MU-NLPC/Calc-aqua_rat huggingface dataset:
In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,-5) and (t,-7). What is the least possible value of the slope of line L?	Options:  A) 6  B) -1  C) -2  D) -6  E) -10

Solution: We need to find out the value of p and L to get to the slope.   Line L and Graph y intersect at point (p,-5). hence, x= p and Y=-5 should sactisfy the graph. soliving   5 = -p2 +9   p2 = 4   p = + or - 2   simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7.   -7 = -t2+9   t = +or - 4   considering p = -2 and t =4, the least slope is (-7+5)/(4-2) = -1   IMO option -1 is correct answer.
Answer: B
A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $30. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard) Choose the most appropriate option:	A) 30xy	B) 270/(xy)	C) xy/9	D) xy/30	E) 270xy

Solution: xy sq ft = $30   1 sq ft = $30/xy   multiplying by 9 on both side   9 sq ft = $270/xy   or 1 sq yard = $270/xy   Hence 270/(xy).
Answer: B
The roots of the equation 3x2 - 12x + 10 = 0 are?  Choose the correct choice from the following answers
A) rational and unequal B) complex C) real and equal D) irrational and unequal E) rational and equal

Solution: Explanation:   The discriminant of the quadratic equation is (-12)2 - 4(3)(10) i.e., 24. As this is positive but not a perfect square, the roots are irrational and unequal.   ANSWER IS irrational and unequal
Answer: D
A father is four times as old as his son. In twenty years, he'll be twice as old. How old are they now?
Choices:
A) 5,40  B) 10,40  C) 20,40  D) 10,30  E) 15,30

Solution: If F is age of father and s is age of son   f=4s   f+20 = 2*(s+20)   4s+20 = 2s+40   2s=20   s=10   F=40   ANSWER:10,40
Answer: B
The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class. Choose the correct choice from the following choices: A) 48.55 B) 42.25 C) 50 D) 51.25 E) 52.25

Solution: Explanation:   48.55verage weight of 16 boys = 50.25   Total weight of 16 boys = 50.25 × 16   48.55verage weight of remaining 8 boys = 45.15   Total weight of remaining 8 boys = 45.15 × 8   Total weight of all boys in the class = (50.25 × 16)+ (45.15 × 8)   Total boys = 16 + 8= 
16 + 8 = 24
24   48.55verage weight of all the boys= (50.25×16)+(45.15×8)/24   =(50.25×2)+(45.15×1)/3   =(16.75×2)+15.05   =33.5+15.05= 
33.5+15.05 = 48.55
48.55   48.55nswer: Option 48.55
Answer: A
The sum of the mean, the median, and the range of the set {5,7,9} equals which one of the following values?
Choose the correct choice from the following choices.
A) 11  B) 17  C) 14  D) 12  E) 10

Solution: Here Mean => 5+7+9/3 => 6   median => 7   and range => 9-5= 
9-5 = 4
> 4   hence sum=> 6+7+4= 
6+7+4 = 17
> 17   Answer: 17
Answer: B
If x is divisible by 4 and 6, which of the following must divide evenly into x?
I. 2
II. 35
III. 70 Choose the correct choice from the following answers:	A) I only	B) I and II	C) II​ and III	D) II​ only	E) I, II, and III

Solution: If x is divisible by 4,6 means it will be = or > 12, 24,48 etc...   That are not divisible by 35, 70.   So, the answer is I only
Answer: A
In the graph below, no axes or origin is shown. If point B's coordinates are (9,3), which of the following coordinates would most likely be A's?
Select:
A) (17, -2) B) (10, 6) C) (6, 8) D) (-10, 3) E) (-2, -17)

Solution: wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 9.   (10, 6) rules..
Answer: B
2y - x = 2xy . If x and y are integers, which of the following could equal y? Choose the correct choice from the following options:	A) 2	B) 1	C) 0	D) 3	E) 4

