MU-NLPC/Calc-aqua_rat huggingface dataset:
A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability R that a + b is prime? Select.
A) 0
B) 1/12
C) 5/12
D) 7/18
E) 4/9

Solution: Total # of outcomes is 6*6= 
6*6 = 36
36;   Favorable outcomes:   a-b --> prime   1-1 --> 2;   1-2 --> 3;   2-1 --> 3;   1-4 --> 5;   4-1 --> 5;   2-3 --> 5;   3-2 --> 5;   1-6 --> 7;   6-1 --> 7;   2-5 --> 7;   5-2 --> 7;   3-4 --> 7;   4-3 --> 7;   6-5 --> 11;   5-6 --> 11.   Total of 15 favorable outcomes   R=15/36.   Answer: 5/12.
Answer: C
A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?
Choose the correct choice from the following options
A) 9! + 10!  B) 2 x 10!  C) 9! x 10!  D) 19!  E) 20!

Solution: If we choose the 10 different digits then they can be arranged (permutations) in 10! ways.   But the question asks at least 9 digits. So we have the possibility of choosing only 9 digits for the password ( but digit shouldn't repeat), so we can have a total of 10 different combinations and each combination can be arranged in 9! ways.   Therefore   10 x 9! + 10!   = 10! + 10!   = 2 x 10!   Therefore 2 x 10!
Answer: B
Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance travelled by them if the slower car takes 1 hour more than the faster car.
Answers.
A) 980 km B) 860 km C) 960 km D) 460 km E) 660 km

Solution: 860 km   60(x + 1) = 64x   X = 15   60 * 16= 
60 * 16 = 960
960 km
Answer: B
Sonika deposited Rs.14500 which amounted to Rs.12200 after 3 years at simple interest. Had the interest been 3% more. She would get how much?
Choose the correct choice from the following answers
A) 13505 B) 12004 C) 15003 D) 14500 E) 16400

Solution: (14500*3*3)/100= 
(14500*3*3)/100 = 1_305
1305   12200   --------   13505   13505nswer: 13505
Answer: A
A train 310 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Choose the correct choice from the following.
A) 40 sec
B) 50 sec
C) 44 sec
D) 36 sec
E) 60 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 310 + 140= 
310 + 140 = 450
450 m   Required time= 450 * 2/25= 
450 * 2/25 = 36
36 sec   Answer:36 sec
Answer: D
An arithmetic Sequence is a number sequence which has a constant difference between terms. Considering this definition which of the following is an arithmetic sequence?
I. e^2, f^2, g^2, h^2, i^2
II. e-6, f-3, g-5, h-3, i-3
III. 2e, 2f, 2g, 2h,2i Choose the correct answer:
A) II and III
B) III only
C) I and III
D) I and II
E) II only

Solution: lets look at the three choices...   I. e^2, f^2, g^2, h^2, i^2   since the difference is not constant, it is not an arithmetic sequence...   II. e-6, f-3, g-5, h-3, i-3   since the difference is not constant, it is not an arithmetic sequence   III. 2e, 2f, 2g, 2h,2i   since the difference is constant it is an arithmetic sequence...   The answer III only)
Answer: B
Tough and Tricky questions: Ratios
1/6 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?  Select the correct option: A) 1/2 B) 2/3 C) 11/15 D) 23/30 E) 4/9

Solution: let total no. of students be 30   students left on a field trip =1/6(30) =5   thus 25 students left behind   1/3(25) students did not want to go. thus 50/3 students want to go on the trip   1/2(50/3)=25/3 were able to join the other students on the field trip.   thus total number of students that went on a field trip =5+ 40/3   thus required fraction = 4/9   4/9
Answer: E
A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 7 more days. How many days would it have taken the second carpenter to do the complete job working alone? Choose the correct choice from the following answers.
A) 4.5  B) 7.5  C) 9.5  D) 14.5  E) 24.5

Solution: A carpenter worked only 1 day on something that takes him 6 MORE days.   Means;   Carpenter finishes his work in 7 days.   Let his buddy finish the same task in x days.   Respective rates per day:   1/7 AND 1/x   To complete 1 work:   First guy worked for 5 days @ rate=1/7 per day.   Second one worked for 7 days @ rate=1/x per day   Expression:   Days*Rate=Work   5*1/7+7*1/x=1   5x+49=7x   2x=49   x=24.5 days.   Ans:24.5
Answer: E
A person borrows Rs. 4000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.  Pick one:
A) 100 rs
B) 80 rs
C) 160 rs
D) 180 rs
E) 200 rs

