MU-NLPC/Calc-aqua_rat huggingface dataset:
A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?	Choices:  A) 1/5  B) 1/3  C) 1/7  D) 1/9  E) 1/12

Solution: Let b stand for boy and g for girl. The sample space of the experiment is   S = {(g, g), (g, b), (b, g), (b, b)}   Let E and F denote the following events :   E : ‘both the children are girls’   F : ‘at least one of the child is a girl’   Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}   Now E n F = {(g,g)}   Thus P(F) = 3/4   and P (E n F )= 1/4   Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3   1/3)
Answer: B
What is the time required for a vehicle to cover a distance of 480 km with a speed of 60 kmh? Choose the correct choice.
A) 6 hours
B) 12 hours
C) 9 hours
D) 10 hours
E) 8 hours

Solution: Time= Distance / Speed   Time = 480 / 60= 
480 / 60 = 8
8   Answer: 8 hours
Answer: E
In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 12 people were made to stand in a column, how many columns could be formed?  Choose the correct choice from the following choices: A) 20 B) 30 C) 40 D) 50 E) 60

Solution: 16*30 = 12*n   n = 40   The answer is 40.
Answer: C
The average age of all the student of a class is 18 years. The average age of boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.  Answers
A) 15 B) 45 C) 30 D) 50 E) 60

Solution: Let Boys in class = B   Girls in class = 20   Now, (20B+15*20)/(B+20) = 18 => B = 30   Answer: 30
Answer: C
If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?	Choose the correct choice from the following answers
A) 245  B) 256  C) 364  D) 370  E) 390

Solution: A particular players is never chosen, it means that 11 players are selected out of 14 players.   => Required number of ways = 1436411   = 14!/11!x3! = 364   364
Answer: C
A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent Q of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?	Pick
A) 9%	B) 11%	C) 15%	D) 25%	E) 90%

Solution: Cost of 12 paper towels individually = 1*12= 
1*12 = 12
12   Cost of a set of 12 paper towels= 9   Cost of one roll = 9/12 = 3/4= 
3/4 = 3/4 = around 0.75
0.75   Savings per roll= 1-.75= 
1-.75 = 0.25
0.25   % of savings is Q= .25/ 1 *100= 
.25/ 1 *100 = 25
25% 25% is the answer.
Answer: D
Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?	Choose the correct option
A) 1
B) 4
C) 5
D) 6
E) 8

Solution: 2: 5: 13   2x 5x 13x   15 7.5 2.5   30x + 37.5x + 32.5x = 100x/20x   Average 30  + 37.5  + 32.5= 
30  + 37.5  + 32.5 = 100
100x/20x   Average = 5   Answer: 5100 /20= 
100 /20 = 5
5   Answer: 5
Answer: C
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is: Choose the most appropriate option:
A) 100 Kmph	B) 110 Kmph	C) 120 Kmph	D) 130 Kmph	E) 150 Kmph

Solution: Let speed of the car be x kmph.   Then, speed of the train =150X/100 = 3X/2 Kmph.   75/X - 75/(3X/2) = 125/(10 *60)   75/X - 50/X = 5/24   X = 25 * 24/5= 
25 * 24/5 = 120
120 Kmph.   Answer 120 Kmph) 120 Kmph
Answer: C
A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Answers:
A) 1.0	B) 1.7	C) 1.2	D) 1.5	E) 1.2

Solution: M = 4.5   S = x   1.5S = 4.5 + x   US = 4.5 + x   4.5 + x = (4.5 - x)2   4.5 + x = 9 -2x   3x = 4.5   x = 1.5.Answer:1.5
Answer: D
The sum of two numbers is 232 and their H.C.F is 29. How many pairs of such numbers are
Select the correct option:  A) 1  B) 2  C) 0  D) 3  E) None of these

Solution: Explanation:   HCF of two numbers = 29   Let the numbers = 29x, 29y   x and y are prime to each other   According to the question,   29x + 29y = 232, 29(x+y) = 232, x + y = 8,   Possible pairs of x and y = (1,7) and (3,5)   numbers are = (29, 203) and (87,145)   Answer: Option 2
Answer: B
What will come in place of the x in the following Number series? 2, 3, 6, 6, 18, 12, 54, 24, x Pick one: A) 162 B) 96 C) 78 D) 144 E) 180

Solution: There are two series here   2, 6, 18, 54, ... (Multiply by 3)   3, 6, 12, 24 (Multiply by 2)   Hence, next term is 54 x 3 = 162   Correct 162nswer is 162
Answer: A
Ratio of ages of three persons is 4:7:9, Eight years ago, the sum of their ages was 56. Find their
present ages	Pick one.
A) 16,35,36	B) 12,28,36	C) 16,28,27	D) 16,28,36	E) None of these

