MU-NLPC/Calc-aqua_rat huggingface dataset:
P and Q had the same number of candies. P gave Q 16 candies so that now Q has five times as many candies as P has. How many candies does Q have now?	Choose the correct choice from the following choices:	A) 25	B) 30	C) 35	D) 40	E) 45

Solution: Let P and Q be the number of candies they had at the start.   P = Q   5(P-16) = Q+16   5(Q-16) = Q+16   4Q = 96   Q = 24   Now person Q has 24+16 candies which is 40 candies.   The answer is 40.
Answer: D
The average weight of 8 persons increases by 3.5 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 the correct choice from the following
A) 75 kg B) 65 kg C) 55 kg D) 85 kg E) 93 kg

Solution: Total weight increased = (8 x 3.5) kg = 28 kg.   Weight of new person = (65 + 28)= 
(65 + 28) = 93
93 kg.   Answer: 93 kg
Answer: E
D and E are two points respectively on sides AB and AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 144:25 and DE=13 cm, then find the length of BC.
Pick
A) 5  B) 13  C) 14  D) 11  E) 15

Solution: ABC and ADE are similar triangles.   So (side of 5BC/side of 5DE)^2=25/169   side of 5BC/side of 5DE = 5/13   So the length of BC = 5   5nswer - 5
Answer: A
0.99999999/1.0001−0.99999991/1.0003
Pick: A) 10^(-8 B) 3*10^(-8) C) 3*10^(-4) D) 2*10^(-4) E) 10^(-4)

Solution: look at the options closely   A. 0.00000001   B. 0.00000003   C. 0.0003   D. 0.0002   E. 0.0001   Only one option is an even number, the rest odd (an esoteric sort of even/odd number)   both fractions in the question are odds   odd minus odd is always even.   So answer must be even.   Only 2*10^(-4) is even.
Answer: D
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth?
Options:
A) Rs. 600	B) Rs. 500	C) Rs. 400	D) Rs. 300	E) None of these

Solution: Explanation :   T = 2 years   R = 10%   TD = (BG ×100)/TR = (24 × 100)/(2×10) = 12 × 10 = Rs. 120   TD = (PW × TR)/100   ⇒ 120 = (PW × 2 × 10)/100   ⇒ 1200 = PW × 2   PW =1200/2 = Rs. 600 Rs. 600nswer : Option Rs. 600
Answer: A
In a 120 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?
Choose one:
A) 49	B) 47	C) 25	D) 43	E) 41

Solution: Solution simple   Out of 120 20% are male i.e 24 and 25% are female i.e 30 , so total homeowner is 54.   Now min number homeowner is 24 and max is 54 so question ask us to find least and 25 has least value among all option.   So ans is 25.   Answer : 25
Answer: C
Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank? Answers:
A) 33	B) 540	C) 287	D) 278	E) 191

Solution: 1/12 + 1/15 - 1/x = 1/15   x = 12   12 * 45= 
12 * 45 = 540
540   Answer:540
Answer: B
John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?  Choose the correct choice from the following
A) 1/16  B) 5/16  C) 3/8  D) 1/2  E) 1/4

Solution: John will run farther if he runs at 5 mph and Amanda runs at 4 mph.   P(John runs farther) = 1/4 * 1/4 = 1/16   The answer is 1/16.
Answer: A
Oranges are bought at 7 for Rs.6. At what rate per hundred must they be sold to gain 33%?
Choose the correct choice.
A) 57 B) 68 C) 95 D) 114 E) 125

Solution: 7 oranges bought for rs 6   1 orange cost =6/7   therefore for 100 oranges =100*(6/7)   gain =33%    600/7+(33/100)*600/7= 
 600/7+(33/100)*600/7 = 114
rate per hundred he want to sell   ans :114   ANSWER:114
Answer: D
If a certain sample of data has a mean of 20.0 and a standard deviation of 2.5, which of the following values is more than 2.5 standard deviations from the mean?
Choose the correct choice from the following:	A) 22.0	B) 13.5	C) 17.0	D) 23.5	E) 12.0

