MU-NLPC/Calc-aqua_rat huggingface dataset:
A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked atrandom, what is the probability that both are red?  Choose the correct choice from the following:
A) 2/13 B) 1/14 C) 5/26 D) 3/31 E) 1/17

Solution: P(Both are red),   =65/262135/262=65/262135/262   =5/26   5/26
Answer: C
The average of 11 numbers is 10.8. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?  Pick
A) 9 B) 9.2 C) 10 D) 11.5 E) 12.6

Solution: 12.6xplanation:   1 to 11 = 11 * 10.8= 
11 * 10.8 = 118.8
118.8   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   63 + 68.4= 
63 + 68.4 = 131.4
131.4 – 118.8= 12.6   6th number = 12.6   12.6)
Answer: E
Helen went to the stationers and bought things worth Euro 30, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Choose the correct choice from the following choices:
A) Euro 15
B) Euro 15.7
C) Euro 19.7
D) Euro 24.7
E) None

Solution: Explanation: Let the amount taxable purchases be Euro x.   Then, 6% of x = 30/100   x = (30/100 x 100/6) = 5.   Cost of tax free items = Euro [30 - (5 + 0.30)= 
30 - (5 + 0.30) = 24.7
Euro 24.70   Answer: Option Euro 24.7
Answer: D
22 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
Options.
A) 19
B) 20
C) 21
D) 22
E) 23

Solution: in case of cycle no of handshakes = no of persons   hence ans = 22   ANSWER:22
Answer: D
Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone?
Choose the correct option.
A) 6 B) 12 C) 14 D) 15 E) 17

Solution: Renuâ€™s one dayâ€™s work = 1/6   Sumaâ€™s one dayâ€™s work = 1/3 - 1/6 = 1/6   Suma can do it alone in 6 days.   6NSWER:6
Answer: A
A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? Select:
A) 20
B) 99
C) 88
D) 77
E) 54

Solution: 100 ---- 100 --- 10   100 --- 10   --------------------   300 ---- 20 years   20nswer: 20
Answer: A
In a race of 200 m. A can beat B by 15 m and C by 19 m then how much time C would take To beat B in the race of 3700 m ?
Select
A) 50  B) 60  C) 70  D) 80  E) 90

Solution: In 200 race A:B=200/185 , A:C=200/181   than in 3700m race B beats by C,3700- (181/185)*3700=80   ANSWER:80
Answer: D
If a and b are consecutive integers (b>a), which of the following statements could be false? 1. a^3+b is always even number. 2. ab is even number 3. (a + b) is always an odd number.	Choose the correct choice from the following answers:  A) II only  B) III only  C) I only  D) I,II only  E) II,III only

Solution: 2^3+3 =8+3= 
8+3 = 11
11 Option I false   odd*even= even. Option II is true   odd + even = odd. Option III is true   Answer : I only
Answer: C
Three numbers are such that the second is as much
lesser than the third as the first is lesser than
the second. If the product of the two smaller numbers
is 85 and the product of two larger numbers is 115.
Find the middle number?
Choose the most appropriate option:
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: Let the three numbers be x,y,z   2y = x+z.....................1   Given that the product of two smaller numbers is 85   x y = 85................2   Given that the product of two larger numbers is 115   y z = 115...............3   Dividing 2 and 3 x y /y z = 85/115   x / z = 17 / 23   From 1   2y = x+z   2y = 85/y + 115/y   2y2 = 200   y2 = 100   y = 10   10NSWER: 10 10
Answer: A
The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Choose the correct choice from the following:
A) 4029
B) 4089
C) 4029
D) 4096
E) 1921

Solution: Principal = [4913 / (1 + 25/(4 * 100))3]   = 4913 * 16/17 * 16/17 * 16/17   = Rs. 4096.   Answer: 4096
Answer: D
A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? Choose the correct choice from the following answers:  A) 2  B) 3  C) 4  D) 1  E) 8

Solution: S = 600/40= 
600/40 = 15
15 mps   S= 3600/15= 
3600/15 = 240
240 sec= 4 min   ANSWER 4
Answer: C
A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost?  Choose the correct answer.
A) $2400  B) $2464  C) $2650  D) $2478  E) $2800

Solution: 1.4x = 2500   x=2500/1.4   so, 1.5X = 2500*1.5/1.4= 2478   Answer:- $2478
Answer: D
A man buys an article for $100. and sells it for $115. Find the gain percent?	Pick:
A) 10%	B) 15%	C) 25%	D) 20%	E) 30%