Solution: Explanation:   Let the present ages are 4x, 7x, 9x.   => (4x-8) + (7x-8) + (9x-8) = 56   => 20x = 80   => x = 4   So their present ages are: 16,28,36   Answer: Option 16,28,36
Answer: D
Rahim is able to sell a hand-carved statue for $840 which was a 20% profit over his cost. How much did the statue originally cost him? Choose the correct choice from the following options
A) $496.30  B) $512.40  C) $555.40  D) $574.90  E) $700

Solution: Cost price = 840/120*100= 
840/120*100 = 700
700   Answer : $700
Answer: E
An express traveled at an average speed of 150 km/hr, stopping for 3 min after every 80 kn. How long did it take to reach its destination 750 km from the starting point? Pick.
A) 5 hrs 24 min	B) 4 hrs 24 min	C) 6 hrs 44 min	D) 6 hrs 21 min	E) 4 hrs 34 min

Solution: A   5 hrs 24 min   Time taken to cover 750 km = 750/150= 
750/150 = 5
5 hrs.   Number of stoppages= 750/80 - 1 = 8   Total time of stoppages = 3 * 8= 
3 * 8 = 24
24 min   Hence, total time taken= 6 hrs 21 min.
Answer: A
A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 1.8 kilometer long bridge, at the same speed? Choose the correct answer:
A) 4 min	B) 2 min	C) 8 min	D) 9 min	E) 3 min

Solution: S = 600/40= 
600/40 = 15
15 mps   S= 1800/15= 
1800/15 = 120
120 sec= 2 min.Answer: 2 min
Answer: B
Rooney, Hernandez, and Robin race each other in a 100 meters race. All of them run at a constant speed throughout the race.
Rooney beats Hernandez by 20 meters.
Hernandez beats Robin by 20 meters.
How many meters does Rooney beat Robin by ?	Choose the correct option.
A) 33 meters.  B) 29 meters.  C) 25 meters.  D) 36 meters.  E) 30 meters.

Solution: D   36 meters.   100/v1 = 80/v2   100/v2 = 80/v3   20+(20/v2)*v3=20+16= 
20+16 = 36
36
Answer: D
A man can row 7 Â½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place?
Select the correct option:
A) 4 km  B) 2 km  C) 5 km  D) 3 km  E) 1 km

Solution: Speed downstream =(7.5+1.5)km/hr=9 km/hr;   Speed upstream=(7.5-1.5)= 
(7.5-1.5) = 6
6kmph.   Let the required distance be x km.then,   x/9+x/6=50/60.   2x+3x=(5/6*18)   5x=15   x=3.   Hence,the required distance is 3km.   ANSWER 3 km
Answer: D
How many times are the hands of a clock at right angle in a day? Choose the correct option:  A) 22  B) 44  C) 41  D) 21  E) 40

Solution: Correct Answer : 44   In 12 hour hands of clock are at right angle 22 times   In 24 hour hands of clock are at right angle 44 times
Answer: B
If 7^k + 7^k = (7^9)^(7^9) - 7^k, then k = ? Choose the correct choice
A) 11/3
B) 11/2
C) 242
D) 3^10
E) 7^11 - 1

Solution: 7^k + 7^k = (7^9)^7^9 - 7^k   7*(7^k) = 7 ^ (49 * 7^9 ) = 7^(7^2 * 7^9) = 7^(7^11)   7^k+1 = 7^(7^11)   So k+1 = 7^11   So k = 7^11 -1   Answer is 7^11 - 1
Answer: E
If a number is 60% more than the another, how much % is the smaller number less than the first ? Choices
A) 32(1/3)%
B) 16(2/3)%
C) 37(1/2)%
D) 36(4/3)%
E) none of these

Solution: Take a number 100,   Then the other number is 160   % the smaller number is less than the first = [(60/(160)) x 100]% = 37(1/2)%.   ANSWER:37(1/2)%
Answer: C
S = { 8,4,7,3,2,9}
T = { 4,5,6,3,1,7}
what is the probability that x chosen from S and y chosen from T will result x*y = even	Choose the correct option.
A) 2/5 B) 4/7 C) 5/3 D) 5/6 E) 1/6

Solution: p: the probability that x*y is even, then p=1-p(x*y is odd)   p(x*y odd)=p(x odd)*p(y odd)=3/6*4/5=1/3   2/5nd p=1-6/10=2/5   Option: 2/5
Answer: A
Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 4 pages a minute more than printer A ?
Choose the correct answer:
A) 600	B) 480	C) 1000	D) 1200	E) 1500