Solution: Gain in 2 years =   [(4000*6*2)/100]-[(4000*4*2)/100]    480-320= 
 480-320 = 160
160   Gain in 1 year=(160/2)= 
(160/2) = 80
80 rs   ANSWER:80 rs
Answer: B
A rectangular garden has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular garden is 1800 square feet, what is the total length of the fence, in feet?  Choose the correct choice
A) 60 B) 100 C) 120 D) 200 E) 300

Solution: two sides EACH = x the third = 2x and the wall length is thus 2x too   x*2x = 2x^2 = 1800 ie x^2 = 900 ie x = 30   L = 60 W= 30   TOTAL LENGHT OF FENCE = 2*30+60= 
2*30+60 = 120
120   MY ANSWER IS C
Answer: D
Gasoline varies in cost from $0.98 to $1.18 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?  Choose the correct choice.
A) $15.10	B) $15.30	C) $15.50	D) $15.75	E) $15.80

Solution: Solution:   We know that the per gallon cost of gasoline varies from $0.98 - $1.18.   Now we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.   Mileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons.   So, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).   Case 1: for 30 gallons the cost is 30*0.98 to 30*1.18 which is $29.40 to $35.40   Case 2: for 20 gallons the cost is 20*0.98 to 20*1.18 which is $19.60 to $23.60   Thus, the maximum cost of the 480 mile trip is $35.40 and minimum is $19.60   so the difference is $35.40 - $19.60 = $15.80   Answer: $15.80 35.40 -  19.60= 
 35.40 -  19.60 = 15.8
$15.80   Answer: $15.80
Answer: E
Find the average of first 40 natural numbers?	Choose the correct choice from the following choices: A) 20.5 B) 22 C) 30.5 D) 35 E) 25

Solution: Sum of first 100 natural numbers = 40*41/2= 
40*41/2 = 820
820Required average= 820/40= 
820/40 = 41/2 = around 20.5
20.520.5nswer is 20.5
Answer: A
Each of the 38 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 12 students sign up for the poetry club, 20 students for the history club, and 19 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?  Choices:
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: The total number in the three clubs is 12+20+19= 
12+20+19 = 51
51.   All 38 students signed up for at least one club.   3 of those students signed up for exactly one more club.   51 - 41= 
51 - 41 = 10
10 so 5 students must have signed up for exactly three clubs.   The answer is 5.
Answer: D
A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is? Choose the correct choice from the following answers
A) 31	B) 42	C) 50	D) 22	E) 60

Solution: LCM = 30 => 30 + 1= 
30 + 1 = 31
31   31NSWER 31
Answer: A
If k^2 is divisible by 240 what is the least possible value of integer K?  Select the correct option:
A) 60
B) 30
C) 12
D) 90
E) 120

Solution: 240 can be written as (2^4)*3*5.   For k^2 to be divisible by 240 it should contain at least 2^4 and 3 and 5 in its factors. We can leave out option C because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^ 2 will have 2 as the maximum power of 2, so we can leave out this option too.   Option C is the right answer if we follow the same method as we followed for other two previous options.   60 = (2^2)*3*5; 60^2 = (2^4)*(3^2)*(5^2). So it shows that 60^2 is divisible by 240 and hence the answer.   60nswer : 60
Answer: A
If the cost price is 99% of selling price then what is the profit percentage.  Choices:
A) 1 B) 1.11 C) 1.01 D) 1.1 E) 1.21

Solution: selling price=Rs100 : then cost price=Rs 99:profit =Rs 1.   Profit={(1/99)*100}%=1.01%   Answer is 1.01.
Answer: C
What is the sum of two consecutive even numbers, the difference of whose squares is 84?	Options
A) 42	B) 44	C) 48	D) 56	E) none

Solution: Sol.   Let the numbers be x and x + 2.   then, (x + 2)² - x² = 84 ⇔ 4x + 4 = 84 ⇔ 4x = 80 ⇔ x=20.   ∴ Required sum = x + (x + 2) = 2x + 2 + (  + 2)= 
+ (  + 2) = 2
2x + 2= 42.   42nswer 42
Answer: A
The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly seven elements each?	Choose the correct choice from the following answers: A) 81 B) 63 C) 54 D) 36 E) 90

