MU-NLPC/Calc-aqua_rat huggingface dataset:
The ratio, by volume, of soap to alcohol to water in a certain solution is 4:40:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 200 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?	Choose the correct answer.
A) 1300 B) 1500 C) 1600 D) 1700 E) 1800

Solution: soap:alcohol   Initial ratio soap:alcohol: water --> 4:40:90   Initial soap:alcohol = 4/40 =4:40   after doubled soap:alcohol =2* 4/40 = 8:40   Initial soap:water = 4/90=4:90   after halved soap:water: 1/2 * 4/90 = 2/90 = 2:90   After soap: alcohol:water --> 8:40:360-->1:5:45   given alcohol 200 cubic centimeter.   ratio is 40:200:1800(1:5:45)   For 200 cubic centimeter of Alcohol --- 1800cubic cm water is required.   Answer-1800
Answer: E
Jerry, an electrician, worked 8 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 8? 12 months = 1 year	Pick
A) 58.33% B) 66.67% C) 78.33% D) 88.33% E) 98.33%

Solution: 1. Multiply the opposites   8 x 100 = 800   100=8/12   Divide by the remaining number   66.67% (rounded to hundredth)   correct answer 66.67%
Answer: B
A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?	Choose the correct choice from the following answers:
A) 20:64:49 B) 49:20:64 C) 49:64:20 D) 64:49:20 E) 20:49:64

Solution: Ratio in which A,B and C shared the profit =5:7:8   Assume that the ratio of their investments =a:b:c   ⇒14a:8b:7c=5:7:8⋯(A)   From (A),   14a:8b=5:7   ⇒14a×7=8b×5   ⇒7a×7=4b×5   ⇒b=49a/20⋯(1)   From (A),   14a:7c=5:8   ⇒14a×8=7c×5   ⇒2a×8=c×5   ⇒c=16a/5⋯(2)   a:b:c=a:49a/20:16a/5   =1:49/20:16/5   =20:49:64   Answer is 20:49:64.
Answer: E
A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?  Choose the correct choice from the following choices
A) 60 km/hr	B) 100 km/hr	C) 110 km/hr	D) 120 km/hr	E) None of these

Solution: Explanation :   Number of gaps between 41 poles = 40So total distance between 41 poles = 40*50= 
40*50 = 2_000
2000 meter= 2 kmIn 1 minute train is moving 2 km/minute.Speed in hour = 2*60= 
2*60 = 120
120 km/hour   Answer : 120 km/hr
Answer: D
Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 8 seconds.What is the length of the fast train?	Options.
A) 23 m	B) 23 2/9 m	C) 47m	D) 37 7/9m	E) 44 4/9 m

Solution: relative speed=20kmph=50/9m/sec   length of the train=50/9*8=44 4/9 m   ANSW44 4/9 mR:44 4/9 m
Answer: E
Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 8 : 4?  Choose one:
A) 16
B) 45
C) 277
D) 92
E) 11

Solution: Let the distances between city A to B and B to C be 8x km and 4x km respectively.   Total time taken to cover from A to C   = (8x)/40 + (4x)/60 = (4x + 8x)/120 = 32x/120 = 4x/15 Average speed = (8*x + 4x)/(4x/15) = 45 kmph.   Answer:45
Answer: B
Rahul went to a shop and bought things worth Rs. 30, out of which 40 Paise went on sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?	Choices:
A) 17.6
B) 24.6
C) 21.6
D) 18.6
E) 20.6

Solution: Total cost of the items he purchased = Rs.30   Given that out of this Rs.30, 40 Paise is given as tax   => Total tax incurred = 40 Paise = Rs.40/100   Let the cost of the tax free items = x   Given that tax rate = 8%   ∴ (30−40/100−x)8/100 = 40/100   ⇒ 8(30 −0.4−x) = 40   ⇒ (30− 0.4 − x) = 5   ⇒ x = 30 − 0.4 − 5 = 24.6.   24.6)
Answer: B
a dealer buys 4 varieties of wheat costing rs. 20,rs.25,rs.30 and rs.35 per kg in the ratio 6:4:3:1 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of wheat? Pick
A) 30.5  B) 31.0  C) 32.0  D) 33.0  E) 34.5

