MU-NLPC/Calc-aqua_rat huggingface dataset:
Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced? Choose the correct choice from the following choices:
A) 1/30
B) 1/5
C) 2/3
D) 3/4
E) 4/5

Solution: Let total paint = 1   Let amount replaced = x   50 (1-x) + 25x = 30   x = 4/5   ANSW4/5R:4/5
Answer: E
There are 56 lights which are functional and each is controlled by a separate On/Off switch. Two children X and Y start playing with the switches. X starts by pressing every third switch till he reaches the end. Y, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?	Choose the correct choice from the following choices:
A) 18
B) 19
C) 17
D) 15
E) 16

Solution: Editing my solution:   Number of switches = 56   Number of switches turned on by X: 3, 6, ... 54 = 18   Number of switches turned on by Y: 5, 10, ....55 = 11   Few switches are turned on by X and later turned off by Y: LCM(3,5) = 15x = 15, 30,....90 = 6.   Subtract the above 6 switches from both X and Y as they are turned off.   Number of switches that are turned on = (18- 6) + (11 - 6)= 
(18- 6) + (11 - 6) = 17
17   Answer: 17
Answer: C
Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 2 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts? Choose one
A) 560 B) 589 C) 562 D) 563 E) 564

Solution: Total price of 8 t-shirts= 8*526= 
8*526 = 4_208
4208   Total price of 6 t-shirts=5*505=3030   Total price of 2 t-shirts=4208-3030= 
4208-3030 = 1_178
1178   Average price of 3 t-shirts=1178/2= 
1178/2 = 589
589   Correct option Answer:589
Answer: B
Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 15 phone numbers by using the readable digits followed by 15 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?	Choose the correct choice from the following: A) 1/9 B) 10/243 C) 1/18 D) 10/271 E) 1/1000000

Solution: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).   If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).   P = 15/(9*9*3+9*3) = 1/18.   Answer: 1/18.
Answer: C
If six boys sit in a row, then what is the probability that three particular boys are always together is?	Choose one:
A) 1/5 B) 1/4 C) 1/3 D) 1/7 E) 2/5

Solution: Six boys can be arranged in a row in 6! ways.   Treat the three boys to sit together as one unit then there 4 boys and they can be arranged in 4! ways.   Again 3 boys can be arranged among them selves in 3! ways.   Favorable outcomes = 3!4!   Required probability = 3!4!/6! = 1/5   1/5
Answer: A
A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?	Choose the correct choice from the following:
A) 1686 B) 1640 C) 6829 D) 2780 E) 2790

Solution: (x*8*3)/100 = ((2665 - x)*3*5)/100   24x/100 = 39975/100 - 15x/100   39x = 39975 => x = 1025   Second sum = 2665 – 1025 = 1640   Answer: 1640
Answer: B
How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?
Choose the most appropriate option
A) 1000  B) 1050  C) 1100  D) 1200  E) 1300

Solution: 50/100 * x = 30 * 20 => x = 1200   ANSWER:1200
Answer: D
All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 91 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only?  Answers:
A) 30	B) 33	C) 36	D) 39	E) 42

Solution: 60% of students are in the band only, so 30% of students are in the orchestra only.   Since 10% of students are in both, then 70% of students are in the band which is 91 students.   The number of students in the orchestra is  (30/70)*91= 
 (30/70)*91 = 39
39.   The answer is 39.
Answer: D
Yesterday it took Robert 3 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 30 minutes in both trips, the speed for the round trip would be 80 miles per hour. What is the distance between city A and city B?	Choose the most appropriate option.
A) 90 B) 180 C) 150 D) 240 E) 300

Solution: 2d/80 = 4.5 ( because time = 3 + 2.5 - 1 hrs)   => d = 180   Answer - 180
Answer: B
Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements E are possible?	Pick.
A) 30	B) 60	C) 90	D) 180	E) 540

Solution: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.   But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.   I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements E including the order of tasks.   could you explain the highlighted step... i'm getting 90 = 15 * 3!   suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z   one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways   X--	Y--	Z   12--	34--	56   12--	56--	34   34--	12--	56   34--	56--	12   56--	12--	34   56--	34--	12   so the answer should be 15*6= 
15*6 = 90
90   But now you can fruther decide which task you want to perform first X Y or Z..90
Answer: C
The difference between the place values of two fives in the numerical 86510529 is Choose the correct option
A) 0
B) 4905
C) 49050
D) 490500
E) None of them

