MU-NLPC/Calc-aqua_rat huggingface dataset:
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 49 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?  Choose the correct choice from the following answers.
A) 48pi/x	B) 75x	C) 34.2x	D) 24x	E) x/75

Solution: C = (pi)d   C(small): (pi)*28   C(large): (pi)*49   Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches   (pi)*(1680) = (pi)*(49)(x)   pi*(34.2) = pi*(x)   34.2=x   Answer: C. 34.2x
Answer: C
If the number of boys in a class are 8 times the number of girls, which value can never be the total number of boys?	Choose the correct answer:
A) A - 16  B) B - 9  C) C - 10  D) D - 11  E) E - 12

Solution: Let the number of girls = x and the number of boys = 8x Then, total number of students = x + 8x = 9x i.e., the total number of boys must be a multiple of 8 From the given choices, only 16 is multiple of 8. A - 16nswer is A - 16.
Answer: A
Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7800 less if they could find two more equal investors. How much is the total investment in the new business.
Select the correct option.
A) a)	$ 58,500
B) b)	$ 54,000
C) c)	$ 21,000
D) d)	$ 5,400
E) e)	$3,600

Solution: Initially each invest in x. Hence total investment is 3x.   Total investment is also 5(x-7800).   3x = 5(x-7800)   x= 5*7800/2= 
5*7800/2 = 19_500
19500   3x= 58500 and the answer is a)	$ 58,500.
Answer: A
Evaluate combination
16C2 Select the correct option:  A) 120  B) 1000  C) 10  D) 1  E) 0

Solution: Explanation:   nCn=1   nCr=n!/r!(n-r)!   16C2=16!/2!(16-2)!=120   Option 120
Answer: A
Find the largest number which divides 62,132,237 to leave the same reminder  Choose the correct answer.
A) 30	B) 32	C) 35	D) 45	E) 55

Solution: Explanation:   Trick is H35F of (237-132), (132-62), (237-62)   = H35F of (70,105,175) = 35   Option 35
Answer: C
Laura took out a charge account at the General Store and agreed to pay 9% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?	Choose the correct choice from the following options.
A) $2.10
B) $37.10
C) $37.16
D) $38.10
E) $38.15

Solution: Principal that is amount taken by Laura at year beginning = 35$   Rate of interest = 9%   Interest = (9/100)*35= 
(9/100)*35 = 63/20 = around 3.15
3.15$   Total amount that Laura owes a year later= 35+3.15= 
35+3.15 = 38.15
38.15 $   Answer $38.15
Answer: E
A number of 47 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?  Choose the correct choice from the following.
A) 10
B) 12
C) 15
D) 16
E) 17

Solution: To maximize # of boxes we should minimize marbles per box: 14*3+1*5= 
14*3+1*5 = 47
47 --> 14+1=15.   Answer: 15.
Answer: C
In the rectangular coordinate system, points (2, 0) and (– 2, 0) both lie on circle C. What is the maximum possible value of the radius of C ?  Choose the correct choice from the following.
A) 2 B) 4 C) 8 D) 16 E) None of the above

Solution: The answer is A   It takes 3 distinct points to define a circle. Only 2 are given here.   The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. 2ll this information tell us is that the radius isgreater 2
Answer: A
In an office, totally there are 6400 employees and 65% of the total employees are males. 25% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
Choose the correct choice from the following answers: A) 3127 B) 3128 C) 3120 D) 3122 E) 3124

Solution: Number of male employees = 6400 * 65/100= 
6400 * 65/100 = 4_160
4160   Required number of male employees who are less than 50 years old= 4160 * (100 - 25)%   = 4160 * 75/100= 
4160 * 75/100 = 3_120
3120.   Answer: 3120
Answer: C
If a and b are nonzero integers such that 2a+1 = 5b+1, then each of the following must be true EXCEPT	Choose the correct choice from the following answers
A) 0 < b/a < 1 B) ab is positive. C) On the number line, b lies between 0 and a. D) The ratio of a to b is equivalent to 10/4. E) a – b is positive.

