MU-NLPC/Calc-aqua_rat huggingface dataset:
Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Friday, how many croissants will Marina eat on the 28th of that month?  Choose the correct answer:  A) 1  B) 2  C) 3  D) 5  E) 6

Solution: She eat as follow   Mon - 1   Tue - 2   Wed - 3   Thr - 5   Fri - 1(since she had more than 4 previous day)   sat - 6   sunday - 1 (since she had more than 4 previous day)   so 28th day of month she will have 5.   Answer is 5
Answer: D
Two stations A and B are 110 km apart on a straight line. One train starts from A at 4 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Select the correct option
A) 11 B) 10 C) 8 D) 12 E) 7

Solution: Suppose they meet x hours after 4 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 7 a.m.   Answer: 7
Answer: E
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was:  Select the correct option
A) 11 years  B) 14 years  C) 77 years  D) 88 years  E) 99 years

Solution: Let the son's present age be x years.   Then, (38 - x) = x   2x = 38 => x = 19   Son's age 5 years back = (19 - 5)= 
(19 - 5) = 14
14 years.   Answer:14 years
Answer: B
64, 81, 100, 144, 196, ?, F ind the missing number(?).
Pick.
A) 225	B) 220	C) 230	D) 238	E) 278

Solution: The series consists of squares of consecutive composite numbers.   225nswer : 225.
Answer: A
A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?  Choose the correct choice from the following answers:
A) 17	B) 12	C) 15	D) 19	E) 65

Solution: Let the average after the 16th inning be P.   So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64   = 16P => P = 19.   Answer:19
Answer: D
If 2x = 3y = 10, then 15xy = ?	Choose the correct choice:  A) 1,200  B) 200  C) 120  D) 40  E) 250

Solution: 2x = 10;x=5   3y = 10;y=10/3   Multiply: 15xy=15*5*10/3= 
15*5*10/3 = 250
250   Answer: 250.
Answer: E
The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?  Choose the correct choice from the following answers.
A) 22 B) 24 C) 27 D) 30 E) 32

Solution: 5:3:4   Total parts = 12   12 parts --> 108   1 part ---->9   The second number of the three numbers is = 3   3 parts ----> 27   27
Answer: C
In a ratio which is equal to 2:4, if the antecedent is 50, then the consequent is?  Choose one.
A) 72
B) 85
C) 100
D) 51
E) 80

Solution: We have 2/4 = 50/x   2x = 50*4   x = 100   consequent = 100   Answer is 100
Answer: C
The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (4,4) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line? Choose the correct option:
A) 0  B) 2/5  C) 4/7  D) 1  E) -4

Solution: CONCEPT: The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals)Draw a figure and know it for yourself.   The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (7,4) OR Midpoint of (0,4) and (7,0)   i.e. -4ither [(0+7)/2, (0+4)/2] OR [(0+7)/2, (4+0)/2] =[3.5, 2]   Slope of line passing through points (4,4) and (3.5,2) = (4-2)/(3.5-4) = -4   -4
Answer: E
Beginning in Town A, Biker Bob rides his bike 8 miles west, 5 miles north, 4 miles east, and then 15 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)  Choose the correct choice from the following:
A) 25 miles B) 20.4 miles C) 30 miles D) 32 miles E) 33 miles

Solution: Using Pythagoras we have one side i,e total distance traveled in north direction = 15+5= 
15+5 = 20
20m   other being the base ie distance traveled west- distance traveled eat=8- 4= 
8- 4 = 4
4 m   now this third side or the distance between town A and Town 20.4 miles=20^2+ 4^2=sq root 416=20.4 miles   Answer : 20.4 miles
Answer: B
A tourist purchased a total of $1,100 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?  Choose the correct option.
A) $1,430 B) $1,310 C) $1,290 D) $1,270 E) $870

Solution: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks   Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3   using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost   Therfore   1100 - 230= 
  1100 - 230 = 870
870 hence answer is $870
Answer: E
Find the cost of fencing around a circular field of diameter 40 m at the rate of Rs.3 a meter?
Answers:  A) 400  B) 370.4  C) 376.98  D) 340.9  E) 350.03