Solution: C.P. = $100   S.P. = $115   Gain = $15   Gain% = 15/100 *100 = 25%   Answer is 15%
Answer: B
A reward of $1400 was divided among a group of 36 rescue workers such that each male in the group received $50. How much did each of the 16 females receive? Choose the correct choice from the following answers:  A) $10  B) $12.50  C) $25  D) $37.50  E) $50

Solution: x = amount each female received   amount each male received = 50   number of females = 16   number of males = 36 - 16= 
36 - 16 = 20
20   total to males= 20(50) = 1000   total to females = 16x   reward = total to males + total to females   1400 = 1000 + 16x   1400 - 1000 = 16x   400 = 16x   25 = x   Answer: $25
Answer: C
A train passes a station platform in 62 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Select: A) 615 m B) 240 m C) 168 m D) 444 m E) 691 m

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/62= 15 => x   = 444 m   Answer: 444 m
Answer: D
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 4 years?	Options:
A) 14300
B) 20736
C) 14500
D) 14600
E) 15400

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 × 120/100^4 = 20736   20736)
Answer: B
By selling an article at Rs.800, a shopkeeper makes a profit of 35%. At what price should he sell the article so as to make a loss of 25%?	Choose one
A) s.416
B) s.480
C) s.429
D) s.128
E) s.419

Solution: SP = 800   Profit = 25%   CP = (SP)*[100/(100+P)]   = 800 * [100/125]   = 640   Loss 800 *  100/125= 
800 *  100/125 = 640
640   Loss= 35% = 35% of 640 = Rs.224   SP = CP - Loss = 640 - 224   = Rs.416   s.416nswer:s.416
Answer: A
John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
Pick.
A) 10.2% B) 16.66% C) 18.7% D) 19.24% E) 20%

Solution: Increase = (10/60)*100 = (1/6)*100 = 16.66%.   16.66%
Answer: B
Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 2 screws and 4 nails? Choices.
A) a. 4 B) b. 5/2 C) c. 2 D) d. 3/2 E) e. 5/4

Solution: let the weight of nail be n and that of screw be s..   so s+w=1/2 * (6s+1n)...   or 1n = 4s..   lets see the weight of 3 s and 3n= 3s+3*4s=15s..   and weight of 2s and 4n3 +3*4= 
3 +3*4 = 15
15s..   and weight of 2s and 4n= 2s+4*2s=10s..   ratio2 +4*2= 
2 +4*2 = 10
10s..   ratio= 15s/10s=15/10=3/2   d. 3/2
Answer: D
A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
Choose the correct option:
A) 30
B) 40
C) 50
D) 60
E) 70

Solution: Explanation:   Let the side of the square(ABCD) be x meters.   Then, AB + BC = 2x metres.   AC = √2x = (1.41x) m.   Saving on 2x metres = (0.59x) m.   Saving % = 0.59x/2x × 100 % =30% (approx)   30nswer: 30
Answer: A
Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?	Choices.
A) 2 <= 335x+4 <= 6
B) 2 <= 32x+4 <= 6
C) 2 <= 334x+4 <= 6
D) 2 <= 3x+4 <= 6
E) 2 <= 3466x+4 <= 6

Solution: The key words in the stem are:a singleline segment offinite length   Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.   Answer: 2 <= 3x+4 <= 6.
Answer: D
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
Choose one
A) Rs.1000  B) Rs.1100  C) Rs.1050  D) Rs.1200  E) Rs.1250

Solution: Explanation:   1120 = P [1 + (5*12/5)/100]   P= 1000   Rs.1000NSWER IS Rs.1000
Answer: A
The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 150 kmph. Find the speed of the boat in still water and the speed of the stream?
Pick one.
A) 25 kmph	B) 17 kmph	C) 19 kmph	D) 17 kmph	E) 29 kmph

Solution: Speed of the boat in still water   = (100+150)/2= 
(100+150)/2 = 125
125kmph. Speed of the stream= (150-100)/2= 
(150-100)/2 = 25
25 kmph.   25 kmphnswer: 25 kmph
Answer: A
A car traveled 75% of the way from town A to town B at an average speed of 90 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?	Choose the most appropriate option:
A) 15  B) 20  C) 25  D) 30  E) 37.5

