MU-NLPC/Calc-aqua_rat huggingface dataset:
If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum W of the 3 greatest of these temperatures, in degrees Fahrenheit, could be	Pick
A) 6x B) 4x C) 5x/3 D) 3x/2 E) 3x/5

Solution: Note that we have 5positivetemperatures.   Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<w<5x --=""> only option B fits.   Answer: 4x.</w<5x>
Answer: B
In how many different number of ways 4 men and 2 women can sit on a bench?	Answers
A) 690  B) 700  C) 720  D) 740  E) 760

Solution: npn = n!   6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720   720
Answer: C
If 5 men can dig a field in 20 days, how much time it will take 4 men to dig the same field?	Choose the most appropriate option:	A) 21	B) 22	C) 23	D) 24	E) 25

Solution: 25   Less the number of men, more time it will take to dig the field (inversely proportion)   5 : 4 :: N : 20   N = 20 X 5 / 4 = 25
Answer: E
If |x| - |y| = |x+y| and xy not equal zero , which of the following must be true ?
Choose the correct choice from the following answers:
A) x-y> 0
B) x-y< 0
C) x+y> 0
D) xy>0
E) xy<0

Solution: |x| - |y| = |x+y|   => (|x| - |y|)^2 = |x+y|^2 = (x+y)^2   => x^2 - 2|x||y| + y^2 = x^2 + 2xy + y^2   => |xy| = -xy   because xy != 0 so xy <0   Ans: xy<0
Answer: E
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 40 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?	Options
A) 20 ft B) 25 ft C) 600ft D) 900 ft E) 1000 ft

Solution: Point to note: Both the wheels would have traveled the same distance.   Now consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).   Equating the distance traveled by front wheel to back wheel: (x+5)*30 = x * 40. (Formula for calculating the distance traveled by each wheel is: # of revolutions * circumference.)   Solving this eqn. gives x=15.   Sub x=15 either in (x+5)*30 or in x * 40 to get the distance, which is 600. So the correct choice is 600ft.
Answer: C
A train speeds past a pole in 15 seconds and a platform 130 meters long in 25 seconds. What is the length of the train (in meters)?	Choose the correct choice from the following options
A) 175 B) 185 C) 195 D) 205 E) 215

Solution: Let the length of the train be x meters.   The speed of the train is x / 15.   Then, x + 130 = 25*(x / 15)   10x = 1950   x = 195 meters   The answer is 195.
Answer: C
How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length?
Options:
A) 18.9 sec B) 88.9 sec C) 22.9 sec D) 30.00 sec E) 72.0 sec

Solution: 30.00 sec = 110 + 390= 
110 + 390 = 500
500 m   S= 60 * 5/18 = 50/3   T = 500 * 3/50= 
500 * 3/50 = 30
30 sec   Answer: 30.00 sec
Answer: D
When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 16 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?
Choose the correct choice:	A) 40	B) 34	C) 42	D) 46	E) 50

Solution: Total # of students 16+28+18-(9+7+10)+4= 
16+28+18-(9+7+10)+4 = 40
40.   40nswer: 40.
Answer: A
In what ratio should a variety of rice costing Rs. 4.5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Choose the correct choice from the following:
A) 5/6
B) 5/9
C) 5/1
D) 5/3
E) 5/12

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties   = x : y   By the rule of allegation, x/y   = (8.75 - 7.50) / (7.50 - 4.5) =5/12   Answer: 5/12
Answer: E
If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 3.
II. x is an integer multiple of 6
III. x is an integer multiple of 5  Pick one
A) a) I only  B) b) II only  C) c) I and II only  D) d) I and III only  E) e) I,II and III

Solution: The answer should be D i.e. X will be an integer and multiple of 3 and 6.   Let us take example n, n+1, n+2 as 3 three consecutive positive integers.   In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12   Hence in a product of 3 consecutive integers, the product is always divisible by 3.   Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.   Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even   Answer c) I and II only
Answer: C
In his wardrobe, Dexter has three trousers. One of them is black the second is blue, and the third brown. In his wardrobe, he also has four shirts. One of them is black and the other 3 are white. He opens his wardrobe in the dark and picks out one shirt and one trouser pair without examining the colour. What is the likelihood that neither the shirt nor the trouser is black? Choose the most appropriate option: A) 1/12 B) 1/6 C) 1/4 D) 1/2 E) None of these