Solution: Answer: 480.
Answer: B
The average age of 15 men of a group is 15 years. Out of these, the average age of 5 men is 15 years and that of the other 9 men is 16 years. The age of the 15th man is?
Choose the correct option:
A) 11 years
B) 17 years
C) 6 years
D) 14 years
E) 12 years

Solution: Age of the 15th student   =[15 * 15 - (15 * 5 + 16 * 9)]   = (225 - 219)= 
(225 - 219) = 6
6 years.   Answer:6 years
Answer: C
A password of a computer used seven digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
Choose the most appropriate option
A) 1/32  B) 1/16  C) 1/8  D) 2/5  E) 1/128

Solution: We have seven digits can be used for password -0,2,3,5,7.   Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)   So, 5/10 * 5/10 * 5/10 * 5/10 * 5/10 * 5/10 * 5/10=1/128 (1/128)
Answer: E
A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5? Select the correct option.
A) 77 cm B) 10 cm C) 88 cm D) 12 cm E) 13 cm

Solution: 30 * 20 * x = (8 * 5.5 * 1.5)/2   Answer: 10 cm
Answer: B
The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?  Choose the correct option
A) 18%	B) 19%	C) 28%	D) 38%	E) 16%

Solution: 1500 ---- 270   100 ---- ? => 18%   18%nswer:18%
Answer: A
At what price must an article costing Rs.47.50 be marked in order that after deducting 12% from the list price. It may be sold at a profit of 25% on the cost price?	Choose the correct choice from the following answers:
A) 62.5	B) 67.5	C) 62.7	D) 62.2	E) 62.9

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(88/100)= 59.375   MP = 67.5   Answer:67.5
Answer: B
The perimeter of a triangle is 32 cm and the inradius of the triangle is 3.5 cm. What is the area of the triangle?
Choose the correct choice from the following options
A) 22 B) 35 C) 56 D) 54 E) 23

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 3.5 * 32/2= 
3.5 * 32/2 = 56
56 cm2   Answer:56
Answer: C
The average of five numbers is 27. If one number is excluded, the average becomes 23. The excluded number is? Select the correct option:  A) 46  B) 45  C) 44  D) 43  E) 42

Solution: Excluded number = (27 * 5) - (23 * 4)   = 135 - 92= 
135 - 92 = 43
43.   Answer: 43
Answer: D
1/2, 1/4, 1/8 ....
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?  Pick:
A) 0.1 < x < 1 B) 0.01 < x < 0.1 C) 0.001 < x < 0.01 D) 0.0001 < x < 0.001 E) 0.00001 < x < 0.0001

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. 0.01 and 0.1.(0.01 < x < 0.1)
Answer: B
A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?	Choose the correct choice from the following answers
A) 144 B) 166 C) 186 D) 199 E) 161

Solution: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.   Let their initial investments be 6x, 2x and 3x respectively.   A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.   B's share = = Rs. 144.   144nswer: 144
Answer: A
A can do a work in 9 days and B can do the same work in 18 days. If they work together, in how many days will they complete the work? Choose the correct choice.
A) 4 days	B) 6 days	C) 8 days	D) 2 days	E) 9 days

Solution: 6 days   6 days   One day's work of A and 6 days = 1/9 + 1/8 = (2+1)/18 = 1/6 So, the time taken to complete the work is 6 days.
Answer: B
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.?	Options:
A) 8:50 a.m
B) 5:50 a.m
C) 7:50 a.m
D) 6:50 a.m
E) 9:50 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: C
A train 140 m in length crosses a telegraph post in 16 seconds. The speed of the train is? Answers:
A) 30.5 kmph B) 31.5 kmph C) 32.5 kmph D) 33.5 kmph E) 21.5 kmph

Solution: S = 140/16 * 18/5= 
140/16 * 18/5 = 63/2 = around 31.5
31.5 kmph   ANSWER:31.5 kmph
Answer: B
How many integers between 100 and 1000 are there such that their unit digit is odd?  Choose the correct answer.
A) 400 B) 420 C) 500 D) 450 E) 350

Solution: 900 numbers between - 100 and 1000   Out of which half would be even, half odd.   Number of odd unit digit number = 450.   correct option is 450
Answer: D
A person works on a project and completes 5/8 of the job in 10 days. At this rate, how many more days will he it take to finish the job?  Pick.
A) 7  B) 6  C) 5  D) 4  E) 3