Solution: The standard deviation is 2.5. 2.5 standard deviations, which is just 2.5 x 2.5 is 6.25. The only answer more than 6.25 away from the mean is 12.0.
Answer: E
The traffic lights at 3 different roads change after every 12 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.  Choices:	A) 9:18:36	B) 9:42:15	C) 10:15:24	D) 9:54:12	E) 10:01:20

Solution: LCM of 12,72,108 =216 = 3mnts 36sec   The lines will change every 3m 36sec   The light will change again after 9:15 9:18:36M is = 9:15+0:03:36 = 9:18:36   9:18:36nswer is 9:18:36
Answer: A
If the ratio of a to b is 11 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?  Choose the correct choice from the following answers
A) 4/15 B) 11/15 C) 2/5 D) 4/5 E) 7/6

Solution: a:b = 11:3 -- 1   b:c = 1:5   =>b:c = 3 :15 --2   From 1 and 2 , we get   a:c = 11:15   Answer 11/15
Answer: B
The face value of a share is Rs 100. It is sold at a discount of Rs 5. How many such shares can be bought by investing Rs 38,000?	Select
A) 360	B) 380	C) 420	D) 400	E) 480

Solution: Face value of a share=Rs.100   400iscount=5%   so,Share is bought at Rs.95   Investing amount=Rs.38,000,so 380 shares are bought without discount   With discount 400 shares can be bought   ANSWER:400
Answer: D
If a traveller was offered 5 destinations in asia and 11 destinations in europe and asked to chose utmost 3 destinations in asia and overall a 11 destinations. How many ways can he travel
Options:
A) 2256 ways
B) 2356 ways
C) 2456 ways
D) 2556 ways
E) 2156 ways

Solution: He can choose atmost 3 out of 5 destinations in Asia and 11 destinations overall.   Also it is mentioned that there are 11 destinations in Europe:   No. of ways this can be done is :-   5c3*11c8+5c2*11c9+5c1*11c10+5c0*11c11= 2256 ways   2256 waysNSWER:2256 ways
Answer: A
Each term of a certain sequence is 4 less than the previous term. The first term of this sequence is 19. If the sum of the first n terms of the sequence is n, what is the value of positive integer n? Select
A) 1
B) 13
C) 15
D) 19
E) 47

Solution: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.   What does this imply?If the sum of the first n terms of the sequence is n   Since number of terms will definitely be positive, we are looking for a positive sum.   19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on   Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...   Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.   Answer (15)
Answer: C
You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many Q different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter? Choose the most appropriate option
A) 5 B) 6 C) 9 D) 12 E) 18

Solution: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:   XYZ   YZX   ZXY   And:   XYZ   ZXY   YZX   Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible Q is   2*6= 
  2*6 = 12
12.   Answer: 12.
Answer: D
John and Peter are among the eight players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter? Choices
A) 2/5
B) 2/7
C) 2/9
D) 5/14
E) 8/21

Solution: The total possible ways of selecting a 5-member team is 8C5 = 56   The possible ways which include John and Peter is 6C3 = 20   The probability of choosing both John and Peter is 20/56 = 5/14   The answer is 5/14.
Answer: D
Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?
Pick:
A) ab/(a+b)	B) (a-b)/(a+b)	C) b/(b+a)	D) a/(a+b)	E) b/(a-b)

Solution: Randy can do the job in a hrs, Alvin can do the job in b hrs.   When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.   Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)   So Randy does a/(a+b) of the work and Alvin does b/(a+b) of the work.   Answer (b/(b+a)).
Answer: C
A train ride from Two P to Town Q costs $6.35 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.85. What is the cost of a bus ride from Town P to Town Q? Choose the most appropriate option:
A) $1.75 B) $2.50 C) $4.10 D) $4.70 E) $8.20