Solution: Solution:   Probability that trouser is not black =2/3=2/3   Probability that shirt is not black =3/4=3/4   Required probability =2/3Ã—3/4=1/2   Answer is 1/2
Answer: D
The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years	Choose the correct choice from the following answers:
A) of these B) B)3:5 C) C)4:3 D) inadequate E) A)3:4

Solution: Let P's age and Q's age be 6x and 7x years respectively.   Then, 7x - 6x = 4 => x = 4   Required ratio = (6x + 4) : (7x + 4)   28 : 32 = 7:8   of theseNSWER:of these
Answer: A
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?  Choose the correct choice from the following choices:
A) 20
B) 10
C) 30
D) 40
E) 50

Solution: 30   30   3W = 2M   15M ------ 21 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   15 * 21 * 8 = 14 * x * 6   x = 30
Answer: C
If the ratio of the roots of the equation 4x2-px+8=0 is equal to that of the roots 2x2-rx+16=0, then:
Pick one.
A) 4r=p
B) r=p
C) 2r=p
D) 2p=r
E) None

Solution: 4x2-px+8=0 for this eqn... roots are R1=p/4 R2=-2   2x2-rx+16=0 for this eqn... roots are R3=r/2 R4=-8   As per Question, p/-8=r/-16   => 2p=r   ANSWER:2p=r
Answer: D
The present worth of $3600 due in 2 years at 20% per annum compound interest is? Choose the correct choice from the following.
A) $1200
B) $1850
C) $2010
D) $3200
E) $2500

Solution: Present worth = 3600/ (1 + 20/100)^2 = 3600 * 5/6 * 5/6= 
3600 * 5/6 * 5/6 = 2_500
$2500   Answer is $2500
Answer: E
The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Select:
A) 75
B) 87
C) 68
D) 99
E) 32

Solution: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.   P + C + M = 150 + P   C + M = 150   Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2= 
150/2 = 75
75.   75nswer:75
Answer: A
During 2003, a company produced an average of 3,000 products per month. How many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 300% over its 2003 average?
Choose the correct option
A) 520,000	B) 540,000	C) 525,000	D) 530,000	E) 550,000

Solution: Company produced 12*3000 = 36,000 products in 2003. If company produces X products from 2004 to 2007, then total amount of product produced in 4 years (2003 through 2007) is X+36,000. The gives the average of (X+36,000)/4.   This average needs to be 300% higher than that in 2003. In math terms, 36,000+300%(36,000) = 144,000. So:   (X+36,000)/4 = 144,000   X+36,000 = 576,000   X = 540,000   The answer is 540,000.
Answer: B
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?  Pick.
A) 399  B) 400  C) 2887  D) 277  E) 1213

Solution: 441 = P(21/20)2   P = 400.Answer: 400
Answer: B
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 18. The larger of the two numbers is:  Choose the correct choice from the following answers: A) 276 B) 414 C) 322 D) 345 E) 355

Solution: Clearly, the numbers are (23 x 13) and (23 x 18).   Larger number = (23 x 18) = 414. Answer: Option 414
Answer: B
what is the remainder when 7^700 is divided by 100? Select the correct option:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: (7^700)mod100= [7^(2*350)]mod100=[49^350]mod100=[(50-1)^350]mod100=[{350C349}*50*(-1)^349 +350C350*(-1)^350]mod100 = [-350*50+1]mod100=1mod100   So, evidently, the remainder will be 1.   1NSWER:1
Answer: A
In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 33rd in an arithmetic progression if the sum of the 15th and 19th terms of the sequence is 108?  Select
A) 38 B) 42 C) 46 D) 50 E) 54

Solution: Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 17th term in the sequence.   Then the mean of the 16th and 18th term is also equal to the overall mean, because the 16th term is (17th term - x) and the 18th term is (17th term + x).   Similarly the mean of the 15th and 19th term is also equal to the mean.   etc...   Thus the mean is   108/2= 
  108/2 = 54
54   The answer is 54.
Answer: E
The circumferences of two circles are 528 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?  Choose the correct option
A) 29963 sq m	B) 28937 sq m	C) 43162 sq m	D) 27688 sq m	E) 17248 sq m

