MU-NLPC/Calc-aqua_rat huggingface dataset:
What fraction is equivalent to 0.8% ?
Options:  A) 1/125  B) 1/129  C) 1/121  D) 1/122  E) 1/124

Solution: Explanation:   0.8% = 0.8/100 = 8/1000 = 4/500 = 2/250 = 1/125   1/125NSWER: 1/125
Answer: A
A basketball is dropped from a height of 30 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces.  Choose the correct choice from the following choices
A) 50 B) 82.5 C) 60 D) 75 E) 80

Solution: Initial distance = 30 feet   first bounce = 15 feet up + 15 feet down = 30 feet   second bouche = 7.5 feet up + 7.5 feet down = 15 feet   third bounce = 375 feet up and 3.75 feet down= 7.5 feet   total distance covered = 30+30+15+7.5= 
30+30+15+7.5 = 82.5
82.5   ANSWER IS 82.5
Answer: B
The product of three consecutive numbers is 990. Then the sum of the smallest two numbers is ?
Answers:
A) 11
B) 15
C) 19
D) 38
E) 56

Solution: Product of three numbers = 990   990 = 9*10*11.   So, the three numbers are 9, 10 and 11.   And Sum of smallest of these two = 9+10= 
9+10 = 19
19.   ANSWER : OPTION 19
Answer: C
During a certain season, a team won 75 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played? Choose the correct choice from the following answers
A) 180  B) 170  C) 156  D) 150  E) 125

Solution: We are first given that a team won 75 percent of its first 100 games. This means the team won 0.75 x 100 = 75 games out of its first 100 games.   We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:   0.5(T – 100) = number of wins for remaining games   0.5T – 50 = number of wins for remaining games   Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:   Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season   75 + 0.5T – 50 = 0.7T   25 = 0.2T   250 = 2T   125 = T   Answer is 125.
Answer: E
Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 34}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64},
II. {10, 16, 26, 42, 68},
III. {46, 59, 67, 72, 75}  Choose the correct choice from the following options:
A) I only	B) I & II	C) I & III	D) II & III	E) I, II, & III

Solution: Original set: Q = {5, 8, 13, 21, 34}.   Notice that Set I is just every number in Q plus 30. When you add the same number to every number in a set, you simply shift it up without changing the spacing, so this doesn’t change the standard deviation at all. Set I has the same standard deviation as Q.   Notice that Set II is just every number in Q multiplied by 2. Multiplying by a number does change the spacing, so this does change the standard deviation. Set II does not have the same standard deviation as Q.   This one is very tricky, and probably is at the outer limit of what the GMAT could ever expect you to see. The spacing between the numbers in Set III, from right to left, is the same as the spacing between the numbers in Q from left to right. Another way to say that is: every number in Set III is a number in Q subtracted from 80. Again, would be very hard to “notice”, but once you see that, of course adding and subtraction the same number doesn’t change the standard deviation. Set III has the same standard deviation.   The correct combination is I and III, so the answer is I & III.
Answer: C
A train speeds past a pole in 10 seconds and a platform 100 m long in 30 seconds. Its length is? Choices
A) 188 m B) 876 m C) 251 m D) 50 m E) 45 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 10 => y = x/10   x + 100 / 30 = x / 10   x = 50 m.   Answer: 50 m
Answer: D
The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?	Pick:
A) 6
B) 4
C) 5
D) 3
E) 1

Solution: P(1 + 20/100)n > 2P or (6/5)n > 2   Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.   Answer: 4
Answer: B
In how many ways a committee consisting of 4 men and 2 women can be formed from 7 men and 3 women? Choose the correct option:
A) A)105
B) B)15
C) C)20
D) D)18
E) E)21

Solution: Required number of ways = 7C4*3C2 = 35*3= 
35*3 = 105
105   105nswer is 105
Answer: A
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:	Choices:
A) 20 B) 80 C) 100 D) 200 E) 220