Solution: Required difference = (500000-500)   =490500.   Answer is 490500
Answer: D
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 90 miles per hour, how fast will it be falling after 18 seconds? Choose the correct choice from the following choices.
A) 18 miles per hour
B) 90 miles per hour
C) 216 miles per hour
D) 324 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 = 90 miles per Hour   i.e. k = 18   i.e. The relation between Velocity and Time becomes   Velocity =18*Time   Time= 18 seconds   Velocity = 18*18= 
18*18 = 324
324 miles per hour   Answer: Option 324 miles per hour
Answer: D
A cement mixture is composed of 3 elements. By weight, 1/2 of the mixture is sand, 1/5 of the mixture is water, and the remaining 15 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?  Pick
A) 30  B) 40  C) 50  D) 60  E) 80

Solution: Let the total weight be x.   Sand content= (1/2)x   Water content= (1/5)x   Gravel=x-(1/2)x-(1/5)x=(3/10)x=15   x=50   Then answer will be 50=50
Answer: C
The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream? Choose the most appropriate option:
A) 10 kmph
B) 20 kmph
C) 12 kmph
D) 97 kmph
E) 15 kmph

Solution: Speed of the boat in still water   = (30+70)/2= 
(30+70)/2 = 50
50 kmph. Speed of the stream= (70-30)/2= 
(70-30)/2 = 20
20 kmph.   Answer: 20 kmph
Answer: B
Between 1980 and 1990 a small town's population increased from 10000 to 12500. Between 1990 and 2000 its population increased from 12500 to 14500. By what percent did the rate of population growth decrease from the period 1980-1990 to the period 1990-2000?
Pick one:
A) 20%
B) 24%
C) 28%
D) 32%
E) 36%

Solution: Solution:   This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.   We first set up the ratios of population growth to initial population for the two periods. The first ratio will be for the period 1980-1990, and the second ratio will be for the period 1990-2000. Because the populations are in hundreds, we do not have to express all the trailing zeros in our ratios.   1980-1990   growth/initial population = 2500/10000 = 1/4   1990-2000   growth/initial population = 2000/12500 = 4/25   Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 100. Keep in mind that we are able to do this only because our answer choices are expressed in percents.   1980-1990   growth/initial population = (1/4) x 100 = 25   1990-2000   growth/initial population = (4/25) x 100 = 16   We can plug 25 and 16 into our percent change formula:   (new – old)/old x 100   [(16 – 25)/25] x 100   -9/25 x 100   At this point we can stop and consider the answer choices. -9/25 x 100 is -36, so the decrease is by 36%.   Answer 36%.
Answer: E
What is the ratio between perimeters of two squares one having 3 times the diagonal then the other? Select the correct option
A) 3: 4 B) 3: 9 C) 3: 2 D) 3: 1 E) 3: 3

Solution: d = 3d d = d   a√2 = 3d a√2 = d   a = 3d/√2 a = d/√2 => 3: 1   Answer: 3: 1
Answer: D
14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term Z of the sequence?  Choose the correct choice from the following:
A) 360
B) 365
C) 369
D) 374
E) 383

Solution: First term , a= 14   Common difference , d = 9   nth term , tn = a + (n-1)d   41st term Z, t41 = a+ 40*d = 14 + 40*9= 
14 + 40*9 = 374
374   Answer 374
Answer: D
A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 3
matches are totally played, how many teams participated?	Choose the correct choice from the following answers
A) 4
B) 5
C) 6
D) 7
E) 3

Solution: 2 ways to solve this problem..   summation(x)=n(n-1)/2   n(n-1)/2=3;   n^2-n-6=0   Ans : 3   ANSW3R:3
Answer: E
Evaluate: 45678 * 8*4*8 = ?  Choose the most appropriate option
A) 730848  B) 705265  C) 730846  D) 730596  E) 731848

