MU-NLPC/Calc-aqua_rat huggingface dataset:
A sum of Rs. 125000 amounts to Rs. 16000 in 4 years at the rate of simple interest. What is the rate of interest?
Choose the correct option: A) 3% B) 4% C) 5% D) 6% E) 7%

Solution: S.I. = (16000 - 12500) = Rs. 3500\   Rate = (100 * 3500) / (12500 * 4)= 
(100 * 3500) / (12500 * 4) = 7
7%   ANSW7%R:7%
Answer: E
A car covers a distance of 540 km in10 hrs. What is its speed in mps.	Choose the correct choice:
A) 40 m/s	B) 25 m/s	C) 20 m/s	D) 15 m/s	E) 16 m/s

Solution: Explanation:   Distance = Speed x Time   Speed = (540/10)= 
(540/10) = 54
54 kmph   Spees in mps= 54 x 5/18 = 3 x 5 = 15 mps.   Answer: Option 15 m/s
Answer: D
How many such three letter passwords can exist? Choose one:
A) 216
B) 26C6 *3
C) (26C6)^3
D) ((26C6)^3) *63
E) 215

Solution: 1st ring: 6 out of 26 alphabets can be selected in 26C6 ways.   And is for 2nd and 3rd ring.   Also, these 3 set of 6 letters can be arranged amongst themselves in 63 ways.   Hence, total number of 3 letter passwords = 26C6 * 26C6 *26C6 *63 ways.   ANSWER:((26C6)^3) *63
Answer: D
The average (arithmetic mean)E of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
Choose one:
A) I only B) II only C) III only D) II and III only E) None of the above

Solution: Given :   p + q = EVEN (odd + odd =even)   p + q + s + t = EVEN (even + even = even) nothing more....   (p + q + s + t) / 4 = x   I.   x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.   II.   Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.   III.   As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.   Answer None of the above, None.
Answer: E
What amount does Kiran get if he invests Rs. 18000 at 12% p.a. simple interest for four years?
Pick:
A) 29893 B) 26640 C) 29989 D) 28800 E) 29883

Solution: Simple interest = (18000 * 4 * 12)/100 = Rs. 8640   Amount = P + I = 18000 + 8640 = Rs. 26640   Answer: 26640
Answer: B
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Choose the correct choice from the following choices:
A) 80/6 sec	B) 80/7 sec	C) 88/7 sec	D) 80/9 sec	E) 82/7 sec

Solution: Relative speed = (54 + 72)* 5/18 = 7 * 5= 
7 * 5 = 35
35 mps.   The time required= d/s = (100 + 100 + 200)/35   = 400/35   =80/7 sec.   Answer:80/7 sec
Answer: B
A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 4120 a year. What is his average monthly income?
Choose one.
A) 2000
B) 2010
C) 2100
D) 2200
E) 2300

Solution: Total expenditure for the first 3 months = 3 × 1600 = 4800   Total expenditure for 4 months = 4 × 1550 = 6200   Total expenditure for 5 months = 5 × 1800 = 9000   Total expenditure and saving (which is income for one year)   = 4800 + 6200 + 9000 + 4120 = Rs. 24120   So, Average monthly income = 24120/12 = Rs. 2010   2010
Answer: B
The Square of a Positive Number A is divided by 2 and then the Result is Multiplied by 4 if the result is equal to A * 8 then what is the value of A?
Choose the correct answer
A) 4	B) 9	C) 6	D) 3	E) 8

Solution: (4*4)/2*4= 2(4*4)   2(4*4)=84   24=8   So the Correct 4nswer is 4
Answer: A
If w,x,y,z are consecutive positive integers ; then which of the following is always odd?
[1] w*x+(y+2)^2*z
[2] w^x + z^y
[3] 2w^3 Choose the correct choice from the following answers:
A) 2
B) 2
C) 3
D) 1 and 2
E) 2 and 3

Solution: Plug in some numbers   w = 1   x = 2   y = 3   z = 4   Check the options -   [1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4= 
2 + 25*4 = 102
102{ Not an odd Number }   [2] w^x + z^y= 1^2 + 4^3 => 1 + 64= 
1 + 64 = 65
65{ Odd number }   3 2w^3= 2*1^3 = even   2   2
Answer: A
A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 27 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?  Choose the most appropriate option.
A) 14 B) 45 C) 54 D) 65 E) 52

Solution: Just check the answers and reverse the numbers until you get 27.   52 - 25= 
52 - 25 = 27
27   Answer 52
Answer: E
A and B can do a piece of work in 3 days. With the help of C they finish the work in 2 days. C alone can do that piece of work in?	Choose the correct choice from the following answers.
A) 6 DAYS	B) 5 DAYS	C) 4 DAYS	D) 3 DAYS	E) 2 DAYS