Solution: CP = 20*6+25*4+30*3+35*1= 
20*6+25*4+30*3+35*1 = 345
345   SP= 1.4*345= 
1.4*345 = 483
483   Total no.of kgs=6+4+3+1= 
6+4+3+1 = 14
14   SP per kg=483/14= 
483/14 = 69/2 = around 34.5
34.50   ANSW34.5R:34.5
Answer: E
If the quantity (p − 4) is 5 times the quantity (q − 5), then what is the relationship between p and q?
Choose the correct choice from the following options.
A) p = 5q + 30  B) p = 5q − 21  C) 5p = q + 20  D) p = 5q  E) p = 5q − 20

Solution: p-4=5(q-5)   p-4=5q-25   p=5q-21   option p = 5q − 21
Answer: B
Kyle, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/8, 1/4 and 3/5, respectively, what is the probability no one will solve the problem?
Choose the most appropriate option:
A) 3/80  B) 21/80  C) 5/16  D) 25/76  E) 9/80

Solution: P(Kyle will not solve)=1 - 1/8 = 7/8   P(David will not solve)= 1 - 1/4 = 3/4   P(Catherine will not solve) = 1- 3/5 = 2/5   P= (7/8)*(3/4)*(2/5) = 42/160 = 21/80   Answer:21/80
Answer: B
What percent of a day is nine hours? Choose the most appropriate option:
A) 20.83%
B) 16x1/2%
C) 18x2/3%
D) 37.5%
E) None of these

Solution: Explanation :   Required percentage = (9/24100)%   = 37.5%.   Answer : 37.5%
Answer: D
If 10 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a four-percent vinegar solution, what was the concentration of the original solution? Choose the correct answer.
A) 20%	B) 24%	C) 25%	D) 28%	E) 30%

Solution: Let x be the concentration of the original solution.   10x = 0.04(60)   x = 0.24   The answer is 24%.
Answer: B
1/x+1/y=1/z where x=12 and y,z positive integer how many possible value of y and z ? Choose the correct choice from the following answers
A) 4
B) 7
C) 12
D) 15
E) infinite

Solution: 1/12 = 1/z - 1/y   y = 12 * z / ( 12 - z )   0 < z < 12   Only for z = 3 ,4 ,6 ,8 , 9 ,10 and 11 , y is intiger   Hence seven solutions   ANSWER:7
Answer: B
For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 94 Θ 33 ) Θ 17 ) - ( 96 Θ (33 Θ 17)) ?	Choose the correct choice from the following options:
A) -10
B) -2
C) 8
D) 13
E) 17

Solution: (( 94 Θ 33 ) Θ 17 )   The remainder of 98 divided by 33 is 28;   The remainder of 28 divided by 17 is 11;   ( 96 Θ (33 Θ 17))   The remainder of 33 divided by 17 is 16;   The remainder of 96 divided by 16 is 0.   11 - 0= 
11 - 0 = 11
11.   Answer: 13.
Answer: D
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 4 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ? Choose the correct choice from the following answers: A) 5 B) 7 C) 15 D) 20 E) 25

Solution: Audery and Ferris collective Work rate:   1/4 + 1/3 = 7/12   Collective work Time = 12/7 = 1.7 Hrs   Job Was actually done in = 2 (Includes breaks)   7reaks = Actual time taken - Collective work time   = 2 - 1.7= 
2 - 1.7 = 0.3
.3 Hrs= 1/2   so ferrais took 4 breaks   =.3/4=.07 hrs = 7 m   so Answer is 7) 10 mins
Answer: B
The product of the digits of the four-digit number Q is 36. No two digits of are identical. How many different numbers are possible values of Q ?	Options:	A) 6	B) 12	C) 24	D) 36	E) 48

Solution: The main question here is how can you arrange 4 different digits Q. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.   Therefore no of ways to arrange 4 diff. digits is 4! which is 24   hence 24
Answer: C
If x is a positive integer, which of the following must be odd?
Choose the correct answer:	A) x+1	B) x^2+x	C) x^2+x+11	D) x^2−1	E) 3x^2−3

Solution: A. X+1 = can be odd or even. Since O + O =E or E + O = O   B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]   C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 11 = ODD   Hence x^2+x+11.
Answer: C
A school committee consists of 2 teachers and 4 students. The number of different committees that can be formed from 5 teachers and 10 students is Options.
A) 3000  B) 2520  C) 2100  D) 2510  E) 2210

Solution: There are C(5,2) ways to select 2 teachers from 5 and C(10,4) ways to select 4 students from 10 where C(n,r) is the combinations of n items taken r at the time. Using the multiplication counting principle,the number of different committees that can be formed is given by   2100(5,2)*2100(10,4) = 2100
Answer: C
A garrison of 2000 men has provisions for 54 days. At the end of 18 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?  Choose the correct choice from the following
A) 1977  B) 1600  C) 1979  D) 1900  E) 1278