Solution: Total distance = 100 miles (easier to work with %)   75% of the distance = 75 miles   25% of the distance = 25 miles   1st part of the trip → 75/90 = 0.833   2nd part of the trip → 25/S = t   Total trip → (75+25)/40 = 0.833+ t » 100/40 = 0.833 + t » 2.5 = 0.833+ t » t = 1.667   Back to 2nd part of the trip formula: 25/S = 1.667 » S = 15   15ns 15
Answer: A
Find the least number which when divided by 31 and 9 leaves a remainder of 3 in each case. Choose the correct answer: A) 280 B) 282 C) 284 D) 286 E) 288

Solution: The least number which when divided by different divisors leaving the same remainder in each case   = LCM(different divisors) + remainder left in each case.   Hence the required least number   = LCM(31, 9) + 3 = 282.   ANSWER:282
Answer: B
A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area T covered by the two roads?	Select
A) 400
B) 1550
C) 1575
D) 1600
E) 1625

Solution: Area 1575overed by Road Along the Length = 5*200= 
5*200 = 1_000
1000 Square Meter   Area 1575overed by Road Along the Width= 5*120= 
5*120 = 600
600 Square Meter   1575ommon Area in both Roads (where the roads intersect)= Square with Side 5 meter = 5*5= 
5*5 = 25
25   Total Area of the Roads T= 1000+600-25= 
1000+600-25 = 1_575
1575   Answer: option 1575
Answer: C
The ratio between the present ages of A and B is 4:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
Select the correct option
A) 3:4  B) 3:0  C) 3:1  D) 3:2  E) 9:5

Solution: Let the present ages of A and B be 4x and 3x years respectively.   Then, (4x - 4)/(3x + 4) = 1/1   1x = 8 => x = 8   Required ratio = (4x + 4):(3x - 4) = 36:20 = 9:5.Answer: 9:5
Answer: E
Vincent has $12,731 dollars in his wallet. What is the least amount of money (in whole number of dollars) that he must add if he wants to split this money evenly among his nine friends?	Choose the correct choice from the following options
A) $1
B) $2
C) $3
D) $4
E) $5

Solution: In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 12,731= 14 and 18 is divisible by 9.   Hence we need to add 4 to this number for it to be divisible by 9   Correct Option: $4
Answer: D
For every positive odd integer n, the function h(n) is defined to be the product of all the odd integers from 3 to n, inclusive. If p is the smallest prime factor of h(200) +3, then p is? Choose the correct option:	A) between 3 and 20	B) between 10 and 20	C) between 20 and 30	D) between 30 and 40	E) 3

Solution: h(200) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 200. So h(200)+3 will have 3 in the units digit so smallest prime factor is 3.   Answer: 3
Answer: E
A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph? Choose the correct choice from the following answers.
A) 27  B) 22  C) 20  D) 87  E) 23

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 4.5   => x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km   Answer: 20
Answer: C
The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 20 minutes after it was poured was how many degrees Fahrenheit? Choose the correct option.
A) 65  B) 75  C) 80  D) 85  E) 90

Solution: Answer: B   The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”.   120 = 120(2 ^ 10a) + 60   2 ^ -1 = 2 ^ 10a   a = -1/10   The temperature of coffee 20 minutes after it was poured is:   F = 120 ( 2 ^ -20/10) + 60   F = 120 * 1/ 4 + 60   F = 30 + 60= 
30 + 60 = 90
90   90
Answer: E
There are 13 South American countries, Anny has won a ticket to fly from Denver to one South American country and then directly to another South American Country before returning home to Denver again. Assuming there are four airports in each country, how many flights paths can Anny choose from?
Select the correct option: A) 13.12.11.10.4.4. B) 13.12.11.10.4 C) 13.12.4.4. D) 13.12.4 E) 13.13.13.13

Solution: flights paths can Anny choose from There are 13 ways to chose the first destination,   then, 12 ways to chose next destination, with option of 4 airports (13x4)   then, to return he has 4 options to chose the airports   Thus, 13*12*4*4 ways.   Using permutations:   If the solution had written 13P1 instead of 13C1 it won't matter. As per the definition - making arrangements of the combinations gives permutations.   Since there are no arrangement for 1 item, permutationscombinations are equal.13.12.4.4.
Answer: C
If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 3m + n?
Choose the correct answer.
A) 11
B) 18
C) 20
D) 45
E) 33

