be 1, 2 or 3 hence nn can be 1^6, 2^6 or 3^6.   Answer: 3.</x^2<10></x^6<10^3>
Answer: B
The ratio of three numbers is 2:3:4 and their sum is 180. The second number of the three numbers is? Choose the correct choice from the following choices.
A) 24	B) 60	C) 27	D) 29	E) 30

Solution: 2:3:4   Total parts = 9   9 parts --> 180   1 part ---->20   The second number of the three numbers is = 3 * 20= 
3 * 20 = 60
60   Answer : 60
Answer: B
P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?
Choose the correct choice from the following:
A) 3  B) 5  C) 6  D) 7  E) 10

Solution: Let P takes x days to complete the work   Then Q takes x/2 days and R takes x/3 days to finish the work   Amount of work P does in 1 day = 1/x   Amount of work Q does in 1 day = 2/x   Amount of work R does in 1 day = 3/x   Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x   6/x = 2   => x = 12   => Q takes 12/2= 
12/2 = 6
6 days to complete the work   Answer is 6.
Answer: C
A metallic sheet is of rectangular shape with dimensions 100 m x 50 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 10 m, the volume of the box (in m cube) is:	Choose the correct choice from the following answers: A) 42500m cube B) 20000 m cube C) 44140 m cube D) 24000m cube E) None of these

Solution: Explanation:   l = (100-20)= 
(100-20) = 80
80 m, [because  10+10= 
 10+10 = 20
20]   b= (50-20)= 
(50-20) = 30
30 m,   h= 10 m.   Volume of the box = (80X30X8) m cube   = 24000 m cube.   Option 24000m cube
Answer: D
Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 7 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
Choose the correct choice from the following options.
A) 30 B) 20 C) 18 D) 12 E) 6

Solution: 21-12 < no of hrs < 21-6   9< no of hrs < 14.   12
Answer: D
If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)? Choose the correct option.
A) 90 B) 100 C) 110 D) 120 E) 130

Solution: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)   Therefore, the product should have factors with a difference of 2.   120 = 10*12, so this is a possible value for the original expression.   The answer is 120.
Answer: D