Solution: Plug in the answer choices in the equation from the question stem.   A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE   B) y = 1 >>> 2 - x = 2x >>> Same, POE   0) y = 0 >>> -x = 0 >>> x This is the answer   Answer 0
Answer: C
A began business with 12500 and is joined afterwards by B with 37500. When did B join, if the profits at the end of the year are divided equally? Select:
A) 8 months
B) 9 months
C) 10 months
D) 7 months
E) None of these

Solution: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.   ∴ Profit ratio is 12 × 12500 : (12 – x) × 37500   or 12 : 3(12 – x)   Since profit is equally divided so   12 = 3(12 – x) or x = 8. Thus B joined after 8 months.   8 monthsnswer 8 months
Answer: A
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? Select the correct option
A) km B) km C) km D) km E) km

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 16 + 21= 
16 + 21 = 37
37   T= 12   D = 37 * 12= 
37 * 12 = 444
444   Answer :km
Answer: B
The percent change from 29 to 43 is approximately what percent of the percent change from 43 to 57? Options:
A) 50%
B) 66%
C) 110%
D) 133%
E) 150%

Solution: Thus, %age change from 29 to 43 = 14/29 ≈≈ 50% or 0.5 (we can approximate in this question as the options given are far apart).   %age change from 43 to 57 = 14/43 ≈≈0.33   Thus, the required value = 50/33 = 1+17/33 ≈≈  1+0.5= 
 1+0.5 = 1.5
1.5 or 150%   150% is thus the correct answer.
Answer: E
By selling 100 pencil, a trader gains the cost of 40 Pencil. Find his gain percentage?  Choose the correct choice from the following answers: A) 26 1/3% B) 51 1/3% C) 40% D) 53 1/3% E) 34 1/3%

Solution: C   40%   Let the CP of each pencil be Rs. 1.   CP of 100 pens = Rs. 100   Profit = Cost of 40 pencil = Rs. 40   Profit% = 40/100 * 100= 
40/100 * 100 = 40
40%
Answer: C
at three different signals,light change after 48 sec,72 sec,108 sec respectively.if at morning 8:20:00 change together,then at what time again they will change together?	Choose the correct option:
A) 8:27:12  B) 8:27:24  C) 8:27:36  D) 8:27:48  E) 8:27:56

Solution: l.c.m of 48,72,108=7min.12sec   again they will change at=8:27:12   answer 8:27:12
Answer: A
A train is 360 meter long is running at a speed of 45 km/hour. In what Ɵme will it pass a bridge of 140
meter length. Options
A) 20 seconds  B) 30 seconds  C) 40 seconds  D) 50 seconds  E) None of these

Solution: Explanation:   Speed = 45 Km/hr = 45*(5/18) m/sec   = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   =500   ∗   225=40seconds   Answer: 40 seconds
Answer: C
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 18 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? Select:
A) 468  B) 444  C) 676  D) 767  E) 663

Solution: 1h ----- 3   ? ------ 60   12 h   RS = 18 + 21= 
18 + 21 = 39
39   T= 12   D = 39 * 12= 
39 * 12 = 468
468   468nswer: 468
Answer: A
The sale price sarees listed for Rs.375 after successive discount is 20% and 15% is?  Choose the correct choice from the following answers:
A) 227  B) 268  C) 342  D) 787  E) 285

Solution: 375*(80/100)*(85/100)   = 285   Answer: 285
Answer: E
A boy pays Rs. 369 for an article marked at Rs. 600, by enjoying two successive discounts. If the first discount is of 25%, how much should be the second discount?
Pick one:
A) 18
B) 99
C) 27
D) 26
E) 18