Solution: 730848ccording to order of operations, 8?4?8 (division and multiplication) is done first from left to right   8/4= 
8/4 = 2
2* 8= 
2* 8 = 16
16   Hence   45678 * 8*4*8= 45678 * 16= 
45678 * 16 = 730_848
730848   correct answer 730848
Answer: A
Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 15 skiers were CPR certified and 25 were not. How many skiers tried out for the ski patrol?
Choose the correct choice from the following answers:
A) 40	B) 50	C) 60	D) 70	E) 80

Solution: Not Selected = 80%   If total is x.   Then 0.8x=15+25= 
15+25 = 40
40   x=50   Hence answer is 50.
Answer: B
Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
Choices:
A) Rs.129  B) Rs.198  C) Rs.189  D) Rs.128  E) Rs.129

Solution: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135   SP = CP[(100 + profit%)/100]   = 135 * [(100 + 40)/100]   = Rs.189.   Answer:Rs.189
Answer: C
A part of certain sum of money is invested at 10% per annum and the rest at 16% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? Choose the correct choice from the following answers:
A) 8:5
B) 4:9
C) 4:3
D) 4:1
E) 4:2

Solution: 16:10   = 8:5   8:5nswer: 8:5
Answer: A
The area of the maximum size of the circle described from the 10 inch square?  Choose the correct choice from the following answers:  A) 75.5 sq inch  B) 76.5 sq inch  C) 77.5 sq inch  D) 78.5 sq inch  E) 79.5 sq inch

Solution: 10 inch square means sides of sq are 10inch   then circle is within square so diameter would be 10 inch maximum and radius is 5inch   so area of the circle is = pi*r*r=3.14*5*5= 
3.14*5*5 = 78.5
78.5 sq inch   ANSWER:78.5 sq inch
Answer: D
What approximate value will come in place of the question mark(?) in the below question?
(47% of 1442 - 36% of 1412) + 63 = ? Choose the most appropriate option.
A) 237
B) 278
C) 278
D) 252
E) 271

Solution: Explanation:   Since there are 5 cups of each kind,prepared with milk or tea leaves added first,are identical hence,total number of different people ways of presenting the cups to the expert is 10!/(5! x 5!)= 252   Answer: 252) 252
Answer: D
Three numbers are in the ratio 4 : 5 : 6 and their average is 30 . The largest number is:	Choices.
A) 33 B) 77 C) 36 D) 18 E) 16

Solution: Explanation:   Let the numbers be 4x, 5x and 6x. Therefore,   (4x+5x+6x)/3 = 30   15x = 90   x = 6   Largest number = 6x = 36.   ANSWER:36
Answer: C
The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is
Pick.
A) 45 kg B) 75kg C) 25kg D) 35 kg E) 55 kg

Solution: Explanation:   Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg.   45 kgnswer: 45 kg
Answer: A
Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?	Select.
A) (x + y) / t
B) 2(x + t) / xy
C) 2xyt / (x + y)
D) 2(x + y + t) / xy
E) x(y + t) + y(x + t)

Solution: Say the distance to school is 10 miles, x=5 miles per hour and y=1 miles per hour, then:   Time Bob spent biking would be  5/5= 
 5/5 = 1
1 hour, and time he s pent walking would be  5/1= 
 5/1 = 5
5 hours, so t=1+5= 
1+5 = 6
6 hours.   Now, plug x=5, y=1, and t=6 into the answer choices to see which one yields the distance of 10 miles. Only answer choice C fits.   Answer: 2xyt / (x + y).
Answer: C
Which of the following numbers is between 1⁄4 and 1⁄5?
Choose one
A) .45	B) .35	C) .29	D) .22	E) .15

Solution: 1/4= 
1/4 = 1/4 = around 0.25
.25   1/5= 
1/5 = 1/5 = around 0.2
.2   The only number between these two is 0.22.   The answer is .22.
Answer: D
A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is? Select:
A) 16 kmph
B) 88 kmph
C) 54 kmph
D) 18 kmph
E) 19 kmph

Solution: S = 240/16 * 18/5= 
240/16 * 18/5 = 54
54 kmph   Answer: 54 kmph
Answer: C
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 8.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?  Answers:  A) 16.5%  B) 9%  C) 35%  D) 55%  E) 65%