Solution: Explanation:   Number of days he worked = 10   Work completed =5/8   Let the required number of days =x   Remaining Work to be completed =1−5/8=3/8   More work, more days(direct proportion)   Hence we can write as   (Work) 5/8 : 3/8:: 10 : x   ⇒5/8×x=3/8×10   ⇒5×x=3×10   ⇒x=3×2=6   Answer: Option 6
Answer: B
What is the difference between the place value of 3 in the numeral 7339?
Select:
A) 170
B) 160
C) 180
D) 190
E) 210

Solution: 300 - 30 = 170   170
Answer: A
Mr. Jones sold two pens at $1 each. Based on the cost, his profit one was 50% and his loss on the other was 40%. On the sale of the pipes. Find the amount of his profit or loss?  Choose the correct choice from the following choices.
A) lost 10 cents	B) lost 4 cents	C) broke even	D) gained 4 cents	E) gained 40 cents

Solution: 50 % profit on $ 1   = $ 50/100 × 1   = $ 0.50× 1   = $ 0.50   Similarly, 40 % loss on $ 1   = $ 40/100 × 1   = $ 0.40× 1   = $ 0.40   Therefore, in one pen his profit is $ 0.50 and in the other pipe his loss is $ 0.40   So profit by amount $0.40.   Answer is gained 40 cents.
Answer: E
If d=1/(2^3*5^10) is expressed as a terminating decimal, how many nonzero digits will d have?
Choose the most appropriate option.
A) One B) Two C) Three D) Seven E) Ten

Solution: Another way to do it is :   We know x^a*y^a=(X*Y)^a   given = 1/(2^3*5^10)   = Multiply and divide by 2^7   =2^7/(2^3*2^7*5^10)   =2^7/10^10   => non zero digits are 128 => Ans Three
Answer: C
Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n =
Options:
A) 27
B) 272
C) 98
D) 25
E) 72

Solution: Given 10m=n.2210m=n.22   ⇒⇒ 2m×5m=n.22⇒2m−2×5m=n2m×5m=n.22⇒2m−2×5m=n   For m = 2 we get least value of n = 25, and for m > 2 we get infinite values are possible for n.   Answer:25
Answer: D
A, B and C started a shop by investing Rs. 10,000, Rs. 10,000 and Rs. 20,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 4,000, then the total profit was :  Pick one
A) 30,000	B) 60,000	C) 8,000	D) 120,000	E) None

Solution: Sol.   A : B : C = 10000 : 10000 : 20000 = 1: 1 : 2. so, Câ€™s share : Total Profit = 2 : 4   Let the total profit be Rs. x. Then, 2/4 = 36000/x or x   = 4000 * 4 / 2= 
4000 * 4 / 2 = 8_000
8000.   Answer 8,000
Answer: C
In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:	Answers: A) 20 B) 99 C) 88 D) 27 E) 21

Solution: Distance covered by B in 9 sec. = \inline \fn_jvn {\color{Black} \left ( \frac{100}{45}\times 9 \right )m} = 20m   \fn_jvn {\color{Black} \therefore } A beats B by 20 metres.   20nswer: 20) 20m
Answer: A
If a+b=−6, and a=10/b, what is the value of a^2+b^2? Choose the correct answer:
A) 22
B) 24
C) 16
D) 18
E) 20

Solution: a^2 + b^2 should make you think of these formulas:   (a+b)(a+b) = a^2+b^2+2ab   We already know (a+b) = -6 and a*b = 10   (a+b)(a+b) = (-6)(-6) = a^2+b^2+2*(10)   a^2+b^2 = 36 - 20= 
36 - 20 = 16
16   Answer : 16
Answer: C
A boy standing idle sounds a whistle to his friend at a distance of 1200 m moving away from him in a speeding car at 108 kms /hr. Find the duration after which his friend is going to hear him. (Speed of sound = 330m/sec). Pick.
A) 3.6 secs B) 4.00 secs C) 40 secs D) 45 secs E) None of these

Solution: If friend hears sound after t secs, then   330*t = 1200 +(108*5/18)*t   300t =1200   t= 4 secs   ANSWER:4.00 secs
Answer: B
In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 80% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that a beginner Trigonometry student is selected? Choose the correct choice
A) 40%  B) 44%  C) 48%  D) 52%  E) 56%