Solution: Explanation:   First discount = 25% of 600 = Rs. 150.   Thus, the reduced price = 600 – 150 = Rs. 450.   Since the person actually paid Rs. 369, the value of the second discount must be equal to Rs. 81 (450 – 369).   Let the second discount be x   Thus, we get, 81 = x of 450   ( 81/450)*100= 
( 81/450)*100 = 18
18%   18NSWER: 18
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 choice from the following options
A) 20%	B) 25%	C) 30%	D) 15%	E) 10%

Solution: 800 --- 200   100 --- ? => 25%   ANSWER:25%
Answer: B
If x, y, and d are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=d and if x is less than y, which of the following could be the value of d?
Choose one:
A) 10	B) 12	C) 15	D) 18	E) 30

Solution: Answer choice C: d= 15   (10x + 20y)/(x+y) = 15   10x + 20y = 15x + 15y   5y = 5x   y = x   Doesn't work because the problem states that x<y.   We need y to be larger, so let's try answer choice D: d=18   10x + 20y = 18x + 18y   2y = 8x   y/x = 8/2   Success! x<y.   The correct answer is 18.
Answer: D
An athlete runs 200 meters race in 36sec. His speed is?  Pick one:
A) 20km/hr B) 15km/hr C) 30km/hr D) 25km/hr E) 40km/hr

Solution: speed = 200/36 = 50/9 m/sec   = 50/9 * 18/5 km/hr = 20km/hr   20km/hrnswer is 20km/hr
Answer: A
When asked what the time is,a person answered that the amount of time left is 1/3 of the time already completed.what is the time.  Options:
A) 2 PM	B) 9 PM	C) 3 PM	D) 8 PM	E) 6 PM

Solution: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)   24−x=1/3x⇒x=18   Time is 6 PM   Answer:6 PM
Answer: E
The speed at which a man can row a boat in still water is 15 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 90 meters? Select.
A) 12  B) 16  C) 17  D) 18  E) 20

Solution: The speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 km/hr   18 km/hr * 5/18= 5 m/s   The time taken to cover 90 meters = 90/5= 
90/5 = 18
18 seconds.   The answer is 18.
Answer: D
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:	Choices:	A) 4:5	B) 3:5	C) 6:8	D) 3:5	E) 5:4

Solution: third number be x.   first no = 120% of x = 6x/5   second no = 150% of x = 3x/2   ratio in first two nos = (6x/5:3x/2)=> 4:5   4:5NSWER 4:5
Answer: A
A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?  Choose one:
A) 14 days  B) 5 days  C) 8 days  D) 4 days  E) 3 days

Solution: WC = 3:1   WT = 1:3   x 3x   1/x – 1/3x = 1/8   x = 16/3   3/16 + 1/16 = 1/4 => 4 days   ANSWER:4 days
Answer: D
A train speeds past a pole in 15 sec and a platform 150 m long in 25 sec, its length is? Choose the correct choice from the following answers
A) 100	B) 150	C) 160	D) 225	E) 180

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 150)/25 = x/15 => x = 225 m.   Answer: Option 225
Answer: D
A shopkeeper purchased 80 kg of potatoes for Rs. 550 and sold the whole lot at the rate of Rs. 9 per kg. What will be his gain percent?  Pick:  A) 22.6 %  B) 30.9 %  C) 35.6 %  D) 39.5%  E) 23.6 %

Solution: C.P. of 1 kg = 550/80 = Rs. 6.875S.P. of 1 kg = Rs. 9Gain % = 2.125/6.875 * 100 = 212.5/6.875 = 30.9 %Answer: 30.9 %
Answer: B
We are given the positive numbers a,b,c, which form an arithmetic progresion in the given order. We know that a+b+c=9. The numbers a+1,b+1,c+3 form a geometric progression in the given order. Find c.  Choose the correct choice from the following:
A) 5  B) 6  C) 7  D) 8  E) 9

