MU-NLPC/Calc-aqua_rat huggingface dataset:
Ten years ago, P was half of Q's age. If the ratio of their present ages is3:4, what will be the total of their present ages? Answers:
A) 45	B) 40	C) 35	D) 30	E) 25

Solution: Let present age of P and Q be   3x and   4x respectively.   Ten years ago, P was half of Q's age   ⇒(3x−10)=1(4x−10)/2   ⇒6x−20=4x−10   ⇒2x=10   ⇒x=5   Total of their present ages   3x+4x=7x3 +4= 
3 +4 = 7
7x=7*5= 
7*5 = 35
35   ANSWER:35
Answer: C
A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 60 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
Pick
A) 160  B) 240  C) 330  D) 440  E) 560

Solution: The number of jumbo tiles = x.   The number of regular tiles = 2x.   Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.   The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.   The area of regular tiles = 2x*a^2 = 60.   The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*60= 
4.5*60 = 270
270.   Total area= 60 + 270= 
60 + 270 = 330
330.   Answer: 330.
Answer: C
Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?  Choose the most appropriate option:
A) 32:21	B) 22:21	C) 21:32	D) 31:21	E) 32:28

Solution: Here capital is not the same.   Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.   Hence his term of ratio   =( 20000*6 + 15000*6)   Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.   Hence his term of ration   = (30000*4 : 50000*4)   Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4)   = (20*6 + 15*6) : (30*4 + 50*4)   = (20*3 + 15*3) : (30*2 : 50*2)   = 105:160   = 21:32   Answer is 21:32
Answer: C
N* is defined as 0.5(N+10) for any number N. What is N, if ((N*)*)*=15?	Choose one
A) 20  B) 30  C) 40  D) 50  E) 60

Solution: N*=0.5(N+10)   (N*)*=0.5(0.5N+5+10)= 0.25N+7.5   ((N*)*)*=0.5(0.25N+7.5+10)= 0.125N+8.75   we know that ((N*)*)*=15   0.125N+8.75=15   0.125N=6.25   N= 6250/125= 
6250/125 = 50
50   ANSWER:50
Answer: D
In an election between two candidates, 10% of votes are were declares invalid. First candidate got 1800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
Select.
A) 9000  B) 9900  C) 10000  D) 11000  E) 12000

Solution: 100 % - 10 % = 90 %   54%-36%=18%   18% ------> 1800 ( 18 × 100   54 -36= 
  54 -36 = 18
18%   18% ------> 1800 ( 18 × 100= 1800)   100% -------> 10000 votes (100 × 100 = 10000)   10000
Answer: C
A man drive his car to the office at 20miles/hr.
After reaching office, he realize that its a new year holiday so he went back home at a speed of 30miles/hr.
Discounting the time spent in the stoppage what was his average speed of his journey ?  Choose the correct choice from the following answers
A) 21	B) 20	C) 25	D) 24	E) 29

Solution: 24   24miles/hr (not 25miles/hr which might be guessed by many)   24 : distance traveled   T1 : time of going to office   T2 : time of returning back   Y : Average Speed   24 = 20 * T1   T1 = 24/20   24 = 30 * T2   T2 = 24/30   224 = Y(T2 + T1)   224 = Y(24/20 + 24/30)   224 = Y(324/60 + 224/60)   224 = Y(524/60)   Y = 12024/524   => Y = 24
Answer: D
Pat is now 22 years older than Dan. If in 6 years Pat will be twice as old as Dan, how old will Pat be in 15 years?	Options
A) 47	B) 49	C) 51	D) 53	E) 55

Solution: P=D+22 so D=P-22.   P+6=2(D+6).   P+6=2(P-22+6).   P+6=2P-32.   P=38.   In 15 years, Pat will be 53 years old.   The answer is 53.
Answer: D
The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?	Choose the correct choice:  A) 299  B) 278  C) 278  D) 480  E) 281

Solution: 262 – 102 = 242   d1 = 20 d2 = 48   1/2 * 20 * 48= 
1/2 * 20 * 48 = 480
480   Answer: 480
Answer: D
The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 8 times the probability that both events A and B occur. What is the probability that event A occurs? Choose the most appropriate option
A) 1/12	B) 1/8	C) 1/6	D) 1/3	E) 2/3