Solution: Let x be the number of students in calculus.   Then the number of students in trigonometry is 1.5x   The number of students on beginner calculus is 0.8x   The number of students in beginner trigonometry is 4/5*(2.5x) - 0.8x = 1.2x   The percentage in beginner trigonometry is 1.2x / 2.5x  4/5*(2.5 ) - 0.8= 
 4/5*(2.5 ) - 0.8 = 1.2
1.2x   The percentage in beginner trigonometry is 1.2x / 2.5x= 48%   The answer is 48%.
Answer: C
If each term in the sum E=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
Select:	A) 38	B) 39	C) 40	D) 41	E) 42

Solution: Min value of 'n' can be 10 i.e 4*22+6*12=E => 22+22+22+22+2+2+2+2+2+2= 
22+22+22+22+2+2+2+2+2+2 = 100
100   Since we don't have 10 in the options proceed further, (10-1)+22/2=> 20 digits, which is again not in the options    (20-1) + 22/2= 
 (20-1) + 22/2 = 30
30 digits ( not in options)   (30-1) + 22/2= 
(30-1) + 22/2 = 40
40 digits   Hence 40.
Answer: C
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is? Pick one
A) 0.5907	B) 0.5904	C) 0.5902	D) 0.5901	E) 0.59023

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36) = 0.5904.Answer: 0.5904
Answer: B
The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 62 kg. What is the correct weight?
Choose the correct option
A) 58kgs
B) 58.85kgs
C) 58.7kgs
D) 59kgs
E) 59.85kgs

Solution: Actual total weight is (20X 58.4 - 56 + 62) = 1174 Kgs   Actual average weight is   1174/20= 
  1174/20 = 587/10 = around 58.7
58.7kgs   58.7kgs
Answer: C
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 170, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
Answers:
A) 30  B) 33  C) 55  D) 77  E) 88

Solution: Let f = pure fuji , g = pure gala and c - cross pollinated.   c = 10% of x where x is total trees.   c = .1x   also 3x/4 = f and c+f = 170 => .1x + 3/4x = 170 => x = 200   200 - 170 = pure gala = 30.   30nswer 30
Answer: A
If 5 less than x is 4 greater than y, then a number z that is 3 greater than x reduced by y is equal to	Choices
A) 4	B) 12	C) 14	D) y + 9	E) y + 14

Solution: 12 it is....nice one....   12
Answer: B
How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?	Choose the correct choice from the following answers.
A) 2 years	B) 3 years	C) 1 year	D) 4 years	E) 5 years

Solution: Explanation:   P = Rs.900   SI = Rs.81   T = ?   R = 4.5%   T= (100×SI)/PR   = (100×81)/(900×4.5) = 2 years   2 yearsnswer: Option 2 years
Answer: A
How many positive, 3-digit integers contain at least one 7?
Options
A) 171 B) 200 C) 243 D) 252 E) 271

Solution: 243ontains only one 7:   7XX:  1*9*9= 
 1*9*9 = 81
81   X7X: 8*1*9= 
8*1*9 = 72
72   XX7: 8*9*1= 72   243ontains two 7s:   77X: 1*1*9= 
1*1*9 = 9
9   X77: 8*1*1= 8   243ontains three 7s:   777: 1   Total 243   ANS:243
Answer: C
How many positive integers D between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?  Choose the correct option
A) 3
B) 16
C) 75
D) 24
E) 26

Solution: 1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.   2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).   3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.   4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!   6) Answer choice 26.
Answer: E
Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part? Choose the correct choice from the following: A) 29 B) 30 C) 31 D) 35 E) 38

Solution: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation   larger number – smaller number = 7   which is equivalent to   Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.   31
Answer: C
A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?  Choose the correct choice
A) Rs.256.75
B) Rs.256.28
C) Rs.256.29
D) Rs.256.21
E) Rs.256.25

Solution: Let the principal be Rs.P   S.I at 5% p.a in 8 years on Rs.P = Rs.500   (P)(8)(5)/100 = 500   P = 1250   C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years   =2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}   = 2500/400(441 - 400)   = 25/4(41) = 1025/4   =Rs.256.25   Answer:Rs.256.25
Answer: E
what no should be subtracted from 92555 to make it a perfect square ? Choose the correct choice from the following answers:	A) 128	B) 158	C) 178	D) 139	E) 140

Solution: root 92555= 304.228   and   304^2=92416   92555-92416= 
92555-92416 = 139
139 should be subtracted from 92555 to make it a perfect square   ANSWER:139
Answer: D
Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms Lucy pick?	Choices:
A) 2 kilograms
B) 4 kilograms
C) 6 kilograms
D) 8 kilograms
E) 10 kilograms

Solution: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2, respectively. So   x+2x+x+2=26   4x=24   x=6   Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.   correct answer 8 kilograms
Answer: D