Solution: nC2 = 36   => n*(n-1)/2 = 36 by middle term factor and n cannot be negative   => n = 9   nC7 = 9C7 = 9!/7!*(9-7)!= 9*8*7!/7!*2 =36   So, Answer is 36.
Answer: D
The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
Select:  A) 72  B) 88  C) 15  D) 10  E) 12

Solution: Sum of the marks for the 12 students = 12 * 36= 
12 * 36 = 432
432. The marks of each student are doubled, the sum also will be doubled.   The new sum= 432 * 2= 
432 * 2 = 864
864. So, the new average= 864/12= 
864/12 = 72
72.   72nswer: 72
Answer: A
Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
Choose the correct choice from the following answers:
A) 11 : 5 B) 11 : 8 C) 13 : 7 D) 15 : 7 E) 16 : 9

Solution: Sol. Distance travelled by 13 : 7ar A = 65 × 8 = 520 km   Distance travelled by 13 : 7ar B = 70 × 4 = 280 km   Ratio = 520/280 = 13 : 7   13 : 7
Answer: C
After a mathematics exam, 20 percent of the students reported that they didn't study, while 20 percent of the students who didn't study refused to admit they hadn't studied. What percent of the students didn't study? Choose one:
A) 15% B) 50% C) 35% D) 20% E) 25%

Solution: Statement: 20% of Students (S) Reported they Didn't Study (RDS). Of the students who didn't study (DS) 20% refused to admit they didn't study (notRDT). [Note: A Venn Diagram is useful to visualize the problem.]   Solution: Sample space is 100%.   S = 100%   RDS/S = 20%   notRDS/DS = 20% => 100% - 20% => RDS/DS = 80%   DS/S = (20)/(80)% = 25%   Answer: 25%
Answer: E
A train covers a distance of 12 km in 10 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
Pick:  A) 177 m  B) 189 m  C) 120 m  D) 178 m  E) 180 m

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec   = 20 m/sec.   Length of the train = 20 * 9= 
20 * 9 = 180
180 m.   Answer: 180 m
Answer: E
If the price of an article went up by 40%, then by what percent should it be brought down to bring it back to its original price? Choose the correct choice from the following answers:
A) 2/3%  B) 28.57%  C) 2/1%  D) 1/3%  E) 2/7%

Solution: Let the price of the article be Rs. 100.   40% of 100 = 40.   New price = 100 + 40 = Rs. 140   Required percentage = (140 - 100)/140 * 100   = 40/140 * 100= 28.57%.   Answer:28.57%
Answer: B
If n is the product of the integers from 1 to 13, inclusive, how many different prime factors greater than 1 does n have?  Choose the correct choice from the following answers:  A) Four  B) Five  C) Six  D) Seven  E) Eight

Solution: n = 1*2*3*4*5*6*7*8*9*10*11*12*13   The prime factors of n are 2, 3, 5, 7, 11, and 13.   There are 6 prime factors.   The answer is Six.
Answer: C
If m=9^(x−1), then in terms of m, 3^(4x−1) must be which of the following?  Pick one
A) m/3  B) 9m  C) 27m^2  D) m^2/3  E) m^2/9

Solution: m = 9 ^ (X-1)   m = 3 ^ (2x-2)   m^2 = 3 ^ (4x-4)   27m^2 = 3 ^ (4x-1)   Answer 27m^2
Answer: C
The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?  Pick one:
A) 4  B) 7  C) 5  D) 9  E) 3

Solution: A + B + 5 = 48   B + 5 + D = 45   A + D = 13   A – D = 3   A + D = 13   2D = 10   D = 5   Answer:5
Answer: C
On a certain date, Pat invested $7,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $28,000, in how many years total will the total value of the investment plus interest increase to $56,000? Options.
A) 15
B) 16
C) 18
D) 20
E) 24

Solution: 28,000 = 7,000(1 + x)^10   4 = (1+x)^10 = 2^2   (1+x)^10 = ((1+x)^5)^2 = 2^2   Therefore, (1+x)^5 = 2   56,000 = 7,000(1 + x)^n   (1+x)^n = 8   (1+x)^n = 2^3   (1+x)^n = ((1+x)^5)^3 = (1+x)^15   Therefore, n = 15.   The answer is 15.
Answer: A
On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 50 percent. What was the total rent the motel actually charged for that night ? Choices
A) $400	B) $800	C) $1,000	D) $1,600	E) $2,400