Solution: Let us say probability of A occurring is a.   Let us say probability of B occurring is b.   a = 2b   Probability (either A or B or both) = 8 times Probability (A and B)   a*(1-b) + b*(1-a) + ab = 8*ab   Substituting a=2b in the second equation:   2b*(1-b) + b*(1-2b) + 2b*b = 8*2b*b   3b-2b^2 = 16b^2   3b = 18b^2   b = 3/18 = 1/6   So, a = 2b = 1/3   ANSWER:1/3
Answer: D
Calculate the average of first 14 even numbers is?
Choose the correct choice from the following answers:
A) 11	B) 15	C) 16	D) 14	E) 12

Solution: Explanation:   Sum of 14 even numbers = 14 * 15= 
14 * 15 = 210
210   Average= 210/14= 
210/14 = 15
15   Answer: Option 15
Answer: B
A and B invests Rs.12000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.30000, find their shares? Choose the correct choice from the following answers: A) s.12000, Rs.15020 B) s.12000, Rs.15700 C) s.12000, Rs.15090 D) s.12000, Rs.15000 E) s.12000, Rs.18000

Solution: The ratio of their profits A:B   = 8:12 = 2:3   Share of A in the total profit   = 2/5 * 30000   = Rs.12000 Share of A in the total profit = 3/5 * 30000   = Rs.18000   Answer: s.12000, Rs.18000
Answer: E
If 10^(z-1)< 0.000125 <10^z, what is the value of an integer z?
Pick.
A) -4 B) -3 C) -2 D) 3 E) 4

Solution: -> Multiply 10^6- > (10^6){10^(z-1)}<125<(10^6)(10^z) -> 125 is bigger than 100   -> (10^6)(10^(z-1))=100 -> 10^(6+z-1)=10^2, z+5=2 -> z=-3   Thus, the answer is -3
Answer: B
If x and y are integer, which of the following must also be an integer?
I. xy
II. y
III. y/x Choose the correct choice from the following options:
A) I alone	B) II alone	C) III alone	D) I and III	E) None of the above

Solution: Let's take X = 4and Y = 3   Then X/Y = 4/3 Not an integer.   Y/X = 3/4 Not an integer.   Y alone is 3 which is an integer.   Hence II alone.
Answer: B
Without any stoppage, a person travels a certain distance at an average speed of 42 km/h, and with stoppages he covers the same distance at an average speed of 28 km/h. How many minutes per hour does he stop?  Choose the correct option:  A) 30 minutes  B) 28 minutes  C) 11 minutes  D) 17 minutes  E) 20 minutes

Solution: Let the total distance to be covered is 84 kms.   Time taken to cover the distance without stoppage = 84/42= 
84/42 = 2
2 hrs   Time taken to cover the distance with stoppage= 84/28= 
84/28 = 3
3 hrs.   Thus, he takes 60 minutes to cover the same distance with stoppage.   Therefore, in 1 hour he stops for 20 minutes.   Answer: 20 minutes
Answer: E
Present ages of souju and tharak are in the ratio of 6:4 respectively. Three years hence, the ratio of their ages will become 12:9 respectively. What is tharak's present age in years?
Choose the correct answer:
A) 2 years 7 months
B) 3 years 2 months
C) 3 years 5 months
D) 3 years 7 months
E) 4 years 7 months

Solution: Ratio of the present age of souju and tharak =6:4   Let present age of Souju =6x   Present age of Tharak =4x   After 3 years, ratio of their ages =12:9   ⇒(6x+3):(4x+3)=12:9   ⇒9(6x+3)=12(4x+3)   ⇒54x+27=44x+36   ⇒10x=36−27=9   =>x=9/10= 
9/10 = 9/10 = around 0.9
0.9   Tharak's present age=4x=4*0.9= 
4*0.9 = 3.6
3.6=3 years 7 months   ANSWER:3 years 7 months
Answer: D
What is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square?
Choices
A) 2	B) 3	C) 5	D) 7	E) 11

Solution: 1008 = 2^4 x 3^2 x 7.   Therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7.   Answer 7.
Answer: D
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 25 grades are D's. What is the number of students in the course? Select the correct option: A) 80 B) 110 C) 160 D) 500 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 25 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) + 25 = T   We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:   4T + 5T + 10T + 500 = 20T   19T + 500 = 20T   500 = T   There are a total of 500 students in the math class.   Answer is 500.
Answer: D
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is	Choose the correct answer:
A) 0.5909
B) 0.5904
C) 0.59076
D) 0.5907
E) 0.59012

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36) = 0.5904   Answer: 0.5904
Answer: B
There are 300 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
Select:
A) 650  B) 700  C) 750  D) 800  E) None of these