Solution: 2000 ---- 54   2000 ---- 36   x ----- 20   x*20 = 2000*36   x = 3600   2000   -------   1600   Answer: 1600
Answer: B
In a group of cows and hens, the number of legs are 12 more than twice the number of heads. The number of cows is :
Select the correct option
A) 5	B) 6	C) 7	D) 10	E) 12

Solution: Let no of cows be x, no of hens be y.   So heads=x+y   Legs=4x+2y   Now, 4x+2y = 2(x+y)+ 12   2x = 12   x = 6.   ANSWER:6
Answer: B
The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.7 the sixth number is?  Choose one:
A) 11.4	B) 11.3	C) 13.3	D) 11.5	E) 11.1

Solution: 1 to 11 = 11 * 10.9= 
11 * 10.9 = 119.9
119.9   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.7= 
6 * 11.7 = 70.2
70.2   63 + 70.2= 
63 + 70.2 = 133.2
133.2 – 119.9= 13.3   6th number = 13.3   Answer: 13.3
Answer: C
A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 17% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?	Choose the correct choice from the following answers.
A) 8° B) 10° C) 26° D) 36° E) 52°

Solution: Here all percentage when summed we need to get 100% . As per data  17+24+15+29+8= 
 17+24+15+29+8 = 93
93%.   So remaining 7% is the balance for the astrophysics.   Since this is a circle all percentage must be equal to 360 degrees.   100% ---- 360 degrees   Then 7% will be 26 degrees..   IMO option 26°.
Answer: C
A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $2,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002? Answers.
A) $18,400	B) $19,500	C) $20,200	D) $20,700	E) $21,100

Solution: Price in 96 = 22000   Price decrease each year = 2.5/100*22000= 
2.5/100*22000 = 550
550   Price in 97= 22000 - 550   Price in 98 = 22000 - 2*550   Price in 99 = 22000 - 3*550   Price in 00 = 22000 - 4*550   Price in 01 = 22000 - 5*550   Price in 02 = 22000 - 6*550= 
22000 - 6*550 = 18_700
18700   Investment in the car= 1500   Net price of the car in 02 = 18700 + 2000= 
18700 + 2000 = 20_700
$20700   Correct Option: $20,700
Answer: D
A reduction of 23% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Select the correct option:
A) s.2.99  B) s.2.4  C) s.2.5  D) s.2.2  E) s.2.1

Solution: 100*(23/100)= 
100*(23/100) = 23
23 --- 10   ? --- 1=> Rs.2.3   100 --- 77   ? --- 2.3 => Rs.2.99   s.2.99nswer:s.2.99
Answer: A
60% of a number is added to 120, the result is the same number. Find the number? Choose one:
A) 300	B) 788	C) 677	D) 256	E) 261

Solution: (60/100) * X + 120 = X   2X = 600   X = 300   300nswer: 300
Answer: A
If A lends Rs.3200 to B at 12% per annum and B lends the same sum to C at 14.5% per annum then the gain of B in a period of 5 years is?  Pick one
A) 157.78
B) 157.98
C) 400
D) 420
E) 430

Solution: (3200*2.5*5)/100= 
(3200*2.5*5)/100 = 400
> 400   Answer: 400
Answer: C
A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 45min will be.  Select the correct option
A) 60 km/h B) 53 km/h C) 40 km/h D) 70 km/h E) 65 km/h

Solution: Time=50/60 hr=5/6hr   Speed=48mph   distance=S*T=48*5/6= 
48*5/6 = 40
40km   time=45/60hr=3/4hr   New speed = 40* 4/3 kmph= 53kmph   Answer : 53 km/h
Answer: B
A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 2.5 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)	Options:
A) 5,500,000	B) 2,800,000	C) 55,000	D) 28,000	E) 280

Solution: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3   2,800,000y volume   40% is X = 400,000 cm^3   60% is Y = 600,000 cm^3   2,800,000y weight,   In 1 cm^3, X is 2.5 gms   In 400,000 cm^3 , X = 2.5 * 400,000 = 1,000,000 grams   In 1 cm^3, Y is 3 gms   In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms   Total gms in 1 m^3 = 1,000,000 + 1,800,000 = 2,800,000   ANSWER:2,800,000
Answer: B
A, B and C have Rs.900 between them, A and C together have Rs.400 and B and C Rs.750. How much does C have?	Choose the correct choice from the following options:
A) 100	B) 150	C) 200	D) 250	E) 350

