MU-NLPC/Calc-aqua_rat huggingface dataset:
The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio? Pick one:	A) 21:29	B) 21:31	C) 21:22	D) 21:31	E) 21:12

Solution: Originally, let the number of boys and girls in the college be 7x and 8x respectively.   Their increased number is (120% of 7x) and (110% of 8x).   i.e., (120/100 * 7x) and (110/100 * 8x)   i.e., 42x/5 and 44x/5   Required ratio = 42x/5 : 44x/5 = 21:22   Answer: 21:22
Answer: C
A taxi leaves Point A 4 hours after a bus left the same spot. The bus is traveling 30 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in two hours.  Choose the correct choice from the following choices: A) 40 B) 42 C) 45 D) 48 E) 49

Solution: Let the speed of bus be v - 30, speed of taxi be v   The bus travelled a total of 6 hrs and taxi a total of 2 hrs.   Hence 6 * (v-30) = 2v   6v - 180 = 2v   4v = 180   v = 45 mph   45
Answer: C
72 67 66 61 60 ...? Select
A) 52  B) 53  C) 54  D) 55  E) 56

Solution: Sequence = 72 67 66 61 60 55   There is 2 series :   1st series = 72 66 60 (decreasing by 6)   2nd series = 67 61 55 (decreasing by 6)   ANSWER:55
Answer: D
John makes $60 a week from his job. He earns a raise andnow makes $68 a week. What is the % increase? Choices.
A) 16.12% B) 16.66% C) 16.56% D) 17.66% E) 13.33%

Solution: Increase = (8/60)*100 = (2/15)*100 = 13.33%.   13.33%
Answer: E
If -4 < x < 8 and -6 < y < 3, which of the following specifies all the possible values of xy?  Select the correct option.
A) -42 < xy < 21  B) -48< xy < 24  C) -28 < xy < 18  D) -24 < xy < 21  E) -24 < xy < 24

Solution: The least value of xy is a bit more than 8*(-6)=-48 and the largest value of xy is a bit less than (-4)*(-6)= 
(-4)*(-6) = 24
24.   Therefore -48 < xy < 24.   Answer: -48< xy < 24.
Answer: B
The average age of 3 children in a family is 20% of the average age of the father and the eldest child. The total age of the mother and the youngest child is 39 years. If the father's age is 26 years. What is the age of the second child?  Select.
A) 15 years
B) 16 years
C) 18 years
D) Cannot be determined
E) None

Solution: Solution   Since the total or average age of all the family members is not given, the given data is inadequate. So, the age of second child cannot be determined.   Answer Cannot be determined
Answer: D
5n + 2 > 17 and 7n - 5 < 44; n must be between which numbers?	Choose the correct option:
A) 1 and 8 B) 2 and 6 C) 0 and 9 D) 3 and 7 E) 2 and 9

Solution: 5n > 15 --> n > 3   7n < 49 --> n < 7   3 < n < 7   Answer: 3 and 7
Answer: D
Anand and Deepak started a business investing Rs. 22,500 and Rs.35,000 respectively. Out of a total profit of Rs.13,800, Deepak’s share is _____  Options
A) 5400
B) 3797
C) 27877
D) 2772
E) 9911

Solution: Explanation:   Ratio of their investments = 22500 : 35000 = 9 : 14   So Deepak' s share = 923923 × 13800 = Rs.5,400   5400nswer: 5400
Answer: A
What is the greatest value of positive integer x such that 2^x is a factor of 100^50?	Pick one: A) 70 B) 80 C) 90 D) 100 E) 120

Solution: Put in simple words, we need to find the highest power of 2 in 100^50   100 = 2^2*5^2   Therefore 100^50 = (2^2*5^2)^50 = 2^100*5^100   Answer : 100
Answer: D
A swimmer can swim in still water at 4 km/h. If the speed of the water current is 2 km/h, how many hours will the swimmer take to swim against the current for 8 km?
Select.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: The swimmer can swim against the current at a speed of 4-2= 
4-2 = 2
2 km/h.   The time it will take is  8/2= 
 8/2 = 4
4 hours.   The answer is 4.
Answer: D
The total of the ages of Jayant, Prem and Saransh is 75 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Saransh? Choose one
A) 30 years B) 32 years C) 34 years D) 38 years E) None