Solution: as per question stem 2/5M (Portion of Men employees who are managers) + 200 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+300= 2/5T, or 2/5(T-M)=300, from here we get that T-M=750, that would be total number of female employees and the answer (750)
Answer: C
A car is running at a speed of 90 kmph. What distance will it cover in 15 second?	Options:
A) 100 m
B) 255 m
C) 375 m
D) Cannot be determined
E) None of these

Solution: Explanation:   Given : Speed = 108 kmph = (90 x (5/18)) m/sec = 25 m/sec   Distance covered in 15 second = (25 x 15) m = 375 m.   ANSWER: 375 m
Answer: C
Two years ago, Claire put $2,000 into a savings account. At the end of the first year, her account had accrued $100 in interest bringing her total balance to $2,100. The next year, her account balance increased by 10%. At the end of the two years, by what percent has Claire's account balance increased from her initial deposit of $2,000 ? Choose one.
A) 10%	B) 12%	C) 15.5%	D) 17%	E) 20%

Solution: investment 2000 dollars   1 st year total gained = 100   total amount end of first year = 2100   second year account increased by 10 % = 2100*0.1= 
2100*0.1 = 210
210   therefore total amount by second year end= 2310   so total percentage increase in money = (2310-2000)*100/2000= 
(2310-2000)*100/2000 = 31/2 = around 15.5
15.5 %   15.5%orrect Answer 15.5%=15.5%
Answer: C
A train ride from Two P to Town Q costs $6.85 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.65. What is the cost of a bus ride from Town P to Town Q? Pick:	A) $1.40	B) $2.50	C) $4.10	D) $4.70	E) $8.20

Solution: Let x be the cost of a bus ride.   x + (x+685) = 965   2x = 280   x = $1.40   The answer is $1.40.
Answer: A
The sum of two numbers is 120. If the greater number is four times the less, what are the numbers? Answers
A) 80  B) 84  C) 85  D) 96  E) None

Solution: Let x = the less number   4x = the greater number   The sum of two numbers is 120   x+4x=120   5x=120   x=24   4x=96   Option 96
Answer: D
Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq meters.  Choose the correct option:
A) 56
B) 28
C) 99
D) 27
E) 19

Solution: Explanation:   clearly the cow will graze a circular field of area 9856 sq m and   radius equal to the length of the rope.   Let the length of the rope be r mts   {\color{Black} then,\Pi r^{2}=9856\Rightarrow r^{2}=\frac{9856\times 7}{22}=3136\Rightarrow r=56m}   56nswer: 56) 56m
Answer: A
Which of the following is a parallelogram?  Choose the correct choice from the following choices.
A) 120,50,120,50(angle in deg)
B) 120,30,130,20(angle in deg)
C) 90,90,90,90(angle in deg)
D) a & c
E) none

Solution: sum of adjacent angles is 180 degrees.   ANSWER:90,90,90,90(angle in deg)
Answer: C
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? Choose the correct choice from the following options
A) 5.78	B) 5.79	C) 5.76	D) 5.74	E) 5.721

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2 = 5.76.Answer: 5.76
Answer: C
What percent is 120 of 90? Choose the most appropriate option:
A) 133 1/3 % B) 134 1/3 % C) 135 1/3 % D) 140 1/3 % E) 143 1/3 %

Solution: 120/90 = 4/3   4/3 × 100 = 400/3 = 133 1/3 %   133 1/3 %
Answer: A
It takes Avery 2.5 hours to build a brick wall while Tom can do it in 5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own? Pick one: A) 15 minutes. B) 30 minutes. C) 1 hour and 30 minutes. D) 1 hour and 40 minutes E) 2 hours

Solution: Avery's efficiency is 100/2.5= 
100/2.5 = 40
40%   Tom's= 100/5= 
100/5 = 20
20%   they worked together for 1 hour and finished 60 % of the job   remaining= 40 %   Tom will complete 20% in 60 minutes , 40% in 120 minutes   Time taken by Tom to finish the remaining on his own = 120 minutes   ANSW2 hoursR:2 hours
Answer: E
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
Select:
A) 4000  B) 345  C) 5673  D) 6342  E) 4566