Solution: A+B+C = 900   A+C = 400   B+C = 750   --------------   A+B+2C = 1150   A+B+C = 900   ----------------   C = 250   ANSWER:250
Answer: D
Mohan purchased 14 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
Choose the correct choice.
A) A)Rs.572
B) B)Rs.594
C) C)Rs.596
D) D)Rs.595
E) E)of these

Solution: Explanation:   Price of 14 kgs of rice at Rs.26/kg = 14x26 = Rs.364   Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208   Therefore, Total amount = Rs.364+Rs.208 = Rs.572.   Rs.572nswer: Option Rs.572
Answer: A
If |20x-10| = 170, then find the product of the values of x? Select.
A) -45  B) 50  C) -72  D) 35  E) -30

Solution: |20x-10| = 170   20x-10 = 170 or 20x-10 = -170   20x = 180 or 20x = -160   x = 9 or x = -8   product = -8*9 = -72   Answer is -72
Answer: C
A pipe can fill a tank in 15 minutes and another one in 10 minutes. A third pipe can empty the tank in 5 minutes. The first two pipes are kept open for 4 minutes in the beginning and then the third pipe is also opened. In what time will the tank be empited ?
Choose the correct choice from the following options:
A) 35 min	B) 15 min	C) 20 min	D) Cannot be emptied	E) None of these

Solution: Proportion of the volume of the tank filled by both the   pipes in 4 min = 4(1⁄15 + 1⁄10) = 2⁄3rd of the tank   Volume of the tank filled by all the pipes working together = 1⁄15 + 1⁄10 - 1⁄5 = -1⁄30   i.e. 1⁄30 tank is emptied in 1 min.   ∴ 2⁄3 rd of the tank can be emptied in 2×30/3=20min   Answer 20 min
Answer: C
A volume of 11780 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
Select
A) 2812	B) 8231	C) 2734	D) 4222	E) 2945

Solution: a volume of 4l can be kept in 1 hemisphere   therefore, a volume of 11780l can be kept in (11780/4) hemispheres   ans.2945   ANSW2945R:2945
Answer: E
Two heavily loaded sixteen-wheeler transport trucks are 855 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway? Choose the correct option:
A) 90
B) 130
C) 135
D) 320
E) 450

Solution: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:   Short version:   Truck A travels for an hour.   Distance remaining = 855-90= 
855-90 = 765
765k   Ratio of speeds 9:8 -> 765/17= 45   Truck A = 90 + 45*9= 
90 + 45*9 = 495
495   Truck B= 45*8= 
45*8 = 360
360   Delta= 135km   Answer 135
Answer: C
If x/(12p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x?  Choose the correct choice from the following answers.
A) 22  B) 33  C) 44  D) 66  E) 72

Solution: x/(12p) = odd prime number   x = odd prime number * 11p   Least value of x = Lowest odd prime number * 11 * Lowest value of p   = 3 * 12* 2= 
3 * 12* 2 = 72
72   Answer 72
Answer: E
For a certain set, the value range of its members is 96.8. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? Choose one:	A) 21.2	B) 24.2	C) 36.3	D) 48.4	E) 96.8

Solution: Let x and z be the smallest and largest of the original set, respectively.   z - x = 96.8   The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.   Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 96.8 / 4= 
96.8 / 4 = 24.2
24.2   The answer is 24.2.
Answer: B
A regular hexagon is there. The mid points of the sides were joined and formed another hexagon.Then What is the percentage reduction in area.  Choose the correct choice from the following choices.
A) 25%  B) 35%  C) 45%  D) 55%  E) 65%

Solution: Let ABCDEF be the regular hexagon with sides AB and ED parallel. P and Q are mid points of AF and EF resp.   25%E=root(3) * s (s is side of hexagon)   then PQ =(root(3) * s)/2 mid point theorem   Now u know side of inner hexagon   use formula area of hexagon = (3 * root(3))2 * s^2   and find diff in area of two hexagon multiply by 100 and divide the product by area of bigger hexagon   25%ns 25%   25%NSWER:25%
Answer: A
In a garden, 26 trees are planted at equal distances along a yard 400 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?  Choose the correct choice from the following choices
A) 10	B) 8	C) 12	D) 14	E) 16

Solution: 26 trees have 25 gaps between them.   Length of each gap = 400/25= 
400/25 = 16
16   i.e., distance between two consecutive trees= 16   Answer is 16.
Answer: E
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 68 kg. What is the correct weight?  Choose the correct choice from the following answers: A) 58kgs B) 58.85kgs C) 58.95kgs D) 59kgs E) 59.85kgs