Solution: C = 1/2 – 1/3= 1/6 => 6 days   6 DAYSnswer:6 DAYS
Answer: A
Manoj borrowed Rs.3600 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
Choose the correct choice:  A) 22877  B) 5455  C) 2778  D) 6787  E) 1771

Solution: Let the sum lent by Manoj to Ramu be Rs.P.   Amount gained by Manoj = P. 3.9 /100 = 3600.3.6/100 = Rs.824.85   27P = 64800 = 82485   P = (82485 + 64800)/27 = 3055 + 2400 = Rs.5455   Answer: 5455
Answer: B
Four friends (A, B, C and D) started a business in partnership by investing capitals in the proportion 3 : 5 : 4 : 6. During the period of one-year, these capitals were utilized in the proportion of 6 : 4 : 5 : 3 respectively. If, at the end of the year, a profit of Rs. 15,550 was made, what will be the share of D?	Pick:
A) 3682.89	B) 3682.87	C) 3682.81	D) 3682.82	E) 6222.33

Solution: Explanation:   A = (Investment * capital utilized) = (3 * 6)= 
(3 * 6) = 18
18   B= (5 * 4)= 
(5 * 4) = 20
20   C= (4 * 5)= 
(4 * 5) = 20
20   D= (6 * 3)= 
(6 * 3) = 18
18   Thus, out of Rs. 76 (18 +20 + 20 + 18), D's share is Rs. 18. Hence, out of Rs. 15,500 the share of D would be given as (18/76) * 15550= Rs. 3682.89   3682.89NSWER: 3682.89
Answer: A
In each term of a sequence, 15 is added to get the next term. If the first term is 10, what is the eighty-first term?  Choose the correct choice from the following.
A) 1630
B) 1210
C) 1110
D) 1720
E) 1750

Solution: 1rst term + 80 terms = 10 + 15+15+15+15+15+15+15+...+15 (80 times)   10 + (15 x 80) = 10 + 1200= 
10 + 1200 = 1_210
1210   Answer 1210
Answer: B
Set #1 = {A, B, C, D, 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?
Choose the most appropriate option:
A) 1/6  B) 1/3  C) 1/2  D) 2/3  E) 5/6

Solution: So Not a vowel in Set-1 : 3/5   And not a vowel in Ser-2:5/6   Now,   3/5∗5/6=12   This is for not a vowel.   Then for at least one vowel will be = 1−1/2=1/2   Answer will be 1/2.
Answer: C
find out the wrong number in the given sequence of numbers
15,16,34,105,424,2124,12756	Choose the correct choice from the following choices:
A) 105
B) 424
C) 2124
D) 15
E) 34

Solution: 15*1+1= 
15*1+1 = 16
16   16*2+2= 
16*2+2 = 34
34   34*3+3= 
34*3+3 = 105
105   105*4+4= 
105*4+4 = 424
424   424*5+5= 
424*5+5 = 2_125
2125   2125*6+6= 
2125*6+6 = 12_756
12756   wrong number is 2124   ANSWER:2124
Answer: C
Lloyd normally works 7.5 hours per day and earns $4.00 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?  Select the correct option: A) $33.75 B) $48.00 C) $51.75 D) $54.00 E) $70.00

Solution: Daily working hour*Regular Rate + Overtime*Increased Rate     7.5*4.0+ 3*4.0*1.5= 
  7.5*4.0+ 3*4.0*1.5 = 48
48   Answer $48.00
Answer: B
If x is an integer, and 225 < x^2 <= 361, which of the following is the sum of all possible values of x?	Choose the correct option:
A) None of the above  B) 124  C) 116  D) 105  E) 135

Solution: The range of x is from 16 .. to 19 and -16 to -19 so the sum is 0 hence ans None of the above, I guess, unless I am missing something!
Answer: A
Which of the following is closer to √0.1+√0.05?	Choose the correct choice.
A) 0.5  B) 0.7  C) 0.9  D) 1.1  E) 1.2

Solution: √0.1+√0.05=approximately √0.09+√0.04=0.3+0.2=0.5. Hence, the correct answer is 0.5.
Answer: A
If A is 25% greater than B then how much percentage is B smaller than A?
Choose the correct choice from the following answers.
A) 10% B) 20% C) 30% D) 40% E) 45%

Solution: A = 125   20% = 100   A-20%/A × 100 = 25/125 × 100 = 20 % smaller smaller than A   20%)
Answer: B
A train 120 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:  Choices.
A) 22	B) 48.2	C) 99	D) 288	E) 12