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 528 and 2∏l = 704   s = 528/2∏ and l = 704/2∏   Difference between the areas = ∏l^2 - ∏s^2   = ∏{264^2/∏^2 - 352^2/∏^2}   = 264^2/∏ - 352^2/∏   = (264 - 352)(264 + 352)/∏   = (88)(616)/(22/7)   =17248 sq m   Answer:17248 sq m
Answer: E
The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 5 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science? Choose the correct option
A) 18 : 35 : 50  B) 3 : 10 : 10  C) 4 : 8 : 5  D) 32 : 35 : 25  E) None of these

Solution: Suppose the number of students studying Arts, Commerce and Science be 3x, 5x and 8x respectively.   When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes   3x × 120% : 5x × 140% :   8x × 125% = 36 : 70 : 100   = 18 : 35 : 50   18 : 35 : 50nswer 18 : 35 : 50
Answer: A
For what value of x between − 9 and 9, inclusive, is the value of x^2 − 10x + 16 the greatest? Choices:	A) − 9	B) − 2	C) 0	D) 2	E) 9

Solution: we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..   so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.   so -9 will give the greatest value..   ans − 9
Answer: A
If x/y = 7/4, then (x + y)/(x - y) = ?
Answers:
A) 5
B) 11/3
C) -1/6
D) -1/5
E) -5

Solution: Any x and y satisfying x/y = 7/4 should give the same value for (x + y)/(x - y).   Say x=7 and y=4, then (x + y)/(x - y) = (7 + 4)/(7-4) = 11/3.   Answer: 11/3.
Answer: B
If 15% of 40 is greater than 25% of a number by 2, the number is Choose the most appropriate option: A) 14 B) 16 C) 18 D) 20 E) 22

Solution: Explanation:   15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16   Option 16
Answer: B
Mr. Hernandez, who was a resident of State X for only 12 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year? Choices
A) $900 B) $720 C) $600 D) $300 E) $60

Solution: Total tax for the year = 22,500 x 4% = 900   As stated Annual tax is prorated as per the duration of stay.   Prorated Tax = 900 (12/12) = 900   $900nswer $900
Answer: A
Look at this series: 35, 36, 42, __, 48, 54, 35, 60, ... What number should fill the blank?	Choose the correct choice from the following options
A) 35
B) 46
C) 44
D) 45
E) 52

Solution: 35   35   In this series, 6 is added to the previous number; the number 35 is inserted as every third number.
Answer: A
A number is increased by 30% and then decreased by 30%, the final value of the number is ?	Answers: A) decreases by 7% B) decreases by 9% C) decreases by 8% D) decreases by 6% E) decreases by 5%

Solution: Here, x = 30 and y = - 30   Therefore, the net % change in value   = ( x + y + xy/100)%   = [30 - 30 + (30 * -30)/100]% or - 9%   Since the sign is negative, there is a decrease in value by 9%.   ANSWER: decreases by 9%
Answer: B
The ratio of two numbers is 1 : 3 and their H.C.F. is 6. Their L.C.M. is
Choose the correct choice from the following choices:
A) 48
B) 18
C) 56
D) 27
E) 67

Solution: Explanation:   Let the numbers be 1x and 5x. Then, their H.C.F. = x. So, x = 6.   So, the numbers 6 and 18.   L.C.M. of 6 and 18 = 18.   Option 18
Answer: B
The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
Choose the correct choice from the following options
A) A)2/3
B) B)5/7
C) C)4/7
D) D)5/9
E) E)None of these

Solution: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.   d = 2n - 1   (n + 1)/(d + 1) = 4/5   5n + 5 = 4d + 4   5n + 5 = 4(2n - 1) + 4 => n = 5/3   d = 2n - 1 => d = 3/7   Hence the fraction is : 5/7   ANSWER:5/7
Answer: B
A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 72 km downstream?  Choose the most appropriate option: A) 30/83 hours B) 33/13 hours C) 31/13 hours D) 30/13 hours E) 36/14 hours