Solution: Let total rent the motel charge for all rooms =x   If 10 rooms that were rented for 60 $ had instead been rented for 40 $,   then total difference in prices = 20 $ * 10 = 200 $   Total rent the motel charged would have been reduced by 50 %   .5x = 200   => x= 400   $400nswer $400
Answer: A
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.?
Choose the correct choice from the following choices
A) 6:50 a.m	B) 5:50 a.m	C) 4:50 a.m	D) 7:50 a.m	E) 8:50 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: D
A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have?
Select the correct option: A) 50 B) 78 C) 267 D) 20 E) 27

Solution: A+B+C = 500   A+C = 200   B+C = 320   --------------   A+B+2C = 520   A+B+C = 500   ----------------   C = 20   Answer: 20
Answer: D
5n + 2 > 12 and 7n - 5 < 30; n must be between which numbers? Pick.
A) 1 and 8	B) 2 and 6	C) 0 and 9	D) 2 and 5	E) 2 and 9

Solution: 5n > 10 --> n > 2   7n < 35 --> n < 5   2 < n < 5   Answer: 2 and 5
Answer: D
If -1 < x < 0, which of the following must be true?
I. x^5 < x^2
II. x^6 < 1 – x
III. x^7 < x^3  Choose the most appropriate option:
A) I,II,III only B) I,II only C) I,III only D) II only E) I only

Solution: I,II,III onlynswer : I,II,III only
Answer: A
An automobile manufacturer offers a station wagon with either a 12-cylinder engine or a 10-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 12-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?  Options:
A) 44 B) 47 C) 48 D) 50 E) 53

Solution: 12-cylinder engine wagons = 2*2*2*2*2= 
2*2*2*2*2 = 32
32 (manual or automatic, with or without trailer);   10-cylinder engine wagons= 2*2*2*2= 
2*2*2*2 = 16
16 (manual or automatic).   Total= 32 + 16= 
32 + 16 = 48
48.   Answer:48.
Answer: C
Express a speed of 252 kmph in meters per second?
Choose one:
A) 10 mps
B) 05 mps
C) 09 mps
D) 12 mps
E) 70 mps

Solution: 70 mps   70 mps    252 * 5/18= 
 252 * 5/18 = 70
70 mps
Answer: E
Express a speed of 60 kmph in meters per second?  Select the correct option:
A) 10 mps
B) 16.67 mps
C) 97.67 mps
D) 17.67 mps
E) 18 mps

Solution: 60 * 5/18   = 16.67 mps   Answer: 16.67 mps
Answer: B
All of the stocks on the over-the-counter market are designated by either a 7-letter or a 7-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?  Choose the correct choice from the following choices:
A) 2(26^5)  B) 26(26^4)  C) 27(26^4)  D) 2(26^7)  E) 27(26^5)

Solution: Number of 4-letter codes: 26 * 26 * 26 * 26 * 26 * 26 * 26 = 26^7   Number of 5-letter codes: 26 * 26 * 26 * 26 * 26 * 26 * 26 = 26^7   Total Number of codes: 26^7 + 26^7 = 2*(26^7)   Therefore, the answer is2(26^7): 2*(26^7).
Answer: D
If t = 20! + 17, then t is divisible by which of the following?
I. 15
II. 17
III. 19	Choose the correct choice from the following answers:
A) None
B) I only
C) II only
D) I and II
E) II and II

Solution: Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.   So t!+17 = xxxx00 +17= 
00 +17 = 17
xxxx17 which is only possibly divisible by 17. Hence Option II only is the answer.
Answer: C
A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 35 per metre of cloth. What is the cost price of one metre of cloth?  Choose the correct choice from the following answers: A) 21 B) 28 C) 90 D) 26 E) 70

Solution: Explanation:   SP of 1m of cloth = 8925/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 105 - Rs. 35 = Rs. 70.   Answer: 70
Answer: E
What will come in place of the x in the following Number series? 6, 12, 21, x , 48	Choose the correct choice from the following options:
A) 33	B) 37	C) 39	D) 41	E) 43

Solution: (A)   The pattern is + 6, + 9, + 12, +15 ………..   So the missing term is = 21 + 12= 
21 + 12 = 33
33
Answer: A
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Choose the correct choice from the following choices:
A) 2 sec B) 1 sec C) 6 sec D) 8 sec E) 12 sec