Solution: Solution:   Since a,b,c form an arithmetic progression, c=b+d=a+2d and a+b+c=a+a+d+a+2d=3a+3d=9, so a+d=b=3 and a+c=6=>c=6−a. Since a+1,b+1,c+3 form a geometric progression, we have (b+1)2=(a+1)(c+3), or 16=(a+1)(6−a+3)=(a+1)(9−a)   16=9a+9−a2−a   a2−8a+7=0, therefore a=7 or a=1. But if a=7, c=6−a=6−7=−1<0 and by definition c is positive, so a=7 is not a solution. Therefore a=1 and c=6−a=6−1=5.   5nswer 5
Answer: A
36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible? Choose one
A) 2 B) 4 C) 5 D) 6 E) 10

Solution: Three conditions have to be satisfied.   1. The number of students per row has to be at least 3.   2. Number of row has to be at least 3.   3. Equal number of students has to be seated in a row.   The following arrangements satisfy all 3 conditions.   Arrangement 1: 3 students to a row; 12 rows.   Arrangement 2: 4 students to a row; 9 rows.   Arrangement 3: 6 students to a row; 6 rows.   Arrangement 4: 9 students to a row; 4 rows.   Arrangement 5: 12 students to a row; 3 rows.   You will observe that the number of students in a row is a factor of 36.   So, an alternative and faster approach is to list down factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.   And then start from 3 and quickly find out if the number of rows is at least 2.   Both the conditions are satisfied for the following factors : 3, 4, 6, 9, and 12. i.e., 5 arrangements.   Option 5 is answer
Answer: C
A and B start a business with Rs.16000 and Rs.32000 respectively. Hoe should they share their profits at the end of one year?
Choose the most appropriate option:
A) 1:2
B) 3:4
C) 2:5
D) 3:7
E) 2:1

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by 1:2 and B =   16000 : 32000 => 1:2   1:2NSWER:1:2
Answer: A
How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together?	Choose the correct choice:
A) 9 B) 10 C) 11 D) 12 E) 13

Solution: (700 – 300)/42 = 9 22/42   => 9 Numbers   9NSWER:9
Answer: A
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?  Choose the correct choice:
A) 152
B) 3^5
C) 125
D) 217
E) 136

Solution: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.   Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.   Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.   Therefore, the total number of ways the 5 letters can be posted in 3 boxes is   3 * 3 * 3 * 3 * 3 = 3^5   Ans: 3^5
Answer: B
Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 342 grams of compound X?
Choose the correct choice from the following choices.
A) 54 B) 162 C) 250 D) 270 E) 280

Solution: total number of fractions =2+10= 
2+10 = 12
12   element B constitutes=10 out of 12 parts of X   So in 342 gms of X have 342*10/12=280 gms of B   and  342-280= 
 342-280 = 62
62 gms of A.   cross check:- A/B= 62/280 =2/10 (as given)   Ans 280
Answer: E
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Choose the correct choice from the following answers.
A) 30	B) 31	C) 36	D) 25	E) 24

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.   Answer: Option 36
Answer: C
If n and k are integers whose product is 3600, which of the following statements must be true?  Answers
A) n+k>0	B) n does not equal k	C) Either n or k is a multiple of 10	D) If n is even, then k is odd	E) If n is odd, then k is even

Solution: If n is odd and k is odd, then the product is odd.   The answer is If n is odd, then k is even.
Answer: E
How many prime numbers exist between 260 and 280? Pick one.
A) None B) One C) Two D) Three E) Four

Solution: Straight a way lets exclude all the Even numbers between 260 and 280.   So now the number starts from 261 to 279 (Only ODD)   261 is a divisible of 3 and next odd divisible by 3 will be 261 + 6= 
261 + 6 = 267
267 + 6= 
267 + 6 = 273
273 + 6= 
273 + 6 = 279
279.   Also we can eliminate numbers ending with '5'   So in Odd, the excluded numbers are 261,265,267,273,279, which leave us with 263,269,271,277.   Checked the above listed four numbers are divisible by any numbers till 20.   ANSWFourR:Four
Answer: E
There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 15 possible combinations in which Jim and Ellen are not selected, what is the value of k? Choose the correct option:  A) 8  B) 9  C) 10  D) 11  E) 12