Solution: The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);   On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.085*fringe benefit costs;   So, 35(S+F) = 30S+85F --> S = 10F --> F/S = 1/10 --> F/(S+F) = 1/(1+10) = 1/11 = 0.09.   Answer: 9%.
Answer: B
The value of C+5C(7C)(5CC)when C= 7 is:	Pick.
A) 420754 B) 420777 C) 420170 D) 420175 E) 420715

Solution: Solution:   C+5C(7C)(5CC)   Put the value of C= 7 in the above expression we get,   7+ 35(7 x 7)(5x7 x 7)   = 7+ 35(49)(5 Ã— 49)   = 7 + 420175   =420175   Answer : 420175
Answer: D
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at?	Choose the correct option.
A) 7.42 am	B) 7.45 am	C) 8.30 am	D) 9.45 am	E) 10.00 am

Solution: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.   Relative speed of A and B = 6 - 1= 
6 - 1 = 5
5 rounds per hour.   Time taken to complete one round at this speed= 1/5 hr = 12 min.   7.42 amNSWER 7.42 am
Answer: A
A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many apples did each person get before 45 people joined the feast?	Choose one
A) 20. B) 21 C) 22 D) 23 E) 24

Solution: if 1430 is divisible by anyone of the answer choices.   A.1430/20 = 143/2   B 1430/21 = 1430/21   C   1430/22= 
  1430/22 = 65
65   If 1430 apple was divided among 65 people, each would have received 22.   After addition of 45 people the answer should be 13. 1430/110= 13.   22 is the answer.
Answer: C
In a coded language
If
tomato = 3
apple = 2
math = 1
then
mathematics = ?
Options:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: mathematics=4   because no. of vowels in mathematics=4   ANSWER:4
Answer: D
Mike needs 30% to pass. If he scored 212 marks and falls short by 22 marks, what was the maximum marks he could have got?	Choose the correct choice from the following answers
A) 343	B) 777	C) 780	D) 867	E) 232

Solution: If Mike had scored 22 marks more, he could have scored 30%   Therefore, Mike required 212 + 22= 
212 + 22 = 234
234 marks   Let the maximum marks be m.   Then 30 % of m= 234   (30/100) × m = 234   m = (234 × 100)/30   m = 23400/30= 
23400/30 = 780
780   Answer:780
Answer: C
Latha travels from A to B a distance of 1000 miles in 10 hours. He returns to A in 5 hours. Find his average speed?  Choose the correct option.
A) 100mph B) 125.98mph C) 156.15mph D) 133.3mph E) 110.5mph

Solution: Speed from A to B = 1000/10= 
1000/10 = 100
100 mph   Speed from B to A= 1000/5= 
1000/5 = 200
200 mph   Average speed= 2*100*200 / 300 = 133.3mph   Answer is 133.3mph
Answer: D
A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 4 %. The rate of interest obtained is  Choose the correct choice from the following choices: A) 5% B) 5.28% C) 5.30% D) 5.50% E) 6%

Solution: Shares = 20 shares   50 at 5 discount   rate divident 4%   req ===> 5.28%   ANSWER 5.28%
Answer: B
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is
45 kmph. For how many minutes does the bus stop per hour?  Choose the correct choice from the following choices:
A) 12	B) 11	C) 10	D) 9	E) 20

Solution: SPEED OF THE BUS EX10LUDING STOPPAGES = 54 KMPH   SPEED OF THE BUS IN10LUDING STOPPAGES = 45 KMPH   LOSS IN SPEED IN10LUDING STOPPAGES = 54-45= 
54-45 = 9
9 KMPH   IN HOUR BUS 10OVERS 9 KM LESS DUE TO STOPPAGES   HEN10E DISTAN10E/SPEED= 9/54 = 1/6 HR = 60/6= 
60/6 = 10
10 MIN   ANSWER 10
Answer: C
A rectangular garden is to be twice as long as it is wide. If 180 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?  Choose the correct choice from the following choices.
A) 60	B) 70	C) 80	D) 90	E) 100