Solution: Solution   Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,   (2x + 10)+(3x + 10)+(4x + 10)	= 75.   ‹=›9x = 45   x = 5.   ∴ Saransh's present age = 4x + 10 = 30 years.   30 yearsnswer 30 years
Answer: A
How many ways are there to award a gold and bronze medal to 10 contending teams? Choose the correct choice from the following answers:
A) 10 × 9 B) 10!/(3!7!) C) 10!/3! D) 360 E) 300

Solution: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 10 ways   if gold medal is given to 1 of the teams then only possible 9 teams can be considered for bronze medal. we can do selection in 9 ways   Total number of ways to select the 3 possible medal winners = 10 * 9   Correct answer - 10 × 9
Answer: A
At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Choose the correct choice from the following
A) Rs.62.50
B) Rs.72.50
C) Rs.75.00
D) Rs.80.00
E) Rs.85.00

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(95/100)= 59.375   MP = 62.5   Rs.62.50NSWER:Rs.62.50
Answer: A
How many 3 digit odd numbers do not use any digit more than once
Choose the correct answer
A) 1720  B) 216  C) 224  D) 2460  E) 280

Solution: The Way i solved it is   A B C ( hundreds, tens, units   )C can be 1 3 5 7 9 ( any of the 5 digits )   A can be anything except (D or 0) so 8 possibilitie   B can be anything execpt ( A D C ) so 7 possibilities   total ways are   7 * 8 * 5= 
  7 * 8 * 5 = 280
280   Ans : 280
Answer: E
A number was divided successively in order by 4,5,6 the remainder was respectively 2,3,4 the numbers are? Choose the correct choice from the following answers:
A) 1	B) 2	C) 3	D) 4	E) 8

Solution: let x=6q+3   then x^2=(6q+3)^2=6(6q^2+6q+1)+3   thus the remainder is 3   The Answer is(3)
Answer: C
one father gave 10 cents to one son and 15 cents to another son so now what is the time	Choose the most appropriate option: A) Quarter to 1 B) Quarter to 2 C) Quarter to 3 D) 2 E) 1

Solution: 10+15= 
10+15 = 25
25 cents .. one quarter given to two sons.   Quarter to 2   ANSWER:Quarter to 2
Answer: B
P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is Choose the correct answer
A) Rs. 40000
B) Rs. 50000
C) Rs. 60000
D) Rs. 70000
E) None

Solution: Solution: Let the amount invested by Q = q.   40000 : q = 2 : 3.   => 40000/q = 2/3.   => q = 40000 * (3/2) = Rs. 60000.   Answer: Option Rs. 60000
Answer: C
The decimal d is formed by writing in succession all the positive integers in descending order after the decimal point; that is d = 0.15141312111098765
What is the 19th and 20th digits of d to the right of decimal point?  Options.
A) 32	B) 43	C) 54	D) 12	E) 21

Solution: The descending order of numbers begins with 15.   0.15141312111098765   So, 15, 14, 13, 12, 11, 10, ...,(first 12 digits are 2 digit numbers).   Then, 9, 8, 7, 6, 5, ...,(next 5 digits are single digit numbers).   It follows that 4, 3, and 2 are the next digits, thus 3 and 2 are the 19th and 20th digits, respectively.   32nswer: 32
Answer: A
Find the simple interest on Rs. 69,600 at 16 2/3% per annum for 9 months.
Pick one: A) s.8500 B) s.8700 C) s.7500 D) s.7000 E) s.6500

Solution: P = Rs.69600,R = 50/3% p.a and T = 9/12 years = 3/4years.   S.I. = (P*R*T)/100 = Rs.(69,600*(50/3)*(3/4)*(1/100))   = Rs.8700   Answer is s.8700.
Answer: B
A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.  Answers
A) 252 B) 432 C) 462 D) 504 E) None

Solution: Solution:   In order to reach (5,6) covering the shortest distance at the same time the man has to make 5 horizontal and 6 vertical steps.   The number of ways in which these steps can be taken is given by,   [11! /(5! *6!)] = 462.   Answer: Option 462
Answer: C
Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 30 grades are D's. What is the number of students in the course?	Answers
A) 80  B) 110  C) 160  D) 600  E) 400

Solution: We start by creating a variable for the total number of students in the math course. We can say:   T = Total number of students in the math course   Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 30 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:   #A’s + #B’s + #C’s + #D’s = Total number of students in the class   1/5(T) + ¼(T) + ½(T) + 30 = T   We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:   4T + 5T + 10T + 600 = 20T   19T + 600 = 20T   600 = T   There are a total of 600 students in the math class.   Answer is 600.
Answer: D
How many liters of water must be evaporated from 50 liters of a 2-percent sugar solution to get a 10-percent solution?	Choose one
A) 25 B) 30 C) 35 D) 40 E) 45