Solution: k^4=5400∗mn   k^4=3^3.2^3.5^2.mn   In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2   mn=3.2.5^2   mn = 150 = 10 * 15 (Least possible)   Answer = 3*10 + 15= 
3*10 + 15 = 45
45   ANSWER:45
Answer: D
Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 9, what is the measure of side XY?	Choose the correct choice.
A) 4	B) 4√2	C) 8	D) 6	E) Cannot be determined from the information provided

Solution: ans D..6..   xy being larger means it is the hyp..   area =(1/2)*(yz)^2=9 or yz=3*\sqrt{2}..   therefore hyp=xy=6
Answer: D
A train 310 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? Choices:
A) 4  B) 6  C) 5  D) 17  E) 13

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 = [310 * 3/55] sec = 17 sec   ANSWER:17
Answer: D
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.40 m space around the room. A side of square tile is given to be 40 cms? Select.
A) 164
B) 476
C) 268
D) 208
E) 276

Solution: Area of the room =3.2 * 8.2= 
3.2 * 8.2 = 26.24
26.24   Area of the tile= 0.4 *0.4= 
0.4 *0.4 = 0.16
0.16   No. of tiles=26.24/0.16= 
26.24/0.16 = 164
164   164nswer : 164
Answer: A
Let the number which when multiplied by 15 is increased by 196.
Choose the correct choice from the following answers:	A) 14	B) 20	C) 26	D) 28	E) 30

Solution: Solution   Let the number be x .   Then, 15x - x = 196   ‹=›14x = 196   x ‹=› 14.   14nswer 14
Answer: A
There are 35 students in a hostel. If the no. of students increases by 8, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?  Choose the correct choice from the following options:
A) 371.87	B) 400.37	C) 420.37	D) 450.37	E) 480.37

Solution: Suppose the average join the mess , total expenditure = 35x + 42   Now, the average expenditure = (35x + 42)/ (35 + 8) = x – 1   or, 35x + 42 = 43x – 43   or, x = 10.625   Thus the original expenditure of the mess = 35 x 10.625 = Rs. 371.87   371.87
Answer: A
In a company, 52 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women? Choose one.
A) 65%  B) 70%  C) 75%  D) 80%  E) 85%

Solution: The percent of employees who are unionized and men is 0.7*0.6 = 42%   The percent of employees who are unionized and women is 60 - 42= 
60 - 42 = 18
18%   48% of all employees are women, so non-union women are 48%-18% = 30%   40% of all employees are non-union.   The percent of non-union employees who are women is 30%/40%  48 -18= 
 48 -18 = 30
30%   40% of all employees are non-union.   The percent of non-union employees who are women is 30%/40%= 75%   The answer is 75%.
Answer: C
The average of 28 numbers is 45. If two numbers namely 40 and 45 are discarded, The average of
remaining numbers is?	Choices:
A) 35.5
B) 37.5
C) 45.1
D) 34.5
E) 38.5

Solution: Total of 50 numbers = 28 * 45= 
28 * 45 = 1_260
1260   Average of 26 numbers= 1260-(40+55) / 26   = 1175 / 26= 45.1   Answer is 45.1.
Answer: C
If the sales tax be reduced from 3 (1/5) % to 2 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 6400? Choose the correct choice from the following choices
A) Rs. 150.40 B) Rs. 44.80 C) Rs. 140.40 D) Rs. 50.48 E) None of these

Solution: Explanation:   Required difference = (3 (1/5) of Rs. 6400) - (2 (1/2) of Rs. 6400)   = (16/5 – 5/2) % of Rs. 6400   = (7/10) x (1/100) x 6400   = Rs. 44.80   ANSWER Rs. 44.80
Answer: B
In how many ways the letters of the word RAIXBON be arranged?	Options
A) 4354  B) 8454  C) 4356  D) 5040  E) 6557

Solution: Total ways of arranging the letters = 7! = 5040 ways.   5040)
Answer: D
Paul's salary was decreased by 50% and subsequently increased by
50%.How much percent does he lose?
Choose the correct choice
A) 0  B) 25  C) 50  D) 30  E) 40

Solution: Let the original salary = $100   New final salary=150% of (50% of Rs.100)=   $((150/100)*(50/100)*100)= 
((150/100)*(50/100)*100) = 75
$75.   Decrease= 25%   Answer option 25)25.
Answer: B
In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Elaine?	Select
A) 1,008
B) 1,296
C) 1,512
D) 2*1008
E) 2,268