Solution: Let x be the cost of a bus ride.   x + (x+635) = 985   2x = 350   x = $1.75   The answer is $1.75.
Answer: A
There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?  Choices.
A) 300  B) 301  C) 302  D) 303  E) None

Solution: They stole 301 diamonds in total.   We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.   60 + 1= 
60 + 1 = 61
61, not a multiple of 7   60 x 2 + 1= 121, not a multiple of 7   60 x 3 + 1 = 181, not a multiple of 7   60 x 4 + 1 = 241, not a multiple of 7   60 x 5 + 1 = 301, a multiple of 7   Answer 301
Answer: B
How many seconds will a 500 m long train take to cros a man walking with a speed of 3 kmph in the direction of the moving train if the speed of the train is 63 kmph  Choose the correct choice from the following answers.
A) 25
B) 30
C) 40
D) 45
E) 50

Solution: time=distance(here length of the train)/relative speed (63-3)   thus time=500/60*5/18=500*18/ 60*5   =30 seconds   ANSWER:30
Answer: B
If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?	Select the correct option
A) 2388  B) 3600  C) 2791  D) 1817  E) 1911

Solution: To arrange 6 periods with 5 subjects, then one subject can be arranged in two slots.   5 Subjects can be arranged in 6 periods in 6P56P5 ways and now we have 1 period which we can fill with any of the 5 subjects in 5 ways. so 6P5×5=6P5×5=3600   Alternate method:   Assume the subjects are X1, X2, A, B , C, D,. Here X is the subject which repeats. So arranging 6 objects in 6 places will be equal to 6! = 720 (here no need to divide this number with 2! as even though the subject is same, but not identical)   But this repeated subect can be any of the five. So total arrangements are 720 x 5 = 3600   Answer:	3600
Answer: B
The diagonals of a rhombus are 10 cm and 12 cm. Find its area?
Choose the most appropriate option
A) 158 B) 60 C) 150 D) 123 E) 117

Solution: 1/2 * 10 * 12= 
1/2 * 10 * 12 = 60
60   Answer:60
Answer: B
A and B start a business with investments of Rs.5000 and Rs.4500 respectively.After 4 months,A takes out half of his capital.After two more months,B takes out one-third of his capital while C joins them with a capital of Rs.7000.At the end of a year,they earn a profit of Rs.5080.Find the share of each member in the profit.  Choose the correct choice from the following choices:
A) A - Rs.1400,B - Rs.1900,C - Rs.1780  B) A - Rs.1600,B - Rs.1800,C - Rs.1680  C) A - Rs.1800,B - Rs.1500,C - Rs.1780  D) A - Rs.1680,B - Rs.1600,C - Rs.1800  E) None of these

Solution: Solution   A : B : C =(5000x4+2500x8) : (4500x6+3000x6): (7000x6)   = 40000 : 42000 : 45000 = 4 : 42 : 45.   A’s share = Rs. (5080x40/127) = Rs. 1600.   B’s share = Rs. (5080x45/127) = Rs. 1800.   C’s share = Rs. (5080x42/127) = Rs. 1680. Answer A - Rs.1600,B - Rs.1800,C - Rs.1680
Answer: B
What is the least number should be added to 1100, so the sum of the number is completely divisible by 23?	Options.
A) 1	B) 2	C) 5	D) 4	E) 8

Solution: (1100 / 23) gives remainder 19   19 + 4= 
19 + 4 = 23
23, So we need to add 4   Answer : 4
Answer: D
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:	Choose the correct choice from the following answers:
A) 22 B) 50 C) 99 D) 288 E) 12

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.Answer: 50
Answer: B
If d<0, which of the following represents a positive number?  Select:
A) d|d|	B) |d|d	C) |d|/d	D) -d|d|	E) d/ |d|

Solution: Answer : -d|d|
Answer: D
A circular mat with diameter 18 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Choose the most appropriate option:
A) 5/12 B) 3/5 C) 1/2 D) 3/8 E) 5/6