Solution: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.   We're told that A and B are NONZERO INTEGERS and that 2a+1 = 5b+1 or 2A = 5b. We're told that each of the answer is always true EXCEPT for one of them...   Before we get to the actual work, it's important to note a few details:   1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...   2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.   Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...   A = 5   B = 2   AND   A = -5   B = -2   Answer A: 0 < B/A < 1   2/5 and -2/-5 both = 2/5. Answer A appears true.   Answer B: AB is positive   (2)(5) and (-2)(-5) both = +10. Answer B appears true.   Answer C: B is between 0 and A on the number line   0....2....5   -5....-2....0   Answer C appears true.   Answer D: A/B = 10/4   5/2 = -5/-2   10/4 = 5/2   Answer D appears true.   Answer E: A - B is positive     5 - 2= 
  5 - 2 = 3
3   -5 - (-2)= -3 *****This is NOT always true.   Final Answer:   a – b is positive.
Answer: E
A corporation seven times its annual bonus to 5 of its employees. What percent of the employees’ new bonus is the increase?	Choose the correct choice from the following choices:
A) 1.35%	B) 85.71%	C) 3.12%	D) 4.78%	E) 3.69%

Solution: Let the annual bonus be X.   A corporation triples its annual bonus.   So new bonus = 7X.   Increase = 7X-X =6X   The increase is what percent of the employees’ new bonus   = (6X/7X)*100   = 85.71%   Hence 85.71%.
Answer: B
A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?
Select the correct option.
A) 1/3 kmph
B) 2/3 kmph
C) 1/4 kmph
D) 1/2 kmph
E) 1/6 kmph

Solution: Explanation:   Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.   Speed in downstream = 3 x 60/18 = 10 km/hr   Rate of current = (10-9)/2 = 1/2 km/hr.   ANSWER IS 1/2 kmph
Answer: D
1/2, 1/4, 1/8, 1/16, 1/32,1/64, 1/128 ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?
Answers
A) 0.1 < x < 1
B) 0.01 < x < 0.1
C) 0.001 < x < 0.01
D) 0.0001 < x < 0.001
E) 0.000001 < x < 0.00001

Solution: In the Sequence notice that the sequence is just the 1/(2^n) ...   so for 1st term=1/2^1=1/2   2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...   Thus the 10th term will be 1/(2^10)=1/1024   Roughly, 1/1024 can be   1/1000= 
  1/1000 = 1/1_000 = around 0.001
0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.   thus the ans will lie btw. 0.000001 and 0.0001.(0.000001 < x < 0.00001)
Answer: E
The population of a town is 10000. It increases annually at the rate of 15% p.a. What will be its population after 2 years?  Pick one:
A) 13300  B) 13350  C) 13225  D) 13500  E) 13600

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 Ã— 115/100 Ã— 115/100 = 13225   13225
Answer: C
Ifaequals the sum of the even integers from 2 to 100, inclusive, andbequals the sum of the odd integers from 1 to 99, inclusive, what is the value of a - b ?  Choose one
A) 1
B) 50
C) 19
D) 20
E) 21

Solution: This is a solution from Beatthegmat:   even numbers:   (100-2)/2 + 1= 
(100-2)/2 + 1 = 50
50 even integers.   (100+2)/2= 
(100+2)/2 = 51
51 is the average of the even set.   sum= avg*(#of elements) = 51*50= 
51*50 = 2_550
2550= a   odd numbers:   (99-1)/2 + 1= 
(99-1)/2 + 1 = 50
50 odd integers.   (99+1)/2= 
(99+1)/2 = 50
50 is the average of the odd set.   sum= avg*(#of elements) = 50*50= 
50*50 = 2_500
2500= b   a-b = 2550 - 2500= 
2550 - 2500 = 50
50. (50)
Answer: B
maximun number of identical pieces(of same size) of a cake by making only 3 cuts? Choose the correct choice from the following.
A) 6 B) 7 C) 8 D) 9 E) 5

Solution: since cake is a 3D object, it will have length,breadth, height...   first cut across length now we will get2 pieces   then cut across breadth we will get 4 parts in total now...   now cut across height, finally we will get 8 parts...   ANSWER:8
Answer: C
The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000?	Choose the correct choice from the following answers
A) $38,796.  B) $29,232.  C) $38,976.  D) $39,679.  E) $36,796.