Solution: ALTERNATE APPROACH   Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.   Given Perimeter is 180   So, 2 ( L + B ) = 180   Or, L + B = 90   Now use the answer options ( Given Length ; Breath will be half the length)   (60) 60   L = 60 ; B = 30   L + b = 90   (B) 70   L = 70 ; B = 35   L + b = 105   (C) 80   L = 80; B = 40   L + b = 120   (D) 90   L = 90; B = 45   L + b = 135   (E) 100   L = 100; B = 50   L + b = 150   Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (60)
Answer: A
Total 90 cows 30 cow gives each 2 liter milk 30 cow gives each 3/4 liter milk 30 cow gives each 1/4 liter milk this is split into 3 son per each 30 cows & 30 liter milk how?  Pick one
A) 10	B) 12	C) 15	D) 16	E) 30

Solution: 30 cow 2 liter each =60 liter   30 cow 3/4 liter each= 3/4= 
3/4 = 3/4 = around 0.75
0.75*30= 
0.75*30 = 22.5
22.5   30 cow 1/4 liter each= 1/4= 
1/4 = 1/4 = around 0.25
0.25*30= 
0.25*30 = 7.5
7.5   add  60+22.5+7.5= 
 60+22.5+7.5 = 90
90   milk split into 3 son each 30 liter then 90/3= 
90/3 = 30
30   ANSW30R:30
Answer: E
Three candidates contested an election and received 3834 votes, 7926 votes, and 16240 votes respectively. What percentage of the total votes did the winning candidate receive?	Choose the correct choice from the following answers:
A) 55%
B) 56%
C) 57%
D) 58%
E) 59%

Solution: The total number of votes polled = (3834 + 7926 + 16240)= 
(3834 + 7926 + 16240) = 28_000
28000   The winner's percentage= 16240/28000 * 100= 
16240/28000 * 100 = 58
58%   The answer is 58%.
Answer: D
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 35 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?  Choose the correct choice from the following answers:
A) 20 ft
B) 25 ft
C) 750 ft
D) 900 ft
E) 1050 ft

Solution: Point to note: Both the wheels would have traveled the same distance.   Now consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).   Equating the distance traveled by front wheel to back wheel: (x+5)*30 = x * 35. (Formula for calculating the distance traveled by each wheel is: # of revolutions * circumference.)   Solving this eqn. gives x=30   Sub x=30 either in (x+5)*30 or in x * 35 to get the distance, which is 1050. So the correct choice is 1050 ft.
Answer: E
If n = (33)^43 + (43)^32 what is the units digit of n?
Select the correct option:
A) 0  B) 2  C) 4  D) 6  E) 8

Solution: First of all, the units digit of (33)^43 is the same as that of 3^43 and the units digit of (43)^32 is the same as that of 3^32. So, we need to find the units digit of 3^43 + 3^33.   Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:   3^1=3 (the units digit is 3)   3^2=9 (the units digit is 9)   3^3=27 (the units digit is 7)   3^4=81 (the units digit is 1)   3^5=243 (the units digit is 3 again!)   ...   Thus:   The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).   The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).   Therefore the units digit of (33)^43 + (43)^32 is 7 + 5 = 2.   Answer: 2.
Answer: B
If x is a whole number, then x2(x2 - 1) is always divisible by	Choose the correct choice from the following options
A) 12  B) 24  C) 12-x  D) multiple of 12  E) NOne

Solution: Sol.   Putting x = 2, we get 22 (22 - 1) = 12.   So, x2(x2 - 1) is always divisible by 12.   12nswer 12
Answer: A
A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?  Select the correct option:
A) $28	B) $82	C) $110	D) $138	E) $194

Solution: by the question, the equation would be 150 p - 84*150 - 16500 = 0   p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.   solving the equation, we get p = $ 194. Answer $194 for me.
Answer: E
The average of first 12 even numbers is?  Select the correct option:
A) 10  B) 11  C) 12  D) 13  E) 14

Solution: Sum of 12 even numbers = 12 * 13= 
12 * 13 = 156
156   Average= 156/13 = 13   ANSWER:13
Answer: D
log 3600 is equal to Choose the correct choice from the following options:	A) 2log6 +1	B) 6log2 + 1	C) 2log6 +2	D) 6log2 + 2	E) 6log2 + 4

Solution: log 3600=log 36 + log 100=2log 6 + 2.   log 36=log 6^2=2log 6   log 100=2.   -->2log 6+2   ANSWER:2log6 +2
Answer: C