Solution: There are k-2 members in the band, and k-4 members without Jim and Ellen.   (k-4)102 = 15   (k-4)(k-5)/2 = 15   (k-4)(k-5) = 30 = 6*5   k = 10   The answer is 10.
Answer: C
Solve the given two equations and find the inequality of X and Y. (a) x^4- 227= 398 and (b) y^2 + 321=346
Pick one
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=+5,-5 and Y= +5,-5   Comparing, we get X=Y, X<y, x="">Y.   Therefore, no relationship can be established between X and Y.   x</y,>=y or relationship cannot be established
Answer: E
Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?  Choose the correct option:	A) 177	B) 132	C) 176	D) 278	E) 267

Solution: 2 * 22/7 * 14= 
2 * 22/7 * 14 = 88
88   88 * 1 1/2=Rs.132   Answer:132
Answer: B
Mala and Usha shared their water from a bottle. If mala and usha both drank for the same amount of time, but usha only drank 2/10 of the total bottle, what was the ratio of mala and usha speed? Choose the correct choice
A) 1:4 B) 2:5 C) 4:1 D) 3:5 E) 2:3

Solution: The answer is suppose to be C. 4:1. It's from the GMATPrep   Answer:option 4:1
Answer: C
A man has $ 10,000 to invest. he invest $4,000 at 5% and $3500 at 4%. In order to have ayearly incom of $500, he must invest the remainder at:	Choose the correct choice from the following answers
A) 6%
B) 5.4%
C) 6.1%
D) 4.4%
E) 6.4%

Solution: income from $4000 at 5% in one year = $4000of 5%= $200, income from $3500 at 4% in one year = $3500 of 4%= $140,total income= $200+$140= $340. Remaining yearly income amount 200+ 140= 
200+ 140 = 340
$340. Remaining yearly income amount=$500-$340= $160, remaining investamount500- 340= 
500- 340 = 160
$160, remaining investamount= $10000-($4000+$3500)= $2500, I10000-( 4000+ 3500)= 
10000-( 4000+ 3500) = 2_500
$2500, I=PNR. 160=2500 x R x 1year, R= 0.064. therefore answer is: 6.4%, correct answer will be (6.4%)
Answer: E
A train 125 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Choose one.
A) 35 km/hr	B) 50 km/hr	C) 45 km/hr	D) 65 km/hr	E) 51 km/hr

Solution: Speed of the train relative to man   = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed   = (x - 6) km/hr. x - 6 = 45 ==> x = 51 km/hr.   Answer: 51 km/hr
Answer: E
The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 5 seconds an object is falling at a speed of 84 miles per hour, how fast will it be falling after 12 seconds?	Choose the correct answer.
A) 204 miles per hour B) 212 miles per hour C) 216 miles per hour D) 1080 miles per hour E) 5400 miles per hour

Solution: Since Velocity is proportional to Time   Velocity =k*Timewhere k is the constant of proportionality   Time= 5 seconds   Velocity = 5k = 84 miles per Hour   i.e. k = 17   i.e. The relation between Velocity and Time becomes   Velocity =17*Time   Time= 12 seconds   Velocity = 17*12= 
17*12 = 204
204 miles per hour   204 miles per hournswer: Option 204 miles per hour
Answer: A
In a game, a player can win by getting five consecutive tails in six throws of a coin. What is the probability of winning if the player gets a tail on the first two throws?
Choose the correct option:
A) 1/4
B) 3/4
C) 5/8
D) 3/8
E) 1/8

Solution: The only way to win is to get a tail on each of the next three throws.   P(three tails)=(1/2)^3=1/8   The answer is 1/8.
Answer: E
A sells a bicycle to B and makes a profit of 50%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A. Pick one
A) 237
B) 126
C) 971
D) 611
E) 120