Solution: Let the number of students in rooms A and B be x and y respectively.   Then, x - 10 = y + 10 x - y = 20 .... (i)   and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)   Solving (i) and (ii) we get: x = 100 , y = 80.   The required answer A = 100.   Answer: Option 100
Answer: C
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 500 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Select.
A) 340	B) 346	C) 352	D) 365	E) 370

Solution: Number of newborns that can die in first month = 1/10 * 500= 
1/10 * 500 = 50
50   Survived= 450   Number of newborns that can die in second month = 1/10 * 450= 
1/10 * 450 = 45
45   Survived= 405   Number of newborns that can die in third month = 1/10 * 405 = 40   Survived = 365   Answer:365
Answer: D
In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?	Choose the correct choice from the following choices: A) A)0.9 B) B)0.6 C) C)0.45 D) D)0.3 E) E)0.25

Solution: Percent of students who are 25 years old or older is   0.4*48+0.4*52= 
  0.4*48+0.4*52 = 40
40, so percent of people who are less than 25 years old is   100-40= 
  100-40 = 60
60.   Answer: 0.6.
Answer: B
If a number p is prime, and 2p+5= q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q? Choose the correct choice from the following answers.
A) 1 B) 2 C) 5 D) 7 E) 9

Solution: 2/9 = 0.2222222222222.. (a repeating pattern one digit long)   2
Answer: B
A worker can load one truck in 6 hours. A second worker can load the same truck in 5 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill one truck? Choose the correct choice from the following options
A) 2.7
B) 2.9
C) 3.1
D) 3.3
E) 3.5

Solution: The workers fill the truck at a rate of 1/6 + 1/5 = 11/30 of the truck per hour.   Then the time to fill one truck is 30/11 which is about 2.7 hours.   The answer is 2.7.
Answer: A
Which of the following equivalent to (1/27)^2?  Pick
A) (0.10)^3	B) (0.11)^3	C) (0.12)^3	D) (0.13)^3	E) (0.14)^3

Solution: (1/27)^2 = (1/3^3)^2 = (1/3)^6 = (1/9)^3 = (0.11)^3   Answer: Option (0.11)^3
Answer: B
In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 210 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
Choose the correct choice from the following options: A) 40 ml B) 70 ml C) 20 ml D) 20/3 ml E) 10 ml

Solution: There are 0.3*100= 
0.3*100 = 30
30 ml of element X in the initial solution.   We need X to be 1/3rd of 210 ml in the resulting solution, so 70 ml. Thus out of 110 ml of solution added, 40 must be X (in order it to become 70 ml) ans the remaining 70 must be Y.   Answer: 70 ml
Answer: B
The sum of two consecutive integers is 51. Find the numbers. Pick:
A) 17, 18
B) 7, 8
C) 5, 6
D) 1, 2
E) 25,26

Solution: n + (n + 1) = 51   2n + 1 = 51   2n = 50   n = 25   Answer: 25,26
Answer: E
An investment of $2000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $8000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $16000 by earning interest at that rate?  Choose the correct choice from the following.
A) 18	B) 12	C) 20	D) 24	E) 30

Solution: In 12 years the investment quadrupled (from $2,000 to $8,000).   Thus, at the same rate compounded annually, it would need additional   12/2= 
  12/2 = 6
6 years to double (from $8,000 to $16,000).   Therefore, 12+6=18 years are needed $2,000 to increase to $16,000.   18nswer: 18.
Answer: A
There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?	Choose the correct choice from the following answers:
A) 100 B) 120 C) 90 D) 95 E) 80

Solution: 200*2= 
200*2 = 400
400   580=>180   1----2   ?----180 = 90   ANSWER 90
Answer: C
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?	Choose the correct choice from the following answers
A) 12/429 B) 12/429 C) 12/455 D) 12/927 E) 12/292

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   When three marbles are drawn, the probability that one is yellow and two are red   = (²12/455₁)(⁴12/455₂)/¹⁵12/455₃   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)   =12/455   Answer: 12/455
Answer: C
A certain account pays 1.5 percent compound interest every 3 months. A person invested an initial amount and did not invest any more money in the account after that. If after exactly 5 years, the amount of money in the account was T dollars, which of the following is an expression for the original number of dollars invested in the account? Choices
A) [(1.015)^4]T	B) [(1.015)^15]T	C) [(1.015)^20]T	D) [T/{(1.015)^15}]	E) [T/{(1.015)^20}]