Solution: Explanation:   Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 110 * 3/55= 
110 * 3/55 = 6
6 sec.   Answer: 6 sec
Answer: C
If A lends Rs.25000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? Choose the correct choice from the following:
A) 1125 B) 1225 C) 1325 D) 1145 E) 2125

Solution: (25000*1.5*3)/100= 
(25000*1.5*3)/100 = 1_125
> 1125   1125NSWER:1125
Answer: A
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?  Pick one
A) 140 sq.units  B) 176 sq.units  C) 675 sq.units  D) 169 sq.units  E) 196 sq.units

Solution: Given that the area of the square = 1225 sq.units   => Side of square = √1225 = 35 units   The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35= 
2/5 * 35 = 14
14 units   Given that breadth= 10 units   140 sq.unitsrea of the rectangle = lb = 14 * 10= 
14 * 10 = 140
140 sq.units   140 sq.unitsnswer:140 sq.units
Answer: A
Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?	Pick:	A) 10 am	B) 12 am	C) 10.30 am	D) 12.30 am	E) 11 am

Solution: 10 amssume both trains meet after x hours after 7 am   Distance covered by train starting from P in x hours = 20x km   Distance covered by train starting from Q in (x-1) hours = 25(x-1)   Total distance = 110   => 20x + 25(x-1) = 110   => 45x = 135   => x= 3   Means, they meet after 3 hours after 7 am, ie, they meet at 10 am   10 amnswer is 10 am.
Answer: A
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?	Pick one.
A) 2	B) 5	C) 6	D) 1	E) 0

Solution: Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.   Thus, when 2n is divided by 4, the remainder is 2.   2NSWER 2
Answer: A
If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 24
III. P is a multiple of 23	Choose the correct choice from the following answers:
A) I only B) II only C) III only D) None of the above E) All of the above

Solution: The correct answer is II only.
Answer: B
In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy. Choose the correct answer
A) 9.4%
B) 9.33%
C) 9.6%
D) 9.8%
E) 10%

Solution: The amount of chromium in the new 15+30= 
15+30 = 45
45 kg alloy is  0.12*15+0.08*30= 
 0.12*15+0.08*30 = 4.2
4.2 kg, so the percentage is 4.2/45*100=   9.33%.   Answer: 9.33%.
Answer: B
What is the largest number that will divide 90207, 232585 and 127986 without leaving a
remainder?	Select:
A) 257  B) 905  C) 351  D) 498  E) 398

Solution: HCF is the best solution. bit its time taking.   see the numbers 90207 , 232585 , 127986.   choose 905. but its not possible because last digit must be 0 or 5.   choose 498. it is also not possible because last dight must be an even number.   only 2 left now.   its easy now to get the answer by division method   ans is 257.   257NSWER:257
Answer: A
A single letter is selected at random from the word 'SIMS'. The probability that it is a vowel is..??  Choose the correct choice:
A) 1/4	B) 3/11	C) 4/11	D) 3/7	E) 1/2

Solution: total vowels = 1, total number of letters = 4   so probability = 1/4   1/4NSWER:1/4
Answer: A
If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 10 percent, how much would she earn per week? Choose one.
A) $374	B) $330	C) $385	D) $392	E) $399

Solution: (348/116)110 =330   In this case long division does not take much time.   (348/116)= 
(348/116) = 3
3   3*110= 
3*110 = 330
330(300+30)   Answer $330
Answer: B
The HCF and LCM of two numbers m and n are respectively 8 and 200. If m + n = 84, then 1/m + 1/n is equal to
Choose the correct option.
A) 1/35  B) 3/50  C) 5/37  D) 2/35  E) None

Solution: Answer   We have, m x n = 8 x 200 = 1600   âˆ´ 1/m + 1/n = (m + n)/mn = 84/1600 = 3/50   Correct Option: 3/50
Answer: B
20 women can do a work in 9 days. After they have worked for 6 days. 6 more men join them. How many days will they take to complete the remaining work?
Choose the correct choice from the following answers
A) 4:87  B) 4:3  C) 4:2  D) 4:7  E) 4:1

Solution: (20 * 16) women can complete the work in 1 day.   1 woman's 1 day work = 1/320   (16 * 15) men can complete the work in 1 day   1 man's 1 day work = 1/240   So, required ratio = 1/240 : 1/320 = 4:3.   Answer:4:3
Answer: B