Solution: 2% of a 50 liter solution is 1L which is 10% of the solution at the end.   The solution at the end must be 1 L.   We need to evaporate 40 liters.   The answer is 40.
Answer: D
The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it? Choose the correct choice:
A) 11%
B) 82%
C) 14%
D) 12%
E) 17%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   80 * 110= 
80 * 110 = 8_800
8800   10000------- 1200   100 ------- ?= 12%   Answer:12%
Answer: D
If the tens digit of positive integers j, y are 6, how many values of the tens digit of 2(j+y) can be there? Choose the correct choice from the following answers:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: If the tens digit of positive integers j, y are 6, how many values of the tens digit of 2(j+y) can be there?   A. 2   B. 3   C. 4   D. 5   E. 6   -> If j=y=60, 2(j+y)=240 is derived. If j=y=69, 2(j+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is 4.
Answer: C
The length of the bridge, which a train 120 meters long and travelling at 45 km/hr can cross in 30 seconds, is:	Options:
A) 230	B) 244	C) 245	D) 255	E) 236

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (120 + X)/30 = 25/2 ==> 2(120 + X) = 750 ==> X = 255 m.   Answer: Option 255
Answer: D
A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:  Options:  A) 5%  B) 8%  C) 10%  D) 12%  E) 6%

Solution: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36)   = Rs. (520 + 1080)   = Rs. 1600.   S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.   Gain =(80/1600x 100)% = 5%.   5%nswer is 5%.
Answer: A
How many plants will be there in a circular bed whose outer edge measure 31 cms, allowing 4 cm2 for each plant ?
Choose the correct choice from the following:
A) 19
B) 750
C) 24
D) 120
E) None of these

Solution: Circumference of circular bed = 31 cm   19rea of circular bed = (31)2â„4Ï€   Space for each plant = 4 cm2   âˆ´ Required number of plants   = (31)2â„4Ï€ Ã· 4 = 19.11 = 19(approx)   19nswer 19
Answer: A
If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?  Select the correct option:
A) 100
B) 110
C) 121
D) 132
E) 143

Solution: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)   Therefore, the product should have factors with a difference of 2.   143 = 11*13, so this is a possible value for the original expression.   The answer is 143.
Answer: E
If B and C are digits and 8BC is a 3-digit number that is divisible by 5, which of the following is a possible product of B and C?
Pick one:  A) 1  B) 2  C) 5  D) 7  E) 14

Solution: Try with the options -   A. If BC = 1 , both B and C must be 1   B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2= 
8 + 1 + 2 = 11
11 which is not divisible by 3   C. If BC= 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5= 
8 + 1 + 5 = 14
14 which is not divisible by 3   D. If BC= 6 , then we can have the following possibilities   i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3= 
8 + 2 + 3 = 13
13 which is not divisible by 3   ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6= 
8 + 1 + 6 = 15
15 which is divisible by 3   E. If BC= 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7= 
8 + 2 + 7 = 17
17 which is not divisible by 5   Thus answer is (7)
Answer: D
A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars?
Choose the correct answer
A) 500 000	B) 1 000 000	C) 2 000 000	D) 5 000 000	E) 250 000

Solution: The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is.   5+3+2= 
5+3+2 = 10
10   10/2= X/100 000   5*100 000 = X   500 000 = X   500 000nswer: 500 000)
Answer: A
A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
Choose the correct choice from the following choices.
A) 3 hrs 48 min B) 3 hrs 45 min C) 3 hrs 75 min D) 6 hrs 45 min E) 3 hrs 55 min

Solution: Time taken by one tap to fill the tank = 3 hrs.   Part filled by the taps in 1 hour = 4 * 1/6 = 2/3   Remaining part = 1 - 1/2 = 1/2   2/3 : 1/2 :: 1 : x   x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min   So, total time taken = 3 hrs 45 min.   Answer: 3 hrs 45 min
Answer: B
a contract was signed to complete a job in 30 days. after how many days can 5 men leave then so that the job can be completed in 35 days  Select the correct option:
A) 30 days.  B) 35 days.  C) 45 days.  D) 55 days.  E) 65 days.