Solution: 30,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.   Only option $29,232. fulfills the condition and hence is the answer
Answer: B
The ratio of two numbers is 4 : 5 and their H.C.F. is 4. Their L.C.M. is Select
A) 48
B) 22
C) 56
D) 80
E) 67

Solution: Explanation:   Let the numbers be 4x and 5x. Then, their H.C.F. = x. So, x = 4.   So, the numbers 16 and 20.   L.C.M. of 16 and 20 = 80.   Option 80
Answer: D
If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?  Choices
A) 36 B) 24 C) 30 D) 18 E) 19

Solution: Explanation:   Let t be his usual time to reach his office and v be his usual speed.   v = d/t ……….(d is the distance Ajay travels while going to his office)   vt = d   At v1 = 4v/5 ; t1 = t + 6   4v/5 = d/(t + 6)   4v/5* (t + 6) = d   4v/5* (t + 6) = vt   On solving we get,   t = 24 minutes   ANSWER 24
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? Select:
A) 150 meter
B) 299 meter
C) 666 meter
D) 155 meter
E) 144 meter

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 9= 
  (50/3) * 9 = 150
150 meter   150 meternswer: 150 meter
Answer: A
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 155 m. Then, A wins by:  Choose one
A) 60 m  B) 20m  C) 40 m  D) 20m  E) 23m

Solution: To reach the winning post A will have to cover a distance of (500 - 155)m, i.e., 345 m.   While A covers 3 m, B covers 4 m.   While A covers 345 m, B covers 4 x 345/3	m	= 460 m.   Thus, when A reaches the winning post, B covers 460 m and therefore remains 40 m behind.   A wins by 40 m.   Answer:	40 m
Answer: C
A city council will select 2 of 9 available firefighters and 1 of 5 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?	Pick.
A) 36  B) 72  C) 144  D) 180  E) 432

Solution: OA 180   9C2 * 5C1   using the combination formula to choose 2 from 9 and 1 from 5   180
Answer: D
A train passes a station platform in 35 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Choose the correct option:
A) 228
B) 240
C) 225
D) 166
E) 1811

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/35= 15 => x = 225 m.   Answer: 225
Answer: C
Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?	Choose the most appropriate option:
A) 5.9% B) 5.6% C) 5.6% D) 9.6% E) 1.6%

Solution: C.P. of 1 toy = 375/12 = Rs. 31.25   S.P of 1 toy = Rs. 33   Profit = 1.75/31.25 * 100 = 28/5= 
28/5 = 28/5 = around 5.6
5.6%   Answer: 5.6%
Answer: C
City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:35 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?	Choose the most appropriate option
A) 5:00 B) 5:30 C) 6:00 D) 6:35 E) 7:00

Solution: Train C has traveled 20 mi in the half hour before Train D has started its journey.   140-20= 
140-20 = 120
120   40+20= 
40+20 = 60
60 mph   120 mi/ 60 mph= 2 hrs   4:35pm + 2 hrs = 6:35pm   Answer:   D. 6:35
Answer: D
Two full tanks one shaped like the cylinder and the other like a cone contain liquid fuel the cylindrical tank held 500 lts more then the conical tank After 200 lts of fuel is pumped out from each tank the cylindrical tank now contains twice the amount of fuel in the canonical tank How many lts of fuel did the cylindrical tank have when it was full? Choose the correct answer.
A) 1200	B) 279	C) 2879	D) 27976	E) 27711

Solution: Let the cylindrical tank capacity x + 500 then the conical tank capacity = x   After 200 lts pumped out, then remaining fuel with the tanks = x +300, x - 200   Given that first term is doubt the second.   x+300x−200=21x+300x−200=21   Solving we get x = 700   Cylindrical tank capacity = 1200 lts   1200nswer:1200
Answer: A
By selling 12 pens for a rupee a woman loses 20%. How many for a rupee should he sell in order to gain 20%?
Choose the correct choice from the following options.
A) 12 B) 14 C) 45 D) 8 E) 65

Solution: 8   80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8
Answer: D
In a class, the teacher wrote a set of consecutive integers beginning with 1 on the blackboard. Little Johnny came and erased one number. The average of the remaining numbers was 2741327413. What was the number that Little Johnny erased? Choose the correct choice from the following answers:
A) 7 B) 9 C) 11 D) 13 E) 15

Solution: We have S = the sum of all integer from 1 to N   x = the missing integer   So as sum = average * Nb of terms   S-x= 27(4/13) * (N-1) (A)   As S-x should be an integer N-1 should be a multiple of 13.   So we have some possible scenario   N-1= 13 => N=14   N-1= 26 => N=17   N-1= 39 => N=40   N-1= 52 => N=53   ....   Back to our formula (A)   x = S - 27(4/13)*(N-1)   x = (N(N+1))/2 - 27(4/13)*(N-1)   As x>0   (N(N+1))/2 > 27(4/13)*(N-1)   approx 27(4/13) by 27   (N(N+1))/2 > 27*(N-1)   N(N+1) > 54*(N-1)   So we see than N=53 is working (indeed 53*54>54*52)   So if N=53:   x = (53(54))/2 - 27(4/13)*(52)   x = (53(54))/2 - (27+4/13)*(52)   x = (53(54))/2 - 27*52-(4/13)*52   x = 53*27 - 27*52-(4/13)*52   x = 53*27 - 27*52-4*4   x = 27*(53-52) - 16   x = 27 - 16= 
27 - 16 = 11
11   ANSWER:11
Answer: C
If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth?  Choose the correct choice from the following answers:
A) Rs.{(b*x)/b}
B) Rs.{(b*x)/a}
C) Rs.{(b*x)/j}
D) Rs.{(b*x)/l}
E) Rs.{(b*x)/as}

