MU-NLPC/Calc-aqua_rat huggingface dataset:
When a natural number N is successively divided by 12,13,14,15. the remainders are 16,17,18,19. What will be the sum of the remainders if the order of the division is reversed?	Choose one:
A) 16  B) 19  C) 12  D) 11  E) 9

Solution: 12 13 14 15   16 17 18 19   leave the top right- most number 8   start with bottom right-most number 5   19*14+18= 
19*14+18 = 284
284   284*13+17= 
284*13+17 = 3_709
3709   3709*12+16= 
3709*12+16 = 44_524
44524   this is the number required   Now, do the successive division in the reverse order   The sum of the remainders is 19   Hence, the correct option is 19
Answer: B
36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible? Options.
A) 6
B) 9
C) 8
D) 7
E) 5

Solution: Three conditions have to be satisfied.   1. The number of students per row has to be at least 3.   2. Number of row has to be at least 3.   3. Equal number of students has to be seated in a row.   The following arrangements satisfy all 3 conditions.   Arrangement 1: 3 students to a row; 12 rows.   Arrangement 2: 4 students to a row; 9 rows.   Arrangement 3: 6 students to a row; 6 rows.   Arrangement 4: 9 students to a row; 4 rows.   Arrangement 5: 12 students to a row; 3 rows.   You will observe that the number of students in a row is a factor of 36.   So, an alternative and faster approach is to list down factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.   And then start from 3 and quickly find out if the number of rows is at least 2.   Both the conditions are satisfied for the following factors : 3, 4, 6, 9, and 12. i.e., 5 arrangements.   Ans: 5
Answer: E
The cross-section of a water channel is a trapezium in shape. If the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 770 square meters, what is the depth of the channel (in meters)?  Pick one.
A) 50 B) 60 C) 70 D) 80 E) 90

Solution: 1/2 * d * (14 + 8) = 770   d = 70   The answer is 70.
Answer: C
What will be the difference between simple and compound interest @10% per annum on a sum of $1000 after 4 years?
Choose the most appropriate option
A) $48.12	B) $52.64	C) $64.10	D) $72.85	E) $60.10

Solution: S.I. = 1000*10*4/100= 
1000*10*4/100 = 400
$400   C.I.= 1000 * (1 + 10/100)^4 - 1000 = $464.10   Difference = 464.10-400= 
464.10-400 = 64.1
$64.10   Answer is $64.10
Answer: C
Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many W hours will it take if Jim types the report and Mary edits it immediately after he is done?
Pick.
A) 41.4
B) 34.1
C) 13.4
D) 12.4
E) 10.8

Solution: Break down the problem into two pieces: typing and editing.   Mary needs 30 hours to type the report--> Mary's typing rate = 1/30 (rate reciprocal of time)(point 1 in theory below);   Mary and Jim can type up a report in 12.5and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone)(point 23 in theory below)--> x=150/7;   Jim needs 12 hours to edit the report--> Jim's editing rate = 1/12;   Mary and Jim can edit a report in 7.5and --> 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) --> y=20;   How many W hours will it take if Jim types the report and Mary edits it immediately after he is done--> x+y=150/7+20=~41.4   41.4nswer: 41.4.
Answer: A
Ram will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?  Choices:
A) 5
B) 6
C) 9
D) 24
E) 26

Solution: Ram will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are   0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1= 
  0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5
5 cases...5
Answer: A
If w/x = 2/3 and w/y = 3/5, then (x + y)/y =	Select the correct option.
A) 4/5 B) 9/10 C) 7/5 D) 8/5 E) 9/5

Solution: W/X = 2/3x=>x=3/2w and W/Y = 3/5=>y=5/3w   (X+Y)/Y = (3/2w+5/3w)/(5/3x)=9/10   Correct Option: 9/10
Answer: B
A train 100 m long crosses a platform 125 m long in 10 sec; find the speed of the train? Choose the correct choice.
A) 81	B) 77	C) 54	D) 33	E) 99