Solution: If no of men used initially is x, then after (35-x) days 5 men can leave so that the job can be completed in 35 days.   ANSWER:35 days.
Answer: B
In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:  Select
A) 86 B) 88 C) 92 D) 94 E) 96

Solution: Divisor = (6 * 3) + 2= 
(6 * 3) + 2 = 20
20   5 * Quotient= 20   Quotient = 4.   Dividend = (Divisor * Quotient) + Remainder   Dividend = (20 * 4) + 6= 
(20 * 4) + 6 = 86
86.   86
Answer: A
In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination? Pick one.
A) 28000	B) 30000	C) 32000	D) 33000	E) 35000

Solution: 85% of the eligible candidate hence remaining 15% eligible candidate   = 4275   eligible candidates = 4275*100/15= 
4275*100/15 = 28_500
28500   5% of the applicants were ineligible   95% of applicants= 28500   no of applicants = 28500*100/95= 
28500*100/95 = 30_000
30000   ANSWER 30000
Answer: B
A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container? Choose the correct option.
A) 26 litres B) 29.16 litres C) 28 litres D) 28.2 litres E) 30 litres

Solution: Explanation:   Suppose a container contains xx units of a liquid from which yy units are taken out and replaced by water. After nn operations, quantity of pure liquid =x(1âˆ’yx)n units   milk contained by the container now   =40(1âˆ’440)3=40(1âˆ’110)3=40Ã—9/10Ã—9/10Ã—9/10   =4Ã—9Ã—9Ã—9 / 100   =29.16   ANSWER IS 29.16 litres
Answer: B
How many numbers from 2 to 7 are exactly divisible by 2? Select the correct option:
A) 2
B) 3
C) 5
D) 7
E) 8

Solution: 2/2= 
2/2 = 1
1 and 7/2= 3   3 - 1= 
3 - 1 = 2
2   2 + 1= 
2 + 1 = 3
3 Numbers.   3)
Answer: B
A software has coding line 5% more than B, B software has coding line 4/12 more than C. C software has 90 lines of coding. find A lines.	Choose the correct answer.
A) 106	B) 107	C) 108	D) 126	E) 110

Solution: C s/w has 90 line of code   B s/w has = 90+90*4/12= 
90+90*4/12 = 120
120 line of code   A s/w 5% more B' code 120+6= 
120+6 = 126
126   ANSWER:126
Answer: D
If a 3 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?	Options:
A) 40%
B) 100%
C) 150%
D) 200%
E) 300%

Solution: The area A of the large cube is 3*3*6= 
3*3*6 = 54
54 square cm.   The area of the 27 small cubes is 27*6= 54*3 = 3A, an increase of 200%.   The answer is 200%.
Answer: D
Cereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?	Choices:
A) 2:5  B) 1:3  C) 2:7  D) 3:4  E) 1:5

Solution: 2% is 2%-points below 4% and 11% is 7%-points above 4%.   The ratio of A:B should be 2:7.   The answer is 2:7.
Answer: C
In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a five. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? Select the correct option.
A) 1/48	B) 5/16	C) 11/12	D) 11/16	E) 22/32

Solution: First lets get the overview   Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2)   Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6)   Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4)   So now as above we have three events A,BC.   1st method(This is lengthy method)   Possible cases in which it's a win( the highlighted green event is a win and red is loose.   1.ABC= 1/2*5/6*3/4   OR   2.ABC= 1/2*1/6*3/4   OR   3.ABC= 1/2*5/6*1/4   OR   4.ABC= 1/2*1/6*3/4   OR   5.ABC= 1/2*5/6*1/4   OR   6.ABC= 1/2*5/6*1/4   OR   7.ABC= 1/2*1/6*1/4   As we now OR means add   Adding up all of them we'll get the probability of winning ie 22/32   Answer : 22/32
Answer: E
The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 36 years, then find the age of the person sitting in the middle of the row?
Answers
A) 9 years B) 29 years C) 18 years D) 13 years E) 17 years

Solution: Total age seven persons = (28 * 7)years   Total age of the first three persons and the last three persons are (25 * 3) years and (36 * 3) years respectively.   Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 36 * 3 = 196 - 75 - 108= 
196 - 75 - 108 = 13
13 years.   ANSWER:13 years
Answer: D
On dividing 13787 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor? Answers
A) 743
B) 155
C) 852
D) 741
E) 785

Solution: Divisor *quotient+remainder=dividend   divisor=(dividend)-(remainder)/quotient   (13787-14)/89=155   Answer(155)
Answer: B
There are some balloons in party, 1/3rd blasted by kids . Then 2/5th of the remaining by men , then 2/3rd of the remaining by women . At last 20 were remaining . How many balloons were in total ?
Pick:	A) 150	B) 27	C) 28	D) 26	E) 91