Solution: Explanation:   Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a).   The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a}   ANSWER:Rs.{(b*x)/a}
Answer: B
A mixture of certain quantity of milk with 16 liters of water is worth 90 P per liter. If pure milk be worth Rs1.08 per liter, how much milk is there in the mixture?
Choose one:
A) 100	B) 90	C) 80	D) 75	E) 70

Solution: The mean value is 90 P and price of water is 0 P   By the alligation rule : Quantity of milk / Quantity of water   = (90 - 0) / (108 - 90)   = 90 / 18= 
90 / 18 = 5
5/1   proportion milk is 5/1 there in the mixture   therefore  5 * 16= 
 5 * 16 = 80
80 liters milk is there in the mixture.   Ans - 80
Answer: C
Tough and Tricky questions: Arithmetic.
(56^2 + 56^2)/28^2 =
Pick.
A) 4 B) 18 C) 29 D) 8 E) 116

Solution: Ans is 8   my approach was:   (56^2 + 56^2)/28^2 =56(56+56)/28*28   =56*112/28*28=2*4= 
2*4 = 8
8   8
Answer: D
A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 840 in 4 years. The rate on interest per annum is. Choose the correct choice:
A) 4%
B) 5%
C) 6%
D) 7%
E) 8%

Solution: S.I. on Rs 800 for 1 year = 40   Rate = (100*40)/(800*1)= 
(100*40)/(800*1) = 5
5%   Answer: Option 5%
Answer: B
A corporation ten times its annual bonus to 25 of its employees. What percent of the employees’ new bonus is the increase? Choose one:
A) 25%	B) 44%	C) 38%	D) 9%	E) 90%

Solution: Let the annual bonus be X.   A corporation triples its annual bonus.   So new bonus = 10X.   Increase = 10X-X =9X   The increase is what percent of the employees’ new bonus   = (9X/10X)*100   = 90%   Hence 90%.(9 /10 )*100= 
(9 /10 )*100 = 90
90%   Hence 90%.
Answer: E
Of the 200 stamps in a collection, 80 are foreign and 50 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old?
Choose the most appropriate option
A) 60
B) 90
C) 100
D) 130
E) 150

Solution: 20 stamps are both foreign and more than 10 years old.   60 stamps are foreign only.   30 stamps are 10 years old only.   The number of remaining stamps is  200 - (20+60+30)= 
 200 - (20+60+30) = 90
90   The answer is 90.
Answer: B
In a tennis match if the first serve is not legal, that means a fault a second serve is allowed. Normally, 20 to 40 serves are required in a set of tennis match. At the end of a set, set summary stats reveal that first serves percentage was 63%. If m out of n were first serves then m + n is equal to Answers
A) 1.43n B) 1.53n C) 1.63n D) 2.63n E) 3.63n

Solution: m=n*(63/100)=63n/100   so,   m+n= 63n/100 + n   = 163n/100   = 1.63n   ANSWER:1.63n163 /100= 
163 /100 = 163/100 = around 1.63
1.63n   ANSWER:1.63n
Answer: C
In the faculty of Reverse-Engineering, 200 second year students study numeric methods, 400 second year students study automatic control of airborne vehicles and 100 second year students study them both. How many students are there in the faculty if the second year students are approximately 60% of the total?	Choose the correct choice from the following answers.
A) 834 B) 750 C) 633 D) 654 E) 812

Solution: Total number of students studying both are 400 + 200 - 100= 
400 + 200 - 100 = 500
500 (Subtracting the 100 since they were included in the both the other numbers already).   So 60% of total is 500, so 100% is approx. 834.   834nswer is 834
Answer: A
Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 180 feet in circumference.After how many minutes are the three of them together again? Choose the correct option: A) 3 mins B) 10 mins C) 15 mins D) 3 mins E) 7 mins