Solution: Speed of the train relative to man = (120/10) m/sec = (12) m/sec. [(12) * (18/5)] km/hr = 43.2 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 43.2 ==> x = 48.2 km/hr.Answer: 48.2
Answer: B
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?  Choices
A) 5 kmph  B) 10 kmph  C) 15 kmph  D) 20 kmph  E) 12 kmph

Solution: Explanation:   M = 15   S = 5   20 kmphS = 15 + 5= 
15 + 5 = 20
20kmph   Answer: 20 kmph
Answer: D
5356 x 51 = ?
Choose the correct option: A) 273156 B) 273243 C) 273247 D) 273250 E) 273258

Solution: 5356 x 51	= 5356 x (50 + 1)   = 5356 x 50 + 5356 x 1   = 267800 + 5356= 
267800 + 5356 = 273_156
273156.   273156
Answer: A
If the cost price of 140 pencils is equal to the selling price of 100 pencils, the gain percent is Choices: A) 36 B) 37 C) 38 D) 39 E) 40

Solution: Let C.P. of each pencil be Re. 1.   Then, C.P. of 100 pencils = Rs. 100; S.P. of 100 pencils = Rs. 140.   Gain % = 40/100 * 100= 
40/100 * 100 = 40
40%   Answer:40
Answer: E
A cistern is normally filled in 6 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?	Choose the correct option.
A) 24 hours B) 20 hours C) 30 hours D) 40 hours E) 50 hours

Solution: If leakage/hour=1/x, then 1/6 -1/x= 1/8, solving 1/x=1/24   So in 24 hours full cistern will be empty.   24 hoursNSWER:24 hours
Answer: A
The pages of a report are numbered consecutively from 1 to 11. If the sum of the page numbers up to and including page number x of the report is equal to six more than the sum of the page numbers following page number x, then x =  Select: A) 5 B) 6 C) 7 D) 8 E) 4

Solution: sum of the first few numbers =1+2+3+4+5+6+7+8= 
1+2+3+4+5+6+7+8 = 36
36   sum of the last few= 9 +10+11= 
9 +10+11 = 30
30 page no.8 answer .8
Answer: D
What is the average (arithmetic mean) of the numbers 100, 150, 200, 200, 250, and 300?  Options:
A) 100 B) 150 C) 140 D) 200 E) 250

Solution: {100, 150, 200, 200, 250, 300}={200-100,200-50, 200, 200,200+50,200+100} --> the average = 200.   Answer: 200.
Answer: D
Ajay can walk 3km in 1 hour. In how many hours he can walk 50km?
Options.
A) 5hrs B) 16.6 hrs C) 15.6 hrs D) 20.4 hrs E) 30hrs

Solution: 1 hour he walk 3km   he walk 50km in = 50/3 * 1 = 16.6hours   Answer is 16.6 hrs
Answer: B
an unbaised coin is tossed until it shows up the same face in 2 consicative throws wat is the probability that the no of tosses is not more than 4.
Pick.
A) 3/4	B) 1/4	C) 7/8	D) 1/8	E) 6/8

Solution: using 0 and 1 for head and tail respectively and considering binary system , we find that   Out of 16 possibilities, 14 are desired options.   Then probability = 14/16=7/8   ANSWER:7/8
Answer: C
A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled or emptied completely as the case may be ?	Choose the correct choice from the following options.
A) Emptied; 16 min
B) Filled; 8 min
C) Emptied; 8 min
D) Filled; 12 min
E) None of these

Solution: If both the pumps are opened together, then the tank will be emptied because the working efficiency of pump empting is more than that of the pump filling it. Thus in 1 min net proportion of the volume of tank filled   = (1⁄8 - 1⁄16) = 1⁄16   or the tank will be emptied in 16 min   ⇒ 1⁄2 tank will be emptied in 8 min.   Answer Emptied; 8 min
Answer: C
A, B and C enter into a partnership. They invest Rs. 60,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
Choose the correct choice from the following.
A) 9 : 3 : 4	B) 9 : 2 : 4	C) 9: 2 : 1	D) 9: 8: 14	E) none

Solution: Sol.   A : B : C = (60000 * 36) : (80000 * 12 + 40000 * 24)   : (120000 * 24 + 40000 * 12) =216 : 192 : 336 = 9: 8: 14   Answer 9: 8: 14
Answer: D
A wheel of a car of radius 21 cms is rotating at 900 RPM. What is the speed of the car in km/hr?  Choose the correct choice: A) 71.28 km/hr B) 47.52 km/hr C) 7.92 km/hr D) 39.6 km/hr E) 3.96 km/hr