Solution: D = 100 + 125= 
100 + 125 = 225
225   T= 10   S = 225/10 * 18/5= 
225/10 * 18/5 = 81
81 kmph   81nswer: 81
Answer: A
There are 7 non-collinear points. How many triangles can be drawn by joining these points?	Pick one.
A) 22  B) 38  C) 35  D) 29  E) 18

Solution: Explanation:   A triangle is formed by joining any three non-collinear points in pairs.   There are 7 non-collinear points   The number of triangles formed = \inline {\color{Black} 735_{3}} = 35   Answer: 35) 35
Answer: C
In how many different number of ways 3 boys and 2 girls can sit on a bench?	Choose the correct answer:	A) 720	B) 730	C) 740	D) 750	E) 120

Solution: npn = n!   5p5 = 5 × 4 × 3 × 2 × 1 = 120   120
Answer: E
The average of 20, 30 and 130 is twice the average of 10, 30, and which of the following ? Pick
A) 1)10  B) 2)50  C) 3)60  D) 4)90  E) 5)180

Solution: 20 30 130 = 130+50= 
130+50 = 180
180/3= 
180/3 = 60
60   60/2= 
60/2 = 30
30   10 30 x= 40+x/3 should be smaller than 30   cross multiply 30*3-40= 
30*3-40 = 50
50   2)50
Answer: B
The jogging track in a sports complex is 594 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
Select the correct option:
A) 5.29 min B) 4.32 min C) 5.08 min D) 9.28 min E) 5.988 min

Solution: Clearly, the two will meet when they are 594 m apart.   To be (4.5 + 3.75)= 
(4.5 + 3.75) = 8.25
8.25 km apart, they take 1 hour.   To be 594 m apart, they take (100/825 * 594/1000) hrs= (594/8250 * 60)= 
(594/8250 * 60) = 108/25 = around 4.32
4.32 min.   Answer: 4.32 min
Answer: B
A couple decides to have 2 children. If they succeed in having 2 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 1 girl and 1 boy?  Choose the correct option
A) 1/2
B) 3/4
C) 1
D) 2
E) 3

Solution: Sample space = 2^2 = 4.   Favourable events = {bg}, {gb},   Probability = 2/4 = 1/2.   1/2ns (1/2).
Answer: A
Kanul spent $3000 in buying raw materials, $2000 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount? Pick one:  A) $5555.555  B) $5543.22  C) $5568.000  D) $5366.521  E) $5365.66

Solution: Let the total amount be x   then, (100-10)% of x = 3000+2000   90% of x = 5000   90x/100 = 5000   x = $50000/9   x = $5555.555   $5555.555nswer is $5555.555
Answer: A
If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is?	Choose the correct choice from the following choices.
A) 250 m B) 112 m C) 117 m D) 125 m E) 123 m

Solution: 250 m   250 m = 180 * 5/18 * 5= 
180 * 5/18 * 5 = 250
250 m
Answer: A
A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 92, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? Choose the correct choice:
A) 80
B) 75
C) 76
D) 77
E) 78

Solution: ratio is 4:6:5 , numbers are 4x, 6x, 5x   total scores of each class is (65*4x + 6x * 92 + 77*5x) = 260x+552x+385x = 1197x   total number of students 260 +552 +385= 
260 +552 +385 = 1_197
1197x   total number of students= 15x   average = 1197x/15x = 80   80 is the answer
Answer: A
4524 - ? = 2456
Answers.
A) 2058	B) 2069	C) 2072	D) 2089	E) None of these

Solution: None of thesexplanation:   None of these   Answer: Option None of these
Answer: E
The average of first ten prime numbers which are odd is?	Choose the correct choice from the following answers.
A) 15.5
B) 15.7
C) 15.2
D) 15.8
E) 15.1