Solution: Answer will be A.   The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 3 mins.
Answer: A
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?
Choose the correct option:
A) 1/26 B) 1/20 C) 1/25 D) 1/29 E) 1/23

Solution: Let E1 be the event of drawing a red card.   Let E2 be the event of drawing a king .   P(E1 ∩ E2) = P(E1) . P(E2)   (1/26s E1 and E2 are independent)   = 1/2 * 1/13 = 1/26.1/26nswer: 1/26
Answer: A
Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 40% in the following week, and increased by 30% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks? Choose the most appropriate option:  A) 0.875G  B) 0.9G  C) 0.925G  D) 0.95G  E) 0.975G

Solution: After 3 weeks, the price was 1.3*0.6*1.25*G=0.975G   The answer is 0.975G.
Answer: E
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 25th in an arithmetic progression if the sum of the 11th and 15th terms of the sequence is 96? Select.
A) 48  B) 63  C) 55  D) 96  E) 108

Solution: Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 13th term in the sequence.   Then the mean of the 12th and 14th term is also equal to the overall mean, because the 12th term is (13th term - x) and the 14th term is (13th term + x).   Similarly the mean of the 11th and 15th term is also equal to the mean.   etc...   Thus the mean is   96/2= 
  96/2 = 48
48   The answer is 48.
Answer: A
A train running at the speed of 90 km/hr crosses a pole in 10 seconds. Find the length of the train.	Choose the correct choice from the following: A) 150 B) 180 C) 250 D) 200 E) 225

Solution: Speed = 90*(5/18) m/sec = 25 m/sec   Length of Train (Distance) = Speed * Time     25 *10= 
  25 *10 = 250
250 meter   Answer:250
Answer: C
Exactly two sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 2 times and the die lands with a red side up for the first time on the second roll?
Answers
A) 0.16
B) 0.2
C) 0.3
D) 0.32
E) 0.56

Solution: Total no. of sides = 10   Sides that are red = 2   Probability that the die lands with red side up = 2/10   Therefore, Probability that the die does not land with red side up = 1 - 2/10 = 8/10   Probability that Kumar rolls the die 2 times and the die lands with a red side up for the first time on the second roll   = (1st roll - non red face) X (2nd roll - red face)   = 8/10 x2/10   = 16/100= 
16/100 = 4/25 = around 0.16
0.16= 0.128   0.16
Answer: A
The average salary per head of the entire staff of an college including the lecturer and professors is Rs.90. The average salary of professors is Rs.600 and that of the lecturer is Rs.84. If the number of professors is 2, find the number of professors in the office?	Options.
A) 900  B) 1000  C) 1020  D) 1200  E) 1240

Solution: 1->12   85->1020   1020
Answer: C
A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The
area of the lawn is (1/6) hectares. Find breadth of the lawn.
Choose the correct choice from the following:
A) 15 m
B) 20 m
C) 25 m
D) 35 m
E) 50 m

Solution: Let length = 2x metres and breadth = 3x metre.   Now, area = (1/6 )x 1000 m2 = 5000/3m2   So, 2x * 3x = 5000/3 <=>x2= 2500/9 <=>x = 50/3   therefore Breadth = 3x = 3(50/3) m   = 50m.   ANSW50 mR 50 m 50 m
Answer: E
The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?	Choose one:
A) 2 years	B) 7 years	C) 9 years	D) 5 years	E) 3 years

Solution: Amount = (30000 + 4347) = Rs. 34347   Let the time be n years. Then,   30000(1 + 7/100)n = 34347   = (107/100)n = 34347/30000 = (107/100)2   n = 2 years.   2 yearsnswer: 2 years
Answer: A
In how many years will a sum of money doubles itself at 5% per annum simple interest  Pick:
A) 25 years
B) 28 years
C) 10 years
D) 20 years
E) 21 years

Solution: let the initial sum be x   then,Amount=2x(because sum will be double)   Amount = Principal + S.I   2x = x + s.I   S.I = x   S.I = (p*r*t)/100   x = (x*5*t)/100   therefore,t = 20 years   ANSWER:20 years
Answer: D
An equity analyst needs to select 5 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 10, in how many ways can she choose and rank her top 5 picks?  Choose the correct choice from the following options: A) 21548 B) 31502 C) 21250 D) 30240 E) 84045

Solution: Number of ways of choosing 5 stocks = 10C5   Number of ways of ranking the chosen stocks = 5!   Hence total ways of chosing and ranking = 10C5 * 5! = 30240   Correct Option: 30240
Answer: D