Solution: 2 * 22/7 * 20 = 125.66   125.66 * 3= Rs.376.98   Answer: 376.98
Answer: C
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?	Choose the most appropriate option.
A) 26 B) 22 C) 12 D) 24 E) None of these

Solution: Explanation :   Let the required number of days be x   More men, less days (indirect proportion)   Hence we can write as   Men36:27}::x:18   ⇒36×18=27×x⇒12×18=9×x⇒12×2=x⇒x=24 . Answer : Option 24
Answer: D
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 80 metres? Select the correct option
A) 16 seconds
B) 65 seconds
C) 78 seconds
D) 12 seconds
E) 21 seconds

Solution: Speed of the boat downstream   = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 80/5= 
80/5 = 16
16 seconds.   16 secondsnswer:16 seconds
Answer: A
The average monthly salary of 660 workers in a factory is Rs. 380. The average monthly salary of officers is Rs. 2100 and the average monthly salary of the other workers is Rs. 340. Find the number of other workers. Choose the correct choice from the following choices: A) 645 B) 650 C) 640 D) 642 E) none

Solution: Solution: Total salary of 660 workers = 660*380 = Rs. 250800;   If other workers be x; then,   [(660-x)*2100]+340x = 250800   Or, 1386000-2100x+340x = 250800   1760x = 1135200   Hence, x = 1135200/1760= 
1135200/1760 = 645
645   Number of other workers= 645.   645nswer: Option 645
Answer: A
There are 6 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? Choices:  A) 90  B) 120  C) 225  D) 180  E) 200

Solution: Number of ways of selecting 2 fiction books = 62252   Number of ways of selecting 2 non fiction books = 62252   62252 * 62252 = 15 * 15= 
15 * 15 = 225
225   Answer: 225
Answer: C
mixture contains alcohol and water in the ratio 4 : 3. If 4 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.  Answers.
A) 20	B) 99	C) 27	D) 22	E) 29

Solution: Let the quantity of alcohol and water be 4x litres and 3x litres respectively   16x = 4(3x+5)   4x = 20   x = 5   Quantity of alcohol = (4 x 5) litres = 20 litres.   20nswer: 20
Answer: A
If the value of a piece of office decreases by 10% while the new tax rate on the office represent 110% of the original tax rate, what is the effect on the taxes?	Choices:
A) a - taxes increase by 10%  B) b- taxes increase by 1%  C) c- there is no change in taxes  D) d- taxes decrease by 1%  E) c- taxes decrease by 10%

Solution: Cansider the value of office = 100, Original tax rate 10%, hence tax value = 100*10% = 10.   Decreased value of office = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9   10-9.9 = decrease by 1%.   Answer d- taxes decrease by 1%.
Answer: D
A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 16,200, then what is B's share in the profit?  Answers.
A) Rs. 2000
B) Rs. 3000
C) Rs. 4000
D) Rs. 5000
E) None of these

Solution: Explanation :   Ratio of the initial investment = 7/2 : 4/3 : 6/5   = 105 : 40 : 36   From this ratio, we can assume that actual initial investments of A, B and C   are 105x, 40x and 36x respectively   A increases his share 50% after 4 months. Hence the ratio of their investments =   (105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12   = 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3   = 105 * 4 : 40 *3 : 36 * 3   = 35 * 4 : 40 : 36   = 35 : 10 : 9   B's share = total profit * (10/54) = 16,200 * 10/54 = 3000. Answer : Option Rs. 3000
Answer: B
The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?  Choices.
A) 1:96 B) 1:29 C) 2:29 D) 1:38 E) 1:97

Solution: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.   (4x)(3x) = 6912   12x2 = 6912   x2 = 576 = 4 * 144 = 22 * 122 (x > 0)   => x = 2 * 12= 
2 * 12 = 24
24   Ratio of the breadth and the areas= 3x : 12x2 = 1 : 4x   = 1:96.   1:96nswer: 1:96
Answer: A
Connie has a number of gold bars, all of different weights. She gives the 24 lightest bars, which weigh 45% of the total weight, to Brennan. She gives the 13 heaviest bars, which weigh 26% of the total weight, to Maya. She gives the rest of the bars to Blair. How many bars did Blair receive? Choose the correct choice from the following choices:
A) 14	B) 15	C) 16	D) 17	E) 18