Solution: Sum of first 10 prime no. which are odd = 158   Average = 158/10= 
158/10 = 79/5 = around 15.8
15.8   Answer:15.8
Answer: D
Matt gets a $1,300 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $400, how many sales has Matt made?  Choose the most appropriate option.
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Let, Average Commission = x   No. of items sold = y   Total Commission = xy   New Commission = xy+1300   New Average = (xy+1300) / (y+1) = 150+x   i.e. (xy+1300) = (y+1)* (150+x)   i.e. (xy+1300) = (xy+x+150y+150)   i.e. (1150) = (x+150y)   New Commission = 400 = 150+x   i.e. x=250   i.e. y = 6   New Sales = y+1 = 7   Answer: option 6
Answer: D
Solve the given two equations and find the inequality of X and Y. (a) x^4- 227= 398 and (b) y^2 + 321=346 Choose the correct choice
A) If x>y
B) If x>=y
C) If x < y
D) If x<=y
E) x=y or relationship cannot be established

Solution: Solution:-   X=+5,-5 and Y= +5,-5   Comparing, we get X=Y, XY.   Therefore, no relationship can be established between X and Y.   x=y or relationship cannot be established
Answer: E
In a certain sequence, the first term is 2, and each successive term is 3 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence? Select.
A) 360/109
B) 421/113
C) 488/135
D) 584/189
E) 821/165

Solution: let five terms in the sequence be a,b,c,d,e   a=3   b= 3+1/3=10/3   c=3+3/10= 33/10   d= 3+10/33 = 109/33   e= 3+33/109 = 360/109   hence answer should be 360/109.
Answer: A
In how many ways can 7 different object be divided among three persons so that either one or two of them do not get any object?	Choose one:
A) 351  B) 361  C) 371  D) 391  E) 381

Solution: Case 1: Two guys don't get anything. All items go to 1 person. Hence, 3 ways.   Case 2: 1 guy doesn't get anything. Division of 7 items among 2 guys. Lets say they are called A & B.   a) A gets 6. B gets 1. 7 ways.   b) A gets 5. B gets 2. 21 ways.   c) A gets 4. B gets 3. 35 ways.   d) A gets 3. B gets 4. 35 ways.   e) A gets 2. B gets 5. 21 ways.   f) A gets 1. B gets 6. 7 ways.   Total = 126 ways to divide 7 items between A & B.   Total number of ways for case 2 = 126*3= 
126*3 = 378
378 (Either A, or B, or C don't get anything).   Answer= Case 1 + Case 2 = 3 + 378= 
3 + 378 = 381
381   ANSW381R:381
Answer: E
A man rows his boat 90 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?	Pick
A) 5 kmph  B) 7 kmph  C) 9 kmph  D) 8 kmph  E) 1 kmph

Solution: Speed downstream = d/t = 90/(2 1/2) = 36 kmph   Speed upstream = d/t = 45/(2 1/2) = 18 kmph   The speed of the stream = (36 - 18)/2= 
(36 - 18)/2 = 9
9 kmph   Answer:9 kmph
Answer: C
Two angles of a triangle have ratio 7:3, and their difference equals the third angle. What is the smallest angle, in degrees, of the triangle?
Options
A) 90/7	B) 150/7	C) 270/7	D) 300/7	E) 350/7

Solution: The angles of the triangle are 7x, 3x, and (7x-3x)=4x for some value x (due to the ratio) [note that 3x is the smallest angle]   the angles of a triangle add up to 180, so   7x+3x+4x  (7 -3 )= 
  (7 -3 ) = 4
4x for some value x (due to the ratio) [note that 3x is the smallest angle]   the angles of a triangle add up to 180, so   7x+3x+4x=180   14x=180   x=180/14   x=90/7   the smallest angle is 3x so 3*(90/7) = 270/7   270/7
Answer: C
At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?  Answers:
A) 12 years  B) 15 years  C) 19 and half  D) 21 years  E) 22 years

Solution: Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,   4x + 6 = 26 4x = 20   x = 5.   Deepak's age = 3x = 15 years. Answer: Option 15 years
Answer: B
Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $250. What is the share of Rahul? Choose the most appropriate option
A) $50
B) $40
C) $60
D) $100
E) $90