Solution: 120xplanation:   Let CP be 100   A sells at 50% profit so SP=150   B sells at 25% profit = 150 x (1+25/100) = 187.50   CP --- SP   100--- 187.50   x --- 225   CP = 225 x 100/187.50 = 120   ANSW120R: 120
Answer: E
One farmer takes 12 hours to plow his field, but another farmer takes 8 hours to plow the same field with an equal tractor. How long would it take them together to plow the field?
Choose the correct option:	A) 12.5 hours	B) 4 hours	C) 4.8 hours	D) 5 hours	E) 5.6 hours

Solution: First we must find the least common denominator.   1/12 + 1/8 =   2/24+3/24=5/24   They can plow the field 5/24 per hour. Now to find the actual time, Lets use T for time as a variable.   1/T = 5/24   T/1 = 24/5= 
24/5 = 24/5 = around 4.8
4.8 hours   Answer is 4.8 hours
Answer: C
P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 8 days. How many days more will P take to finish the work?	Choose the correct choice from the following options
A) 10	B) 15	C) 18	D) 20	E) 24

Solution: Let work done by P in 1 day = p,   Work done by Q in 1 day = q,   Work done by R in 1 day = r   p + q = 1/30   q + r = 1/24   r + p = 1/20   Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8   => p + q + r = 1/16   => Work done by P,Q and R in 1 day = 1/16   Work done by P, Q and R in 8 days = 8 × (1/16) =8/16 = 1/2   Remaining work = 1 = 1/2= 1/2   Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day   = 1/16 – 1/24 = 1/48   Number of days P needs to work to complete the remaining work = (1/2) / (1/48)= 
(1/2) / (1/48) = 24
24   Option 24
Answer: E
Set #1 = {J, K, L, M, E}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel? Options
A) 1/6 B) 1/8 C) 1/3 D) 1/4 E) 1/9

Solution: At least questions are best solved by taking the opposite scenario and subtracting it from 1. Probability of choosing no vowel from set 1 is 4/5 and set 2 is 5/6. Multiply these to get 2/3. Therefore, probability of picking at least one vowel = 1-2/3=1/3.   ANSWER : 1/3
Answer: C
Bobby bought 2 shares, and which he sold for $106 each. If he had a profit of 120% on the sale of one of the shares but a loss of 47% on the sale of the other share, then on the sale of both shares Bobby had... Choose the correct choice from the following answers:  A) a profit of 10  B) a profit of 8  C) a loss of 38  D) a loss of 10  E) neither a profit nor a loss

Solution: a loss of 38ost of the first stock: 106/2.2=48.18, so profit from it 106-48.18=57.18   a loss of 38ost of the second stock:  106/0.53= 
 106/0.53 = 200
200, so loss from it 106-200=-94   Overall loss 57.18-94=-36.82   Answer: a loss of 38.
Answer: C
When 33 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
Choose the most appropriate option.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: This means that 30 must be a multiple of k.   The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.   Out of these, k can be 5, 6, 10, 15, and 30.   The answer is 5.
Answer: E
If 1st October is Sunday, then 1st November will be  Options:
A) Saturday B) Thursday C) Wednesday D) Tuesday E) None of these

Solution: Explanation :   Given that 1st October is Sunday   Number of days in October = 31   31 days = 3 odd days   (As we can reduce multiples of 7 from odd days which will not change anything)   Hence 1st November = (Sunday + 3 odd days) = Wednesday   Answer : Option Wednesday
Answer: C
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?	Choose the correct choice from the following choices:  A) 1  B) 61  C) 63  D) 64  E) 120

Solution: We need to select 5 men from 7 men and 2 women from 3 women.   Number of ways to do this   = 7635 × 3632   = 7632 × 3631 [∵ n63r = n63(n-r)]   = 21 * 3= 
21 * 3 = 63
63   63
Answer: C