Solution: Solution: The average weight of the bars given to Brennan (light) < the average weight of the bars given to Blair < the average weight of the bars given to Maya (heavy).   Let the total weight of all the bars be X.   The weight of the bars given to 15rennan,   = 45% of X = 0.45X   The weight of the bars given to Maya,   = 26 % of X = 0.26X   The weight of the bars given to Claire = rest = 29% of X = 0.29X   The average weight of the bars given to 15rennan,   = Weight / number of bars = 0.45X/24   The average weight of the bars given to Maya = Weight / number of bars = 0.26X/13   Similarly, if the number of bars given to 15lair = 15,   then the average weight of the bars given to 15lair = 0.29X/15   As, the average weight of the bars given to 15rennan (light) < the average weight of the bars given to 15lair < the average weight of the bars given to Maya   Answer: Option 15
Answer: B
If thrice the age of the son is added to the father then the sum would be 56. But if twice the age of father is added to the son then the total would be 72. Find the ages of father and son.
Choose the correct choice from the following:
A) 32, 8 B) 8, 32 C) 56, 72 D) 72, 56 E) 32, 4

Solution: Let the age of the father be x and the age of the son be y   x+3y=56---Eq1   2x+y=72--Eq2   multiplying Eq1 by 2 and solving the above equations we get y=8   Substitute y=8 in 2 we get x=32   answer is 32, 8 correct ans is 32, 8
Answer: A
A box contains 8 red marbles, 6 green marbles & 10 pink marbles. One marble is drawn at random from box. What is the probability that the marble drawn is green?
Choose the correct choice from the following answers:
A) 6/4
B) 8/4
C) 10/4
D) 7/4
E) 1/4

Solution: 6c1/24c1=6/24=1/4   ANSW1/4R:1/4
Answer: E
A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?	Pick one:	A) 10 years	B) 77 years	C) 88 years	D) 44 years	E) 33 years

Solution: P ---- 2P ---- 8 years   2 1/4 P ---- 10 years   10 yearsnswer:10 years
Answer: A
If x > 0, which of the following could be true?
I. x^3 > x^2
II. x^2 = x
III. x^2 > x^3
Pick one.
A) I only B) I & II C) II & III D) All of the above E) None of the above

Solution: I. x^3>x^2   For x = 2,   2^3>2^2   II. x^2=x   For x = 1,   1^2=1   III. x^2>x^3   For x=1/2,   (1/2)^2>(1/2)^3   All conditions could satisfy   Answer = All of the above
Answer: D
A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?  Select the correct option:
A) 5 B) 6 C) 7 D) 54 E) 3

Solution: US = 25   DS = 35   M = (35 - 25)/2 = 5.5nswer:5
Answer: A
Company A has an annual budget for a certain project, and 1/4 of this budget was spent during the first quarter of the year. If 1/8 of the remainder of the budget was spent during the second quarter, what fraction of the budget was left at the end of the second quarter?
Choices:
A) 5/8
B) 13/16
C) 21/32
D) 37/48
E) 53/64

Solution: Let x be the company budget.   At the end of the first quarter, the remaining budget was (3/4)x.   At the end of the second quarter, the remaining budget was (7/8)(3/4)x = (21/32)x.   The answer is 21/32.
Answer: C
Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?	Choose the correct choice from the following choices:  A) $40,000  B) $56,000  C) $64,000  D) $66,667  E) $80,000

Solution: Equation is correct, so math must be a problem.   0.12*40,000+0.2*(x-40,000)=8,000 --> 4,800+0.2x-8,000=8,000 --> 0.2x=11,200 --> x=56,000.   Answer: $56,000.
Answer: B
A professor will assign seven projects to three students. If two students each got 2 projects, and the other one got 3 projects, how many ways are possible?  Choose the correct choice.
A) 600
B) 630
C) 650
D) 670
E) 690