Solution: SO we are looking for the area of the cloth over the area of the table   Area of the Cloth = (pi)(r)^2 which is about (3)(9)(9)   Area of the Table = (24)(24)   So the quick way to estimate is looking at the fraction like this: (3/24)(81/24)   I hope this is easy to follow, so with some simplification i get (1/8)(3) = (3/8) Answer is 3/8
Answer: D
A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 7/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
Answers
A) 9/80  B) 3/10  C) 387/800  D) 35/80  E) 497/800

Solution: The first circuit doesn't matter.   Prob(relay fails) = 1 - Prob(relay succeeds)   Prob(2+3 work) = 1 - 21/80 = 59/80   Prob(4+5 work) = 1 - 3/10 = 7/10   Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (59/80)(7/10) = 1 - 413/800 = 387/800   387/800
Answer: C
If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 24 days, then C alone can do it in? Choose the correct choice from the following answers
A) 1
B) 7
C) 8
D) 9
E) 6

Solution: 8 = 1/4 - 1/12 – 1/24 = 1/8 => 8 days'   Answer: 8
Answer: C
If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price? Pick
A) 16 2/3% B) 16 2/6% C) 16 8/3% D) 17 2/3% E) 16 2/1%

Solution: Let the price of the article be Rs. 100.   20% of 100 = 20.   New price = 100 + 20 = Rs. 120   Required percentage = (120 - 100)/120 * 100   = 20/120 * 100 = 50/3 = 16 2/3%.   16 2/3%nswer:16 2/3%
Answer: A
Both Robert and Alice leave from the same location at 6:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 40 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?	Pick one:
A) 2 p.m. B) 3 p.m. C) 4 p.m. D) 8 p.m. E) 9 p.m.

Solution: 6:00 am so 6 hours later is 12:00 pm   In six hours, Robert will have driven  6*30= 
 6*30 = 180
180 miles   In six hours, Alive will have driven 6*40= 
6*40 = 240
240 miles   So Robert needs  240-180= 
 240-180 = 60
60 miles do catch Alice up.   So at 30 mph, he will need 2 hours   12:00 pm  + 2= 
 + 2 = 2
2:00 pm   2 p.m.NS : 2 p.m.
Answer: A
a merchant sold an article at a loss of 12%,. if the selling price had been increased by $50 the merchant would have made a profit of 8%. what is the cost price of the article?
Pick: A) $550 B) $500 C) $510 D) $565 E) $520

Solution: Let C.P. be $x   Then 108% of x - 88% of x = 100   20% of x = 100   x/5 = 100   x = 500   Answer is $500
Answer: B
Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year 12 members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 0 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?	Choose the correct choice from the following choices:	A) 52	B) 67	C) 71	D) 66	E) 79

Solution: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)   n(E or F or I) = 26 + 26 + 32 - 12 - 0 - 6 + 0   Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.   n(E or F or I) = 66   Answer (66)
Answer: D
A glass was filled with 25 ounces of water, and 0.04 ounce of the water evaporated each day during a 10-day period. What percent of the original amount of water evaporated during this period?
Choose the correct choice from the following answers:  A) 0.004%  B) 0.04%  C) 0.4%  D) 1.6%  E) 20%

Solution: In 10 days 10*0.04= 
10*0.04 = 0.4
0.4 ounces of water evaporated, which is 0.4/25âˆ—100=1.6 of the original amount of water.   Answer: 1.6%.
Answer: D
How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length?	Pick:
A) 12.9 sec	B) 12.1 sec	C) 24.2 sec	D) 16.8 sec	E) 14.9 sec

Solution: Speed = 36 * 5/18= 
36 * 5/18 = 10
10 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/10= 
242/10 = 121/5 = around 24.2
24.2 sec.   Answer: 24.2 sec
Answer: C
The wheel of a motorcycle 70cm in diameter makes 40 revolutions in every 10sec.What is the speed of motorcycle n km/hr? Choose the correct choice from the following answers:
A) 31.65 B) 31.68 C) 31.62 D) 31.61 E) 31.67