Solution: Explanatory Answer   The radius of the wheel measures 21 cm.   In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.   ∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.   In a minute, the distance covered by the wheel = circumference of the wheel * rpm   ∴ this wheel will cover a distance of 132 * 900= 
132 * 900 = 118_800
118800 cm in a minute.   In an hour, the wheel will cover a distance of 118800 * 60= 
118800 * 60 = 7_128_000
7128000 cm.   Therefore, the speed of the car= 7128000 cm/hr = 71.28 km/hr   Choice 71.28 km/hr is the correct answer.
Answer: A
If n is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?  Choose the correct choice from the following answers
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.   Hence, n=2mn=2m, where mm is a positive integer. Then,   (n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)   =4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8   Hence, the answer is (8).
Answer: D
A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day? Choose one:
A) 22
B) 77
C) 12
D) 41
E) 76

Solution: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48   Remaining work = (1 - 7/48) = 41/48   Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48   Number of boys required = 41/48 * 41 = 41.   Answer: 41
Answer: D
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 160 meter length? Select the correct option:
A) 11 seconds	B) 41.6 seconds	C) 40 seconds	D) 88 seconds	E) 19 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+160= 
360+160 = 520
520 meter   Time= Distance/speed   = 520 * (2/25)= 
520 * (2/25) = 208/5 = around 41.6
41.6 seconds   Answer: 41.6 seconds
Answer: B
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?  Choose the correct choice from the following answers:
A) Rs.10595 B) Rs.10529 C) Rs.10598 D) Rs.10508 E) Rs.10500

Solution: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4   Simran's share = 24500 * 3/7   = Rs.10500   Answer:Rs.10500
Answer: E
A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? Choose the correct choice from the following choices:
A) 4 min	B) 8 min	C) 9 min	D) 6 min	E) 1 min

Solution: S = 600/40= 
600/40 = 15
15 mps   S= 3600/15= 
3600/15 = 240
240 sec= 4 min   4 minnswer:4 min
Answer: A
Simplify: 256 x 256 - 144 x 144  Answers:	A) 761200	B) 44800	C) 761800	D) 761500	E) None of them

Solution: (256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800   Answer is 44800
Answer: B
If the integer c is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when c is rounded to the nearest ten. which of the following is a possible value of c?	Choose the correct choice from the following answers.
A) 64  B) 67  C) 99  D) 133  E) 147

Solution: We have to check options 1 by 1.   64 rounded to nearest hundred = 100   64 rounded to nearest ten = 60   now difference = 40   the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.   therefore 40/60)*100 = 66 2/3 ==>this is the answer.   99 rounded to nearest ten = 100   133 rounded to nearest ten = 130   133 rounded to nearest hundred c= 100=64
Answer: A
20-3*4^2+20 = ?
Options
A) 287 B) -13 C) -73 D) 13 E) None

Solution: 20-3*4^2+20   = 20-3*16+20   =20-48+20=-8..   None
Answer: E
At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 50¢?	Choose the correct choice
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: If the average price is 56, then Mary has 8 oranges and 2 apples (a ratio of 4:1).   For the average price to be 50, the ratio should be 1:1.   Mary must put back 6 oranges.   The answer is 6.
Answer: E
At a meeting of the 6 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?	Select the correct option:  A) 56  B) 64  C) 72  D) 80  E) 88

Solution: 6 people can be arranged around a table in 5! ways.   Consider the two chiefs who will not sit together as a single unit.   The number of ways to arrange 5 units around a table is 4!   We need to multiply this by 2 as the two people can be switched in each arrangement.   The total number of ways to arrange the chiefs is 5! - 2*4! = 3*4! = 72   The answer is 72.
Answer: C
If a - b = 3 and
a2+b2=29
, then find the value of ab  Choose the correct choice from the following answers
A) 7
B) 8.5
C) 10
D) 12
E) 14

Solution: Explanation:   2ab=(a2+b2)−(a−b)2   => 2ab = 29 - 9= 
29 - 9 = 20
20=> ab = 10   Option 10
Answer: C
A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?	Choose the correct choice from the following answers
A) 11:10:15  B) 20:17:23  C) 19:19:18  D) 5:4:9  E) 1:3:6

Solution: Explanation:   A:B:C =(25 lakhsÃ—Ã—1)+(35 lakhsÃ—Ã—2) :(35 lakhsÃ—Ã—2+25 lakhsÃ—Ã—1) :(30 lakhsÃ—Ã—3)   = 95 lakhs : 95 lakhs : 90 lakhs =19:19:18.   Answer IS 19:19:18
Answer: C
The average age of 12 men in a group is increased by 2 years when two men whose ages are 20 years and 22 years, are replaced by new members. What is the average age of the new men included?
Choose the correct choice:
A) 22	B) 767	C) 77	D) 33	E) 99