Solution: The projects are all distinct and so are the students. So in both the cases, you are doing essentially the same. In the first case, you are assigning 7 things to 3 people and in the second case, you are assigning 7 people to 3 things.   So in both the cases, you choose the person/thing that will get 3 things/person in 3C1 = 3 ways.   Next, you choose 3 things/people out of 7 in 7C3 ways.   Next, you choose 2 things/people out of the remaining 4 in 4C2 ways.   3C1 * 7C3 * 4C2 = 3*(7*6*5)/(3*2) * 6= 
3*(7*6*5)/(3*2) * 6 = 630
630 ways	ANS:630
Answer: B
If C + D = 9 and C and D are any numbers, which of the following is a possible value for 2C+3D?
Choose the correct choice from the following
A) 19
B) 09
C) 29
D) 39
E) 38

Solution: c + d = 9   2c + 3d = 2c + 2d + d = 2(c+d) + d = 9 + d=d=-9.   Now this reults in   c+d=9   c=18   2c + 3d=2(18)+3(-9)   2c + 3d= 9   Hence, 09 is the right answer.
Answer: B
A & B are two towns. A person covers the distance from A to B on cycle at 17kmph and returns to A by a boat running at a uniform speed of 8kmph. His average speed for the whole journey is Select the correct option
A) 12.5 km/h  B) 12.33 km/h  C) 10.75 km/h  D) 10.88 km/h  E) 10.78 km/h

Solution: When same distance is covered with different speeds, then the average speed = 2xy / x+y = 10.88kmph   Answer : 10.88 km/h.
Answer: D
Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent E? Choose the most appropriate option: A) 20% B) 80% C) 100% D) 180% E) 200%

Solution: C.   Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).   E=[(2 - 1)/1] * 100% = 100%.100%(2 - 1)/1  * 100= 
(2 - 1)/1  * 100 = 100
100%.100%
Answer: C
A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
Choose the correct choice from the following answers: A) 5 B) 10 C) 11 D) 16 E) 18

Solution: Let the ten's digit be x and unit's digit be y.   Then, number = 10x + y.   Number obtained by interchanging the digits = 10y + x.   (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.   Answer:11
Answer: C
To fill an art exhibit, the gents in an art course are assigned to create one piece of artwork each in the following distribution: 1/3 are sculptures, 1/8 are oil paintings, 1/2 are watercolors, and the remaining 10 pieces are mosaics. How many gents are in the art class?	Choose the correct choice from the following options
A) 80 B) 120 C) 240 D) 320 E) 400

Solution: Let the total number of gents in the art class = s   Distribution of artwork is as   1/3 are sculptures   1/8 are oil paintings   1/2 are watercolors, and the remaining 10 pieces are mosaics   (1/3)s +(1/8)s +(1/2)s + 10 = s   Since remaining 10 pieces are mosaics , (1/24)s = 10   s = 240   Answer 240
Answer: C
Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 12 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed? Pick one
A) 3
B) 6
C) 9
D) 12
E) 15

Solution: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.   So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes.   If the average of 10 and 20-pound boxes is to be 12, the ratio of 10-pound boxes:20-pound boxes should be 4:1.   The number of 10 pound boxes remains the same so we still have 4 of them.   To get a ratio of 4:1, the number of 20-pound boxes must be 1.   We need to remove 15 of the 20-pound boxes.   The answer is 15.
Answer: E
fill in ht blank:(a) the point with coordinates (0,0) is called ____ of a rectangular coordinate system,(b) to find the y-intercept of a line, we let ___ equal ___ and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___ Pick.
A) (a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y B) (a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for x ; to find x- intercept , we let y equal 0 and solve for y C) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let y equal z and solve for x ; to find x- intercept , we let x equal 0 and solve for z D) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x E) none of the above

Solution: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer ((a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x)
Answer: D
Jack and Paul are running 1000m. Jack runs 1.5Km/hr faster than Paul but also finishes the race 1.5 sec earlier. What is the speed of Jack??	Choose the correct option:	A) 20.61	B) 21.61	C) 22.61	D) 23.61	E) 24.61

Solution: distance(given) 1000m   paul speed(let)= x m/s   time(paul take)= 1000/x sec   jack speed= x + 1.5*(5/18) m/s   tym (jack)= 1000/(x+7.5/18) s   tym(paul) - tym (jack) = 1.5   solving for x we get 20.20   speed of jack is 20.20+ 7.5/18=20.61   20.61NSWER:20.61
Answer: A
A shop keeper marked 20% above the cost price and offered 15% discount then find it's net profit?
Choose the correct choice:
A) 2% B) 5% C) 8% D) 10% E) 15%