Solution: Explanation:   In this type of question, we will first calculate the distance covered in given time.   Distance covered will be : Number of revolutions x Circumference   So we will be having distance and time, from which we can calculate the speed.   Radius of wheel = 70 / 2= 
70 / 2 = 35
35 cm   Distance covered in 40 revolutions will be= 88 m   Distance covered in 1 sec =   Answer: 31.68) 31.68kmph
Answer: B
On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. Find the divisor. Answers.
A) 179 B) 189 C) 199 D) 169 E) None of them

Solution: Divisor = Dividend - Remainder / Quotient   = 15968-37 / 89   = 179.   179nswer is 179.
Answer: A
A garrison of 500 persons had provisions for 27 days. After 3 days a reinforcement of 300 persons arrived. For how many more days will the remaining food last now?  Choose the correct choice
A) 12 days B) 16 days C) 14 days D) 15 days E) None of these

Solution: Explanation :   Given that fort had provision for 500 persons for 27 days   Hence, after 3 days, the remaining food is sufficient for 500 persons for 24 days   Remaining persons after 3 days = 500 + 300= 
500 + 300 = 800
800   Assume that after 10 days,the remaining food is sufficient for 800 persons for x days   More men, Less days (Indirect Proportion)   ⇒Men500:800}::x:24   ⇒500 × 24= 800x   ⇒ 5 × 24 = 8x   ⇒ x = 5 × 3 = 15. Answer : Option 15 days
Answer: D
A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 75$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?  Select
A) 69.55$  B) 50.63$  C) 60.95$  D) 52.15$  E) 53.15$

Solution: let x is the cost of the food   1.07x is the gross bill after including sales tax   1.15* 1.07x=75   x=60.95   Hence, the correct option is 60.95$
Answer: C
A highway is to be divided into 3 lanes. For this purpose, two yellow stripes are painted so that stripes divide the highway into 3 lanes. If 2 gallons of paint cover an area of 3P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
Choose the correct choice: A) 440P/mx B) 880mx/P C) 880mx/3P D) 1760mx/3P E) 1760P/3mx

Solution: 1 square foot needs 2/3P gallons of paint.   The width of each stripe is x/12 feet.   The length of each stripe is 5280m feet.   The area of each stripe is (5280m)(x/12) = 440mx square feet.   For two stripes, the total area is 880mx square feet.   The number of gallons needed is (880mx)*(2/3P) = 1760mx/3P gallons.   The answer is 1760mx/3P.
Answer: D
A train 330 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose the most appropriate option:  A) 5  B) 6  C) 7  D) 18  E) 9

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [330 * 3/55= 
330 * 3/55 = 18
18 sec   Answer: 18
Answer: D
What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent? Choose one:
A) 288	B) 500	C) 299	D) 2766	E) 2912

Solution: 70 = (P*4*7/2)/100   P = 500.Answer: 500
Answer: B
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?  Choose the correct choice from the following answers.
A) 1/455
B) 1/487
C) 1/429
D) 1/876
E) 1/429

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue   = 3C3/15C3   = (1 * 3 * 2 * 1)/(15 * 14 * 13)   = 1/455   1/455nswer:1/455
Answer: A
r=4^(n+2), then in terms of r, 9^n= Choose the most appropriate option.
A) r^2/81 B) r^2/9 C) r^2/256 D) r/3 E) r

Solution: Questions in terms of variables can be easily solved by plugging in some values: Say n = 0   r = 4^2 = 16   and you need the value of 16^n which is 16^0 = 1   So when you put r = 16 in the options, you should get 1. Only option (A) satisfies.   Answer (r^2/256)
Answer: C
How many positive integers Q between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?
Choose the correct choice from the following answers.
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