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 72 km downstream= d/s = 72/26   = 36/13 hours.   Answer:36/14 hours
Answer: E
Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m. ?	Choose the correct choice from the following choices.
A) 72 kmph
B) 92 kmph
C) 12 kmph
D) 82 kmph
E) 14 kmph

Solution: Explanation:   Let the distance traveled be x km.   Then, x/10 - x/15 = 2   3x - 2x = 60 => x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60/10= 
60/10 = 6
6 hrs.   So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.   Required speed= 60/5= 
60/5 = 12
12 kmph.   Answer: 12 kmph
Answer: C
If W=x^4 + y^4 = 100, then the greatest possible value of x is between  Pick:
A) 0 and 3
B) 3 and 6
C) 6 and 9
D) 9 and 12
E) 12 and 15

Solution: My attempt:   If W=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.   Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is 3 and 6   Hence answer is --   b) 3 and 6.
Answer: B
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?	Select:
A) 7:5 B) 7:0 C) 7:3 D) 7:2 E) 7:1

Solution: Let the age of father and son 10 years ago be 3x and x years respectively.   Then, (3x + 10) + 10 = 2[(x + 10) + 10]   3x + 20 = 2x + 40 => x = 20.   Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3.Answer:7:3
Answer: C
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 5 years the amount to be paid is?
Choose the correct answer:
A) 8118
B) 8127
C) 8618
D) 9125
E) 8128

Solution: A = 7500(26/25)5   = 9125   Answer: 9125
Answer: D
A man purchased 3 blankets @ Rs.100 each, 3 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Choose one.
A) 750 B) 277 C) 878 D) 450 E) 272

Solution: 10 * 150= 
10 * 150 = 1_500
1500   3 * 100 + 3 * 150= 
3 * 100 + 3 * 150 = 750
750   1500 – 750= 750   750nswer:750
Answer: A
If P(A) = 8/15, P(B) = 4/15, and P(A âˆª B) = 16/15 Find P(B|A)  Pick one:	A) 1/2	B) 2/3	C) 3/2	D) 2	E) 4/7

Solution: P(B|A) = P(A âˆª B)/P(A)   P(B|A) = (16/15)/(8/15)= 
(16/15)/(8/15) = 2
2.   2
Answer: D
Each face of a cube is painted with exactly one colour. What is the smallest number
of colours needed to paint a cube so that no two faces that share an edge are the
same colour?  Select the correct option:
A) 2 colours B) 3 colours C) 4 colours D) 5 colours E) 6 colours

Solution: Assume the top face of the cube is coloured green.   Since the front face of the cube shares an edge with the top face, it cannot be coloured green.   Thus, we need at least two colours.   Thus, we assume that the front face is coloured blue, as shown in Figure 1.   Since the right face shares an edge with the top face and with the front face, it cannot be   coloured green or blue. Thus, we need at least three colours.   Thus, we assume that the right face is coloured red, as shown in Figure 2.   We have shown that at least 3 colours are needed. In fact, the cube can be coloured with   exactly 3 colours by colouring the left face red, the back face blue, and the bottom face green   (Figure 3).   In this way, the cube is coloured with exactly 3 colours and no two faces that share an edge   are the same colour.   Therefore, 3 is the smallest number of colours needed to paint a cube so that no two faces that   share an edge are the same colour.which is=3   correct answer 3 colours
Answer: B
Virginia, Adrienne, and Dennis have taught history for a combined total of 102 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?
Select.
A) 23	B) 32	C) 35	D) 43	E) 44

Solution: Let number of years taught by Virginia = V   number of years taught by Adrienne = A   number of years taught by 43ennis = 43   V+A+43 = 96   V= A+9   =>A = V-9   V= 43-9   => A = (43-9)-9 = 43-18   43-9 + 43-18 + 43= 
43-9 + 43-18 + 43 = 102
102=> 343 = 102 + 27= 
102 + 27 = 129
129=> 43 = 43   Answer 43
Answer: D
Christine and Siri have 21rs between them. Christine has 20rs more than Siri. How much does Christine have.  Select:
A) 16.5
B) 17.5
C) 18.5
D) 19.5
E) 20.5