Solution: Area of the four walls = 2h(l + b)   Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.   Total cost = 906 * 7 = Rs. 6342   Answer: Option 6342
Answer: D
Calculate the distance covered by 420 revolutions of a wheel of radius 23.1 cm. Choose the most appropriate option:  A) 609.84 m  B) 409.84 m  C) 509.84 m  D) 109.84 m  E) 709.84 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 420 * 2 * 22/7 * 23.1= 
420 * 2 * 22/7 * 23.1 = 60_984
60984 cm= 609.84 m   609.84 mNSWER:609.84 m
Answer: A
Sawyer is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be peanut oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Sawyer accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be peanut oil? Options
A) 15/29 B) 5/8 C) 5/16 D) 1/2 E) 13/27

Solution: peanut oil = 5/8 = 15/24 --> 15 parts out of 24;   Vinegar = 1/4 = 6/24 --> 6 parts out of 24;   Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;   If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0= 
15+12+1+1+0 = 29
29 parts out of which 15 parts are peanut oil --> proportion= 15/29.   15/29nswer: 15/29.
Answer: A
A bag contains 50black pens and 60 white pens. One ball is drawn at random. What is the probability that the ball drawn is black?	Choose the correct option.
A) 2/3  B) 3/14  C) 1/7  D) 5/11  E) 6/13

Solution: total number of pens = 110   number of black pens = 50   drawing a black pens= 50/110 = 5/11   Answer is 5/11
Answer: D
The ratio of the area of a square to that of the square drawn on its diagonal is?  Choose the correct choice from the following answers.
A) 1:2	B) 2:4	C) 3:5	D) 4:6	E) 5:7

Solution: Explanation:   a^2:(a√2)^2   a^2 : 2a^2=1:2   1:2nswer : 1:2
Answer: A
A committee of three people is to be chosen from 3 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee? Choices:  A) 12  B) 24  C) 26  D) 30  E) 32

Solution: One of the approaches:   Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 3 to send only onerepresentativesto the committee: 3C2=3.   But each of these 3 couples can send two persons (husband or wife): 2*2=2^2=4.   Total # of ways: 3C2*2^2=12.   12nswer: 12.
Answer: A
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.  Choices.
A) 60/63	B) 125/126	C) 1/126	D) 8/178	E) 9/191

Solution: Explanation:   Required probability = 1 - 1/126 = 125/126   ANSWER 125/126
Answer: B
A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 30 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat? Choices.
A) 5/12
B) 2/5
C) 1/2
D) 3/4
E) 5/6

Solution: It is a circle inscribed in a square.   Square side=24---> square(table) area=24^2   Circle diameter=20---> Circle area=PiR^2=100Pi (where Pi=~3.14)   covered fraction=100*3.14/9*100=3.14/9 = 0.3489   5/6
Answer: E
If P(x) = ax^4+bx^3+cx^2+dx+e has roots at x = 1, 2, 3, 4 and P(0) = 48, what is P(5)? Choices:
A) 48
B) 24
C) 0
D) 50
E) 40

Solution: Roots are 1,2,3,4   So we can write this   equation As p(x)=   a(x-1)(x-2)(x-3)(x-4).....eq1   Put x=0here we p(0)=48=24a   TheN a=2   Now put a in eq1   And get the answer...   P(5)=a.4.3.2.1=48   48NSWER:48
Answer: A
How many keystrokes are needed to type numbers from 1 to 1000? Choose the correct choice from the following answers: A) 3001 B) 3001 C) 2704 D) 2890 E) None of these

Solution: Explanatory Answer   While typing numbers from 1 to 1000, there are 9 single digit numbers: from 1 to 9.   Each of these numbers requires one keystroke.   That is 9 key strokes.   There are 90 two-digit numbers: from 10 to 99.   Each of these numbers requires 2 keystrokes.   Therefore, 180 keystrokes to type the 2-digit numbers.   There are 900 three-digit numbers: from 100 to 999.   Each of these numbers requires 3 keystrokes.   Therefore, 2700 keystrokes to type the 3-digit numbers.   1000 is a four-digit number which requires 4 keystrokes.   Totally, therefore, one requires   9 + 180 + 2700 + 4= 
  9 + 180 + 2700 + 4 = 2_893
2893 keystrokes.   Choice 3001 is the correct answer.
Answer: B
Look at this series: V, VIII, XI, XIV, __, XX, ... What number should fill the blank? Choose the correct choice from the following answers
A) IX	B) XXIII	C) XV	D) XVII	E) None

Solution: Explanation: This is a simple addition series; each number is 3 more than the previous number.   Answer: Option XVII
Answer: D
If |x - 9| = 3x, then x=? Choices
A) 1.5  B) 3.1  C) 4.5  D) -2.25  E) -4.5