Solution: The original formula of "annual compound interest rate" is:   t = number of years   i = annual interest rate   T = future value (FV)   P = Present value (PV)   After t year:   FV = PV[1 + i]^t   If interest rate is quarterly, then   new interest rate/period = i/4   new number of periods = t*4   The new formula is:   FV = PV[1 + i/4]^4t   Apply to this question:   T = PV[1 + 0.015]^20   Because i/4 = 1.5%   number of periods = 4*5= 
4*5 = 20
20   So, PV= T/[1.015]^20   --Or--   PV = T*[1.015]^-20   ANSW[T/{(1.015)^20}]R:[T/{(1.015)^20}]
Answer: E
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 options: A) 130 B) 145 C) 140 D) 144 E) None of these

Solution: Explanation :   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. (378 * 8/21) = Rs. 144.   Answer : 144
Answer: D
A test has 150 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?  Pick one.
A) 19 B) 21 C) 23 D) 25 E) 27

Solution: A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points.   Let C be the number of correct answers and let I be the number of incorrect answers.   To get 40 points, a test taker must have at least 40 correct answers. Then C=> 40.   For every correct question above 40, the test taker has 4 incorrect answers.   Then, the I = 4*(C - 40).   Also, I + C <= 150. Thus 5C <= 310 and so C <= 62.   Then 40 <= C <= 62 and C can have 23 possible values.   The answer is 23.
Answer: C
A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is: Select the correct option
A) 33
B) 15
C) 66
D) 77
E) 81

Solution: Dividend on Rs. 20 = Rs. 9	x 20 = Rs.	9	.   100	5   Rs. 12 is an income on Rs. 100.   Rs.	9	is an income on Rs. 100	x	9 = Rs. 15.   Answer:15
Answer: B
the present worth of a sum due sometimes hence is Rs. 5760 and the banker's gain is Rs.10 . what is the true discount?  Choose the correct choice from the following.
A) 480
B) 420
C) 240
D) 120
E) 380

Solution: TD= square root of PW * BG = square root of 5760 * 10= 
5760 * 10 = 57_600
square root of 57600= Rs. 240   correct answer : (240)
Answer: C
David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?	Choose the correct answer:	A) 19	B) 28	C) 37	D) 53	E) 30

Solution: Suppose their paths cross after x minutes.   Then, 11 + 57x = 51 - 63x 120x = 40   x =	1/3   Number of floors covered by David in (1/3) min. =(1/3)x 57   = 19.3   So, their paths cross at (11 +19) i.e., 30th floor.   Answer is 30.
Answer: E
Rectangular tile each of size 70cm by 30cm must be laid horizontally on a rectangular floor of size 900cm by 600cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: Choose the most appropriate option: A) 50 B) 70 C) 80 D) 90 E) 100

Solution: Area of tile = 90*30= 
90*30 = 2_700
2700   Area of floor= 900*300= 
900*300 = 270_000
270000   No of tiles= 270000/2700= 
270000/2700 = 100
100   So, the no of tile=100   ANSW100R:100
Answer: E
Calculate 1307 x 1307 =?	Options
A) 1601249 B) 1607249 C) 1701249 D) 1708249 E) none

Solution: Answer   1307 x 1307 = (1307)2   = (1300 + 7 )2   = (1300)2 + (7)2 + 2 x 1300 x 7   = 1690000 + 49 +18200= 
1690000 + 49 +18200 = 1_708_249
1708249   Option: 1708249
Answer: D
A train 960 m long passed a pole in 96 sec. How long will it take to pass a platform 2600 m long?	Options
A) 350 B) 352 C) 354 D) 356 E) 358