Solution: Sol:   45   If x persons were there in total , then   x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 20   x×2/3 × 3/5 × 1/3 = 20   x = 150   150nswer:150
Answer: A
Find the compound interest on Rs. 16,000 at 20% per annum for 9 months, compounded quarterly	Choose the correct choice from the following answers: A) 3378 B) 2522 C) 2778 D) 2567 E) 1781

Solution: Explanation:   Principal = Rs. 16000; Time = 9 months =3 quarters;   Rate = 20% per annum = 5% per quarter.   Amount = Rs. [16000 x (1+(5/100))3] = Rs. 18522.   CJ. = Rs. (18522 - 16000) = Rs. 2522   Answer: 2522) 2522
Answer: B
On a map, 7 centimeters represents 35 kilometers. Two cities 245 kilometers apart would be separated on the map by how many centimeters?  Choose the correct choice:
A) 15
B) 37
C) 49
D) 110
E) 180

Solution: 1 centimeter represents 5 kilometers ( 35/7 )   X=245/5= 
245/5 = 49
49   Answer: 49
Answer: C
There are 60 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 14 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?
Pick one: A) 20 B) 37 C) 42 D) 53 E) 64

Solution: x + (x - 14) = 60 --> x = 37.   Answer: 37.
Answer: B
x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 5 will be equal to:	Choose the correct choice from the following choices
A) 3	B) 6	C) 1/9	D) 1/3	E) 9/25

Solution: Explanation :   Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.   .'. x = 9/y^2   => x =9 /5^2 = 9/25   Answer : 9/25
Answer: E
If k is a positive integer, which of the following must be divisible by 25? Choose the correct choice from the following options
A) (k – 4)(k)(k + 3)(k + 7)
B) (k – 4)(k – 2)(k + 3)(k + 5)
C) (k – 2)(k + 3)(k + 5)(k + 6)
D) (k + 1)(k + 3)(k + 5)(k + 7)
E) (k – 3)(k + 1)(k + 4)(k + 6)

Solution: 24=8*3.   Note that the product of two consecutive even integers is always divisible by 8 (since one of them is divisible by 4 and another by 2). Only option B offers two consecutive even numbers for any integer value of k: k-4 and k-2, if k=even or k+3 and k+5 if k=odd.   Also from the following 3 consecutive integers:(k-4), (k-3),(k-2)one must be divisible by 3, if it's not k-4 or k-2 then it must be k-3 (if it's k-4 or k-2 option B is divisible by 3 right away). But if it's k-3 then (k-3)+6=k+3must also be divisible by 3.   So, option B: (k – 4)(k – 2)(k + 3)(k + 5) is divisible by 8 and 3 in any case.   Answer: (k – 2)(k + 3)(k + 5)(k + 6).
Answer: C
If PINTU is coded as 79523 in a certain code language, how would you code MUMBO in the same language?  Pick:
A) 43426
B) 14236
C) 13436
D) 14263
E) 15263

Solution: 1 2 3 4 5 6 7 8 9   a b c d e f g h i   j k l m n o p q r   s t u v w x y z   sooo...MUMBO is 43426...   43426NSWER:43426
Answer: A
Amy has two decks of 52 cards each: Deck 1 and Deck 2. She takes 7 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack?
Choose the correct choice from the following.
A) 1/6	B) 1/8	C) 1/9	D) 1/10	E) 1/12

Solution: Your solution is correct answer should be 1/8.   1/8
Answer: B
A, B and C can do a work in 5 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work? Choose the correct choice.
A) 2 22/49  B) 2 2/49  C) 2 2/0  D) 2 2/2  E) 2 2/19

Solution: Work done by all three of them in one day = 1/5 + 1/8 + 1/12 = 49/120.   The number of days required = 120/49 = 2 22/49 days.   2 22/49nswer:2 22/49
Answer: A
Exactly 36% of the numbers in set W are even multiples of 3. If 40% of the even integers in set W are not multiples of 3, what percent of the numbers in set W are not even integers?	Pick one
A) 76%  B) 60%  C) 50%  D) 40%  E) 24%

Solution: Everything is correct except the red part with a typo: it should be N=0.6W --> even numbers are 60% of W --> 40% of W are not even integers.   Answer: 40%.
Answer: D