Solution: Place D and H first: 8 options for D, 7 options for H   We are left with 6 empty places. A, B and C must take first 3 places and F, G, Emust take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for F, G, and E   Total = 8*7*3!*3! = 2*1008   Answer: 2*1008.
Answer: D
A room contains 180 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room? Select the correct option:
A) 25
B) 35
C) 45
D) 55
E) 65

Solution: Say group of x people left the room.   # of women in the room was 0.15*180= 
0.15*180 = 27
27;   # of women in the group that left 0.3x;   # of women in the room after the group left it is 0.1(180-x);   So, 27-0.3x= 0.1(180-x) --> x=45.   Answer: 45.
Answer: C
A can finish a piece of work in 4 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?  Options.
A) 3
B) 5
C) 6
D) 7
E) 8

Solution: 2/4 + (2 + x)/10 = 1 => x = 3 days   3nswer: 3
Answer: A
If a, b, c, and d are integers; w, x, y, and z are prime numbers; w < x < y < z; and (wa)(xb)(yc)(zd)=660(wa)(xb)(yc)(zd)=660, what is the value of (a + b) – (c + d)?
Choose the correct choice from the following options:  A) –1  B) 0  C) 1  D) 2  E) 3

Solution: 660660= 2^2 x 3^1 x 5^1 x 11^1   w < x < y < z = 2 < 3 < 5 < 11   So, can can say -   w = 2   x = 3   y = 5   z = 11   Hence a = 2 , b = c = d = 1   (a + b) – (c + d) will be (2 + 1) – (1 + 1) = 1   Answer will be (1)
Answer: C
5358 x 51 = ?	Options.
A) 273435
B) 272651
C) 273258
D) 273898
E) 273299

Solution: 273258   5358 x 51 = 5358 x (50 + 1)   = 5358 x 50 + 5358 x 1   = 267900 + 5358= 
267900 + 5358 = 273_258
273258.
Answer: C
HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 10%
Options
A) 36  B) 40  C) 32  D) 42  E) 45

Solution: Let the weight of tea(25 per kg) to be used - X   The total cost of the blend - total cost of 25 RS tea + total cost of 30 RS tea   - 25X + 900 ( as the total weight of 30 RS tea is already given i.e 30)   total weight of the blend = X + 30 ( which should be sold per 30 RS and result in 10% profit)   The equation follows like this   25X + 900 + (10 % of (25X + 900)) = 30( X + 30)   25X + 900 +2.5 X + 90 = 30 X + 900   27.5 X + 990 = 30 X + 900   2.5 X = 90   X= 90/2.5= 
90/2.5 = 36
36   36NSWER:36
Answer: A
Round off the given number to nearest hundreds
10158 Choices:  A) 10000  B) 10200  C) 11000  D) 10150  E) 10100

Solution: the given number is 10158   its tens digit is 5. so replace each of the tens and ones digit by 0 and increase the hundreds digit by 1 to get the rounded off number to the nearest hundred.   correct answer (10200)
Answer: B
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is: Choose the correct choice from the following:
A) 2 : 3
B) 5 : 3
C) 6 : 7
D) 9 : 16
E) None of these

Solution: Let us name the trains as A and B. Then,   (A's speed) : (B's speed) = âˆšb : âˆša = âˆš25 : âˆš9 = 5 : 3.   Answer 5 : 3
Answer: B
Each of 7 workers will pick a day of the week as his vacation day. What is the probability that exactly one worker will pick a different day? Answers.
A) 7!/7^7
B) 1/7!
C) 1/7^7
D) 7/7!
E) 7/7^7

Solution: Each worker out of 7 has 7 options (Sunday, Monday, Tuesday,.., Saturday), hence total # of outcomes is 7^7;   Favorable outcomes will be 7!, which is # of ways to assign 7 different day to 7 workers.   P=favorable/total=7!/7^7   7!/7^7nswer: 7!/7^7.
Answer: A
The H.C.F of two numbers is 8. Which of the following can never be their L.C.M? Choose the correct choice from the following options:
A) 24  B) 48  C) 56  D) 60  E) 62

Solution: H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60.   ANSWER:60
Answer: D
-84 x 29 + 365 = ?  Select.
A) 2071 B) 2436 C) 2801 D) -2801 E) -2071

Solution: E   Given Exp. = -84 x (30 - 1) + 365   = -(84 x 30) + 84 + 365   = -2520 + 449   = -2071
Answer: E