Solution: Speed = 960/96= 
960/96 = 10
10 m/sec.   Required time= (960 + 2600)/10= 
(960 + 2600)/10 = 356
356 sec.   Answer:356
Answer: D
A trained covered x km at 40 kmph and another 4x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.  Choose the correct choice from the following answers:
A) 11.33 kmph	B) 12.33 kmph	C) 13.33 kmph	D) 14.33 kmph	E) 23.33 kmph

Solution: Total time taken = x/40 + 4x/20 hours   = 9x/40 hours   Average speed = 3x/(9x/40) = 13.33 kmph   ANSWER:13.33 kmph
Answer: C
In how many ways the letters of the word REDUCTION be arranged?	Choose the correct answer:
A) 344500
B) 325479
C) 226478
D) 362880
E) 344900

Solution: Total ways of arranging the letters = 9! = 362880 ways.   362880)
Answer: D
An engineer undertakes a project to build a road 10 km long in 30 days and employs 30 men for the purpose. After 10 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
Choose one.
A) 30
B) 40
C) 50
D) 60
E) 70

Solution: 30 workers working already   Let x be the total men required to finish the task in next 20 days   2 km done hence remaining is 8 km   30lso, work has to be completed in next 20 days (30 - 10 = 20)   We know that, proportion of men to distance is direct proportion   and, proportion of men to days is inverse proportion   Hence, X = (30 * 8 * 10) / (2 *20)   thus, X = 60   Thus, more men needed to finish the task = 60-30= 
60-30 = 30
30   30nswer : 30
Answer: A
r = number of flags;n = number of poles;Any number of flags can be accommodated on any single pole.r= 5 n = 3 . If first pole has 2 flags ,third pole has 1 flag, how many ways the remaining can be arranged? Pick
A) 4 ways
B) 5 ways
C) 7 ways
D) 8 ways
E) 6 ways

Solution: 2 flags are remaining and as it is given that 3 poles can have any no. of flags therefore   3p2=3!/(3-2)!   =3*23 /(3-2)= 
3 /(3-2) = 3
3*2= 
3*2 = 6
6 ways   ANSW6 waysR:6 ways
Answer: E
There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 15, then find the smaller number?  Pick
A) 25  B) 81  C) 86  D) 16  E) 27

Solution: Let the two positive numbers be 5x and 8x respectively.   8x - 5x = 15   3x = 15 => x = 5   => Smaller number = 5x = 25.   25nswer: 25
Answer: A
A can do a piece of work in 4 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? Choose the correct choice from the following answers:
A) 22 days  B) 12 days  C) 67 days  D) 17 days  E) 18 days

Solution: C = 1/2 - 1/6 - 1/4 = 1/12   => 12 days   Answer:12 days
Answer: B
There are certain number of hats and gloves in a box.They are of 41 red,23 green,11 orange.Power gone but a woman can differentiate between hats and gloves.How many draws are required to obtain a pair of each color?
Choose the correct answer.
A) 66
B) 67
C) 68
D) 69
E) 70

Solution: the worst case senario will be   first take 40 red   then take 22 green   then take 1+1 red+green   then take 2 orange.   so total 40+22+2+2= 
40+22+2+2 = 66
66   66NSWER:66
Answer: A
A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.	Select
A) 227 B) 390 C) 287 D) 2771 E) 0212

Solution: The total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in AP whose first term is 30 and last term is 48 = 10/2 [30 + 48] = 390 km.   Answer: 390
Answer: B
A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.280, find the number of 50 paise coins ? Select.
A) 498 B) 488 C) 300 D) 528 E) 418

Solution: 50*3k + 20*4k + 10*5k = 28000   280k = 28000 => k = 100   50p coins = 3k = 3*100= 
3*100 = 300
300   ANSWER:300
Answer: C
Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.82 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
Choose one:
A) 9%
B) 10%
C) 11%
D) 12%
E) 15%

Solution: Let x be the discount on Pony jeans. Then 0.22-x is the discount on Fox jeans.   3(0.22-x)(15) + 2x(18) = 8.82   9.9 - 45x + 36x = 8.82   9x = 1.08   x = 0.12   The answer is 12%.
Answer: D
If 2 < x < 7 and 8 << y < 9, then the lowest possible value for xy is	Choices:
A) between 60 and 70
B) between 0 and 60
C) 0
D) between 0 and -70
E) less than -70