Solution: Actual total weight is (20X 58.4 - 56 + 68) = 1180 Kgs   Actual average weight is   1180/20= 
  1180/20 = 59
59kgs   59kgs
Answer: D
The ratio between b and y is 7/9; b and y are increased by 4, what is the ratio between the new values of b and y? Choose the correct choice from the following answers.
A) 7/9  B) 14/9  C) 7/18  D) 11/13  E) It Cannot Be Determined

Solution: Ratio = 7k/9k = 7/9, 14/18, etc.   b and y are increased by 4 --> (7k + 4)/(9k + 4)   New ratio can be 11/13, 18/22, etc.   Answer: It Cannot Be Determined
Answer: E
A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes. Choose the correct choice:  A) 50 km/hr  B) 60 km/hr  C) 65 km/hr  D) 70 km/hr  E) None of these

Solution: Explanation:   We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.   Lets solve it.   Time = 50/60 hr = 5/6 hr   Speed = 48 mph   Distance = S × T = 48 × 5/6 = 40 km   New time will be 40 minutes so,   Time = 40/60 hr = 2/3 hr   Now we know,   Speed = Distance/Time   New speed = 40 × 3/2 kmph = 60kmph   Answer: 60 km/hr
Answer: B
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 6, and 7, what is the greatest number of four-digit extensions that the company can have?	Choose the correct choice from the following options:
A) 4
B) 6
C) 11
D) 12
E) 24

Solution: Since the phone number must be even, the unit's digit can be either 2 or 6.   When the unit's digit is 2 --> number of possibilities is 3! = 6   When the unit's digit is 6 --> number of possibilities is 3! = 6   Largest number of extensions = 6 + 6= 
6 + 6 = 12
12   Answer:12
Answer: D
Barbara has 8 shirts and 11 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?	Select the correct option:	A) 41	B) 86	C) 100	D) 70	E) 104

Solution: 8 shirts   9 pants   we can combine 2 shirts with (11-3) pants   2*8= 
2*8 = 16
16   we can combine the other shirts (6) with any pants (9)   8*11= 
8*11 = 88
88   Thus total :16+88= 
16+88 = 104
104	ANS:104
Answer: E
Alice is now 10 years older than Bob. If in 6 years Alice will be twice as old as Bob, how old will Alice be in 5 years?	Choose the correct choice from the following answers:
A) 19
B) 21
C) 23
D) 25
E) 27

Solution: A=B+10 so B=A-10.   A+6=2(B+6).   A+6=2(A-10+6).   A+6=2A-8.   A=14.   In 5 years, Alice will be 19 years old.   The answer is 19.
Answer: A
The sides of a square region, measured to the nearest centimeter, are 4 centimeters long. The least possible value of the actual area of the square region is  Choose the correct choice from the following answers:
A) 15.25 sq cm
B) 18.25 sq cm
C) 12.25 sq cm
D) 21.25 sq cm
E) 25.25 sq cm

Solution: Though there might be some technicalities concerning the termnearest(as 3.5 is equidistant from both 3 and 4) the answer still should be : 3.5^2=12.25.   Answer: 12.25 sq cm
Answer: C
A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^16, respectively, what is the value of A?	Choose the correct answer.
A) -24(5^12)
B) -27(5^12)
C) -24(5^6)
D) 23(5^12)
E) 24(5^12)

Solution: Ans : B   Assume that the numbers appear as shown below on the number line   A-----B-----C-----D-----E-----F-----G-----H   (5^12) (5^13)   As the values for G and H are given , we can calculate the difference between any two terms of the series .   Common Difference ,d = (5^13) - (5^12)   = (5^12) *[ 5-1 ]   = (5^12)*(4)   Also F + d = G as the terms are in equidistant and in increasing order.   So F + (5^12)*(4) = (5^12).   That is , F = (5^12) - (5^12)*(4)   = (5^12)[ 1-4]   = (5^12) (-3)   Similarly , E = F - d   = (5^12)[-3-4]   = (5^12)*(-7)   You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , D SHOULD -27(5^12)E (5^12)*(-7-4)= (5^12)*(-11)   Following this pattern , A = (5^12)*(-27)   -27(5^12)
Answer: B
The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
Choose the correct choice
A) 2333
B) 1015
C) 2683
D) 2693
E) 1113

Solution: Explanation:   Required Number = (L.C.M of 12, 16, 18,21,28)+7   = 1008 + 7= 
1008 + 7 = 1_015
1015   Answer: 1015) 1015
Answer: B