Solution: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3   Rahul's share = 250*2/5= 
250*2/5 = 100
$100   Answer is $100
Answer: D
The H.C.F. of two numbers is 42 and the other two factors of their L.C.M. are 12 and 14. The larger of the two numbers is:	Choose the correct choice from the following.
A) 588  B) 642  C) 567  D) 344  E) 789

Solution: Explanation:   Clearly, the numbers are (42 x 12) and (42 x 14).   {\color{Blue} \therefore } Larger number = (42 x 14) = 588.   588nswer: 588) 588
Answer: A
Square OCAB has an area of 9 square units. Point O is found where the axes meet. What are the coordinates of point A?  Pick one
A) (3, 1)
B) (3, 2)
C) (3, 3)
D) (3, 4)
E) None

Solution: Solution:   If the square has an area of 9 square units, then its side has a length of 3 units. If O is where the axes meet, then points C and B are found on the x- and y-axes and they have the coordinates (3, 0) and (0, 3). Point A is at 3 units from the x-axis and at 3 units from the y-axis and it has the coordinates (3, 3).   Answer (3, 3)
Answer: C
Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 20kmph and Prasanna moves southward at a speed of 30 kmph. How far will be Prasanna from Laxmi after 60 minutes ?  Answers
A) 11 B) 50 C) 28 D) 27 E) 18

Solution: Explanation:   We know 60 min = 1 hr   Total northward Laxmi's distance = 20kmph x 1hr = 20 km   Total southward Prasanna's distance = 30kmph x 1hr = 30 km   Total distance between Prasanna and Laxmi is = 20 + 30= 
20 + 30 = 50
50 km.   Answer: 50
Answer: B
If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many Q digits does this integer consists of?  Choices:
A) 150  B) 339  C) 342  D) 359  E) 362

Solution: Number of single digit integers = 9   Number of 2 digit integers = 99 - 10 + 1= 
99 - 10 + 1 = 90
90   Number of 3 digit integers= 150 - 100 + 1= 
150 - 100 + 1 = 51
51   Number of digits in the integer Q= 1*9 + 2*90 + 3*51 = 9 + 180 + 153= 
9 + 180 + 153 = 342
342   Answer: 342
Answer: C
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 100000. If the profit at the end of a year is Rs. 108000, then the share of B is?	Select.
A) 40000
B) 50000
C) 70000
D) 60000
E) 80000

Solution: Ratio of investments of A and B is (70000 * 12) : (100000 * 6) = 7 : 20   Total profit = Rs. 108000   Share of B = 20/27 (108000) = Rs. 80000   Answer: 80000
Answer: E
Insert the missing number.
3, 4, 6, 8, 9, 12, 12, 16, 15, (....) Select
A) 18
B) 19
C) 20
D) 25
E) 22

Solution: Explanation:   There are two series, beginning respectively with 3 and 4. In one 3 is added and in another 4 is added.   The next number is  16 +4= 
 16 +4 = 20
20.   Answer: 20) 20
Answer: C
One year ago, the ratio of Roonie’s and Ronaldo’s age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Ronaldo ?	Select
A) 32 B) 33 C) 34 D) 35 E) 36

Solution: 7(x-1)=6(y-1)=> 7x-6y-1=0 ----eq1   8(x+4)7 -6 -1= 
7 -6 -1 = 0
0 ----eq1   8(x+4)=7(y+4)=> 8x-7y+4=0 ----eq2   on solving eq1 n eq2   y=36   ANSW36R:36
Answer: E
A plane moves from a place 9N 40E to a place 9N 40W taking 8 hours to travel. If the plane had left at 10.00 a.m. then what is the local time of arrival at the destination?
Choose the correct choice from the following choices.
A) 11.40 p.m.  B) 12.40 p.m.  C) 1.40 p.m.  D) 2.40 p.m.  E) 4.40 p.m.