Solution: If 2 < x < 7 and 8 << y < 9,   Say y = 8.9 (8<<y<9)   x = 6   So xy =53.4 which is less than 60.   Answer is between 0 and 60.
Answer: B
By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 meters, inclusive, the breadth is between 1 to 1.1 meters, inclusive and the height is between 2 to 2.1 centimeters, inclusive. If the actual length, breadth and height of the box do indeed fall within the respective ranges estimated by the carpenter, which of the following is the closest to the maximum possible magnitude of the percentage error K that the carpenter can make in calculating the volume of the rectangular box? Select the correct option:
A) 1%	B) 3%	C) 10%	D) 18%	E) 22%

Solution: the dimensions are between 2-2.1, 1-1.1 and 2-2.1..   so MAX error in Volume=?..   IMPORTANT POINTS TO NOTE   1) Max ERROR would be when actuals and estimate are at the extreme ends..   2) BUT what about MAX % ERROR--   It will be when the base is the lowest...   so the ACTUALS should be lowest or at lower end and the ESTIMATE at the higher end..   SOLUTION   Actuals= 2*2*1=4..   Estimate=2.1*2.1*1.1=4.841..   Max % error K=(4.841-4)/4 *100= 84.1/4 = 21.25%..   21.25% is closest to 22% in the choices..   ans 22%
Answer: E
Victor gets 92 % marks in examinations. If these are 460 marks, find the maximum marks. Choices
A) 334	B) 500	C) 376	D) 288	E) 271

Solution: Let the maximum marks be m   Then 92 % of m = 460   ⇒ 92/100 × m = 460   ⇒ m = (460 × 100)/92   ⇒ m = 46000/92= 
46000/92 = 500
500   Therefore, maximum marks in the examinations are 500.   Answer:500
Answer: B
If y exceeds x by 25%, then x is less than y by?	Answers
A) 20%	B) 16 3/3%	C) 16 2/3%	D) 12 2/3%	E) 16 1/3%

Solution: X=100	y=125   125------25   100-------? => 20%   20%nswer:20%
Answer: A
From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected?	Pick
A) 1/10  B) 4/9  C) 1/2  D) 3/5  E) 2/3

Solution: prob reqd= 1- probab of not having eq numbers   prob of not having eq no's is = prob of having 3 Boys and 1 girl or prob of having 3 girls and 1 boy   =(1* 3/15) +(3/15 * 1)=2/5   reqd prob= 1-2/5=3/5   Answer:3/5
Answer: D
A, B and C can do a work in 6 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work? Choose the correct choice from the following answers
A) 2 2/3 days
B) 2 8/3 days
C) 2 23/3 days
D) 8 2/3 days
E) 3 2/3 days

Solution: Work done by all three of them in one day = 1/6 + 1/8 + 1/12 = 3/8.   The number of days required = 8/3   = 2 2/3 days.   2 2/3 daysnswer: 2 2/3 days
Answer: A
A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?  Choose the correct answer
A) 2%	B) 25%	C) 22%	D) 29%	E) 45%

Solution: 800 --- 200   100 --- ? => 25%   Answer:25%
Answer: B
The product of all the prime numbers less than 18 is closest to which of the following powers of 10?
Choices:
A) 10^9  B) 10^8  C) 10^7  D) 10^6  E) 10^5

Solution: OA: 10^6
Answer: D
The H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:  Choose the correct choice:	A) 276	B) 280	C) 322	D) 345	E) 354

Solution: Clearly, the numbers are (20 x 13) and (20 x 14).   Larger number = (20 x 14) = 280.   Answer: Option 280
Answer: B
Which of the following fractions Q, if written as a decimal, would have a 2 in the thousandths place ?
Choose one
A) 3/11 B) 7/9 C) 1/8 D) 4/7 E) 1/6

Solution: (A) Q=3/11 = 0.2727272727....   3/11nswer: 3/11
Answer: A