Solution: Let Siri has x Rs, then Christine has 20+x Rs   Given x + (20+x)= 21   => 2x= 1 or x= 0.5   So Christine and Siri has 20.5 and 0.5 Rs respectively.   ANSW20.5R:20.5
Answer: E
Group A has 2 boys and 7 girls, group B has 3 boys and 4 girls and group C has 2 boys and 2 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?
Choose the correct choice from the following answers:
A) 312/445
B) 105/378
C) 291/105
D) 209/315
E) 77/272

Solution: Group A has 2 boys and 7 girls; 9   Group B has 3 boys and 4 girls; 7   Group C has 2 boys and 2 girls. 4   Selected group should have one girl and two boys.   Girl from A, boy from B, boy from C: 7/9*3/7*2/4 = 1/6;   Boy from A, girl from B, boy from C: 2/9*4/7*2/4 = 4/63;   Boy from A, boy from B, girl from C: 2/9*3/7*2/4 = 3/63.   Sum = 1/6 + 4/63 + 3/63 = 105/378.   Answer: 105/378.
Answer: B
he number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is? Choose the correct choice from the following answers:
A) 43288 B) 2377 C) 4320 D) 2882 E) 2782

Solution: x Not younger_______ ↑   The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.   The required number of ways = 6(6!) = 4320   Answer:4320
Answer: C
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary? Choose the correct choice from the following options
A) 2277 B) 2997 C) 1000 D) 2688 E) 2677

Solution: X * (110/100) * (95/100) = 1045   X * (11/10) * (1/100) = 11   X = 1000   Answer: 1000
Answer: C
The radius of a cylindrical vessel is 7cm and height is 5cm. Find the whole surface of the cylinder?  Choose the correct option
A) 281 B) 528 C) 440 D) 767 E) 1981

Solution: r = 7 h = 5   2πr(h + r) = 2 * 22/7 * 7(12) = 528   Answer:528
Answer: B
A man can row upstream at 10kmph and downstream at 14kmph. Find man's rate in still water ?  Choose the correct answer: A) 5km/hr B) 15km/hr C) 10km/hr D) 12km/hr E) 7.5km/hr

Solution: Rate in still water = 1/2 (10+14) = 12km/hr   Answer is 12km/hr
Answer: D
In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket inchours, and the hot-water leak alone would fill the same bucket inhhours, wherec < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it tookthours to fill the bucket, which of the following must be true?
I. c < t < h
II. 0 < t < h
III. (c/2) < t < (h/4)	Choose the correct answer:	A) a) I only	B) b) II only	C) c) III only	D) d) I and II	E) e) I and III

Solution: I picked numbers for this problem   C = 2 hours   H = 3 hours   C<H   2 people working together formula is   1/C + 1/H = 1/t   1/2 + 1/3 = 1/t   t = 6/5= 
6/5 = 6/5 = around 1.2
1.2   Substitute the values of C, H and t in the 3 choices given below   Only 2 is valid.Therefore b) II only is the best answer
Answer: B
If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?	Select the correct option:
A) 22 1/2 %
B) 22%
C) 21 %
D) 30%
E) 40 %

Solution: 9 = (1*40*R)/100   R = 22 1/2 %   22 1/2 %NSWER 22 1/2 %
Answer: A
Machine E can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?  Choose the correct answer: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33

Solution: Let the following be true:   E makes x in time t   Then the following follows:   N makes x in 4t/3   O makes x in 3/2(4t/3) = 2t   M:N:O = 1:4/3:2=3:4:6   So N=4/(3+4+6)=4/13=4/13
Answer: C
How many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?	Answers:
A) 45 B) 50 C) 56 D) 60 E) 63

Solution: Selling Price(SP) of 1 kg mixture= Rs. 9.24   Profit = 10%   Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP   =100(100+10)×9.24=100110×9.24=92.411= Rs.8.4   By rule of alligation,   CP of 1 kg sugar of 1st kind CP of 1 kg sugar of 2nd kind   Rs. 9 Rs. 7   Mean Price   Rs.8.4   8.4 - 7= 
8.4 - 7 = 1.4
1.4 9 - 8.4= 0.6   i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3   Suppose x   kg of kind1 sugar is mixed with 27 kg of kind2 sugar.   then x : 27 = 7 : 3   ⇒3x=27×7⇒x=9×7=63   63
Answer: E