Solution: Explanation:   Total age of two men replaced = 20 + 22= 
20 + 22 = 42
42 years   Total increase in age on replacement= 2 × 12 = 24 years   Total age two new persons included = 42 + 24= 
42 + 24 = 66
66 years   Therefore, Average age of new persons= 66/2= 
66/2 = 33
33 years   Answer:33
Answer: D
Three years ago the average age of a class of six members was 24 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?  Select.
A) A)1 B) B)2 C) C)3 D) D)4 E) E)6

Solution: 6 * 27= 
6 * 27 = 162
162   7 * 24= 
7 * 24 = 168
168   `6   6
Answer: E
Last week David spent 20 percent of his wages on recreation. This week, his wages are 30 percent less than last weekʼs wages and he spent 20 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week Choose the correct choice from the following:
A) 75%	B) 72%	C) 70%	D) 73%	E) 74%

Solution: Say David's wages last week were $100, so he spent  0.20*100= 
 0.20*100 = 20
$20 on recreation;   This week's wages is 0.70*100= 
0.70*100 = 70
$70, so he spends   0.2*70= 
  0.2*70 = 14
$14 on recreation;   14/20= 
14/20 = 7/10 = around 0.7
0.70, hence the amount he spends on recreation this week is 70% of the amount he spent on recreation last week:   20*0.7= 
  20*0.7 = 14
14   Answer: 70%
Answer: C
A can do a work in 12 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work? Choose the most appropriate option
A) 3  B) 5  C) 8  D) 2  E) 6

Solution: A rate = 1/12   B rate = 1/24   (A+B) rate = (1/12)+(1/24) = 1/8   A & B finish the work in 8 days   correct option is 8
Answer: C
If x and y are even integers, which of the following is an odd integer?	Choose the correct choice from the following answers
A) xy
B) y^2
C) x+y+3
D) x^2
E) None of these

Solution: even * even = even   even + odd = odd   Answer : x+y+3
Answer: C
A baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter, and then spilled 3/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with? Choose one.
A) 1/8 cup  B) 3/8 cup  C) 1/4 cup  D) 1/2 cup  E) 9/8 cup

Solution: 3/4 is the original water in cup .half in batter.So left is 3/8 out which 3/8 is spilled out.So again left with 0/8.   so 50% more than what he started was = 3/4+1/2*(3/4)=9/8   Amount of water needed to add = 9/8 - 0/8=9/8   ANSW9/8 cupR:9/8 cup
Answer: E
The measures of the 2 acute angles of a triangle are in the ratio of 2 : 7. What arethe measures of the 2 angles?	Choices: A) 20° B) 70° C) 110° D) 120° E) 140°

Solution: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence   2x + 7x = 90   9x = 90   x = 10   Measures of the two acute angles are   2x = 2 × 10 = 20°   7x = 7 × 10 = 70°   70°
Answer: B
If y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer, then y must be
Choices:
A) 2 B) 4 C) 6 D) 7 E) 14

Solution: i just tried plugging in the numbers and found out that   4*11025 = 44, 100, which is a square of 210   4
Answer: B
#p is defined as 2p+20 for any number p. What is p, if #(#(#p))=4?	Pick one
A) –108
B) –44
C) 10
D) -17
E) 18

Solution: #p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = 4 ---> 8p= -136 ---> p = -17, -17 is the correct answer.
Answer: D
If Tim had lunch at $60.50 and he gave 20% tip, how much did he spend? Choose the correct answer:
A) $30.60
B) $72.60
C) $70.60
D) $40.60
E) $50.60

Solution: The tip is 20% of what he paid for lunch. Hence   tip = 20% of 60.50 = (20/100)*60.50= 
(20/100)*60.50 = 12.1
$12.1   Total spent     60.50 + 12.1= 
  60.50 + 12.1 = 72.6
$72.6   correct answer $72.60
Answer: B
Solve the equation:
(2x - 1)2 – x(10x + 1) = x(1 – x)(1 + x) – (2 – x)3  Choose the correct answer:
A) 1 B) 1/2 C) 2 D) 2/1 E) None

Solution: Solution:   (2x - 1)2 – x(10x + 1) = x(1 – x)(1 + x) – (2 – x)3 <=>   4x2 - 4x + 1 -10x2 – x = x – x3 - 8 + 12x - 6x2 + x3 <=>   18x = 9 <=> x = 1/2   Answer 1/2
Answer: B