Solution: Net profit = 20-15 + (20*(-15)/100)= 
20-15 + (20*(-15)/100) = 2
2%   2%nswer is 2%
Answer: A
If q is not equal to zero, andq+1/q = 3, then what is the value of q^4 + (1/q)^4?  Choose the correct choice from the following answers:
A) 184	B) 194	C) 254	D) 324	E) 354

Solution: q + 1/q=4   we square both sides so we have q^2 + 1/q^2 +2 = 16   or q^2 + 1/q^2= 14   squaring again we have q^4 + 1/q^4 + 2 = 196   or q^4 + 1/q^4 = 194   answer =194 (194)
Answer: B
Pipes A and B can fill a tank in 9 and 6 hours respectively. Pipe C can empty it in 18 hours. If all the three pipes are opened together, then the tank will be filled in?  Choose the correct choice from the following options:  A) 3 9/97 hrs  B) 4 2/4 hrs  C) 3 9/17 hrs  D) 3 9/27 hrs  E) 3 9/19 hrs

Solution: Net part filled in 1 hour = 1/9 + 1/6 - 1/18   = 4/18   The tank will be full in 18/4 hrs, i.e., 4 2/4 hrs.   Answer:4 2/4 hrs
Answer: B
A batsman had a certain average of runs for 16 innings. In the 17th innings, he made a score of 87 runs thereby increasing his average by 3. What is his average after 17 innings?  Choose the correct choice from the following options:  A) 39  B) 88  C) 266  D) 278  E) 221

Solution: Explanation:   39ssume his initial average = xx   His total runs after 16 innings = 16xx   39fter scoring 87 runs his average got increased by 3 to xx + 3   So his total runs after 17 innings = 17 × (xx+3)   But it was given that the difference in the total scores after 16 innings and 17 innings = 87   Therefore 17×(x+3)−16x=87⇒x=3617×(x+3)−16x=87⇒x=36   His new average = 36 + 3= 
36 + 3 = 39
39   39nswer:39
Answer: A
If x ≠ 0 and (y-x)/x=(y+x)/y, which of the following expressions is equal to its opposite?
Choose the correct option:
A) (x+y) (x-y)
B) x^2 – y^2
C) y^2
D) (y + x)^2
E) (x – y)^2

Solution: (y+x)/x=(y+x)/y   => y^2 + xy = xy + x^2   => x^2 - y ^2 = 0   => (x+y) (x-y) = 0   (x+y) (x-y)nswer (x+y) (x-y)
Answer: A
Approximately how many cubic feet of water are needed to fill a circular swimming pool that is 70 feet across and 9 feet deep?  Choose the correct option:
A) 4000
B) 10000
C) 20000
D) 35000
E) 45000

Solution: Answer Should be D.   V= \pir^2h= \pi*35^2*9= approximately 35000
Answer: D
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is  Choose the correct option:
A) 1/216
B) 1/36
C) 5/9
D) 5/12
E) 7/12

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= 
6 * 6 * 6 = 216
216 ways.   Hence the probability is 6/216= 1/36   ANSWER:1/36
Answer: B
Solve the given two equations and find the inequality of X and Y. (a) x^2-1=0 and (b) y^2+4y+3=0
Choose the correct choice from the following options
A) If x>y  B) If x>=y  C) If x < y  D) If x<=y  E) x=y or relationship cannot be established

Solution: Solution:-   X=+1,-1 and Y= -1,-3   Comparing we get X>=Y   If x>=y
Answer: B
After decreasing 50% in the price of an article costs Rs.1200. Find the actual cost of an article?
Choose the correct answer:
A) 1200
B) 50
C) 2400
D) 100
E) 600

Solution: 2400P* (50/100) = 1200   2400P2400 * (50/100)= 
2400 * (50/100) = 1_200
1200   2400P= 24 * 100= 
24 * 100 = 2_400
> 2400P= 2400   Answer:2400
Answer: C
In f is a positive integer smaller than 200 and (14f)/60 is an integer, then f has how many different positive prime factors? Choices.
A) 2	B) 3	C) 5	D) 6	E) 8

Solution: 7f/30 tells us that f is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.   Answer: 3
Answer: B