Solution: |x - 9| = 3x ...(given)   x^2 - 18x + 81 = 9x^2   8*x^2 + 18*x - 81 = 0 ....(by solving above eq. we get) , x = -4.5 or 2.25 ===> Ans - -4.5
Answer: E
If two positive numbers are in the ratio 1/8 : 1/7, then by what percent is the second number more than the first? Choose the correct choice:
A) 70% B) 14.28% C) 60% D) 50% E) 65%

Solution: Given ratio = 1/8 : 1/3 = 3 : 8   Let first number be 7x and the second number be 8x.   The second number is more than first number by 1x.   Required percentage = 1x/7x * 100 = 14.28%.   Answer:14.28%
Answer: B
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?	Choose the correct option:
A) Rs.5000
B) Rs.4672
C) Rs.8262
D) Rs.2618
E) Rs.5267

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 – 96 =Rs. 4   100 ------ 4   ? --------- 200 => 5000   Rs.5000nswer:a
Answer: A
How many different pairs of numbers (s, t) such that s = 3t can be obtained if s and t are selected from the set of number {3, 4, 5, 6, 7, 8, 9} Options.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Given s=3t   t can take 3   and so s = 9   1 such pairs can be formed.   answer 1
Answer: A
A warehouse is labeling computer inventory with 3-digit codes. Each code is to consist of four digits between the numbers 0 and 8. The manager is debating whether to allow any 3-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.
The manager wants to measure the magnitude of the number of 3-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
Choose the correct choice from the following answers:
A) 981
B) 1000
C) 1011
D) 1101
E) 200

Solution: The number of codes possible if leading zero is allowed = 10*10*10=10^3   The number of codes possible if leading zero is NOT allowed = 8*10*10=9*10^2   The difference = 10^3 - 8*10^2 = 10^2(10-8) = 2*10^2.   Answer: E.   Similar questions to practice:   Hope it helps.
Answer: E
find two integers, neither of which ends in a zero, and whose product is exactly 1,00,000  Choose the correct choice from the following choices.
A) 64 and 15,625 B) 32 and 3,125 C) 64 and 15,620 D) 64 and 15,635 E) 64 and 16,625

Solution: 1,00,000=10^5   =10x10x10x10x10   =(2x5)x(2x5)x(2x5)x(2x5)x(2x5)   =(2^5)x(5^5)   = 32x3125   so the numbers are 32 and 3,125   ANSWER:32 and 3,125
Answer: B
Calculate how many ways a woman who has 2 bags and 4 books can put the books in her bag?  Choose the correct choice from the following answers
A) 12 B) 15 C) 19 D) 17 E) 16

Solution: First paper can be put in 2 ways, similarly second, third and forth books also can be put in 2 ways.   So total number of ways = 2 x 2 x 2 x 2 = 16   16
Answer: E
How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers?  Choose the correct choice from the following answers
A) 1 B) 5 C) 7 D) 8 E) 9

Solution: slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6   y = mx + b => 12 2/3 = -22*5/6 + b => b = 31   y = -5x/6 + 31   Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point.   1
Answer: A
When 12 is divided by the positive integer k, the remainder is 7, for how many different values of k is this true?	Answers.
A) 2	B) 3	C) 4	D) 7	E) 8

Solution: When 20 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2.   It also means that 18 is completely divisible by k.   Factors of 18 are 1, 2, 3, 6, 9, 18   Out of these, k can be 3, 6, 9 and 18.   Answer (4)
Answer: C
On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 20 miles on Saturday and Sunday, how many miles did Bill run on Sunday?	Pick one.
A) 5 B) 6 C) 7 D) 8 E) 9

Solution: Let Bill run x on saturday, so he will run x+4 on sunday..   Julia will run 2*(x+4) on sunday..   totai= x+x+4+2x+8=20..   4x+12=20..   x=2..   ans =x+4=2+4= 
2+4 = 6
6   Answer 6
Answer: B
A worm is at the bottom of a forty foot hole. It can crawl upwards at the rate of four feet in one day, but at night, it slips back three feet. At this rate, how long will it take the worm to crawl out of the hole?  Choose the correct choice from the following answers:  A) 33  B) 87  C) 37  D) 28  E) 921

Solution: Explanation:   For each day worm climb only 4 - 3= 
4 - 3 = 1
1feet.   After 36 days worm reach the 36 foot.   Exactly the 37th day worm reach 40 foot and won't slips back.   Answer: 37
Answer: C