Solution: Time difference between places will be 4*(40+40)= 
4*(40+40) = 320
320 min=   5 hrs 20 min   as change of 1 degree in longitude cause change of 4 minutes in time.   and that change is 80 degrees here.   so when plane land. time will be = 10.00 + 8.00 -5.20 = 12.40 p.m.   ANSWER:12.40 p.m.
Answer: B
An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 3 ?	Choose the correct choice from the following choices.
A) 1/9  B) 1/3  C) 1/2  D) 2/3  E) 5/6

Solution: n(n+2) to be divisible by 3 either n or n+2 must be a multiples of 3.   In each following group of numbers: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, ..., {97, 98, 99} there are EXACTLY 2 numbers out of 3 satisfying the above condition. For example in {1, 2, 3} n can be: 1, or 3. Thus, the overall probability is 2/3.   Answer: 2/3.
Answer: D
On a certain road 12% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?	Pick:	A) 10.5%	B) 12.5%	C) 15%	D) 22%	E) 30%

Solution: Answer is C.   This question is in the OG and thus well explained by ets.   those who exceed : X   so X = 12%+0,2X   id est X = 15%
Answer: C
Set R has a mean of 9 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?	Pick:
A) {18, 20}  B) {8, 10}  C) {28, 38}  D) {6, 10}  E) {5, 10}

Solution: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 9,the values (8,10) are closer than others.   Hence Answer : {8, 10}
Answer: B
If a2 - b2 = 9 and a*b = 4, find a4 + b4.
Choose the correct choice
A) 32	B) 90	C) 113	D) 92	E) 81

Solution: a2 - b2 = 9 : given   a4 + b4 - 2a2b2 = 92 : square both sides and expand.   a*b = 4 : given   a2b2 = 42 : square both sides.   a4 + b4 - 2(16) = 81 : substitute   a4 + b4 = 113   correct answer 113
Answer: C
If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 750 responses are needed, what is the minimum number of questionnaires that should be mailed?  Choices: A) 1160 B) 1190 C) 1220 D) 1250 E) 1280

Solution: Let x be the minimum number of questionnaires to be mailed.   0.6x = 750   x = 1250   The answer is 1250.
Answer: D
Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? Choose the most appropriate option:
A) 66
B) 70
C) 72
D) 75
E) 78

Solution: Let the distance one way be x   Time from home to work = x/60   Time from work to home = x/100   Total time = 2 hrs   (x/60) + (x/100)= 2   Solving for x, we get x = 75   Time from home to work in minutes= (75)*60/60= 
(75)*60/60 = 75
75 minutes   Ans= 75
Answer: D
Line J has a y-intercept of 8 and passes through point (a,b). What is the slope of Line J in terms of a and b?  Choices
A) (a−6)/b
B) (b-8)/a
C) (6−a)/b
D) (6−b)/a
E) (b−6)/a

Solution: You know that the line goes through point (a,b) and the y-intercept of 8 tells you that the line also goes through point (0,8).   slope m = (y-y1)/(x-x1) = (b-8)/(a-0)= (b-8)/a   (b-8)/a
Answer: B
Jancy had 100 currency notes in all, some of which are of Rs 70 denomination and the remaining of Rs 50 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 50?  Pick one:
A) 103
B) 102
C) 100
D) 105
E) 106

Solution: Let the number of 50-rupee notes = x   Then, the number of 70-rupee notes = (100 – x)   50x + 70(100 – x) = 5000 : x = 100   ANSWER:100
Answer: C
A reduction of 10% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Pick
A) 1.1  B) 2.2  C) 2.5  D) 2.1  E) 2.9

Solution: 100*(10/100)= 
100*(10/100) = 10
10 --- 10   ? --- 1=> Rs.1   100 --- 90   ? --- 1 => Rs.1.1   1.1nswer: 1.1
Answer: A
A man whose speed is 3 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?	Choices:
A) 7  B) 4  C) 3  D) 9  E) 3.6

Solution: M = 3   S = 1.5   DS = 4.5   US = 3   AS = (2 * 4.5 * 3) /7.5= 
(2 * 4.5 * 3) /7.5 = 3.6
3.6   Answer:3.6
Answer: E
A number when multiplied by 3 is odd and divisible by 9. This number when multiplied by 4 is 108. What is the original number? Choose the correct answer:	A) 10	B) 18	C) 13	D) 21	E) 27

Solution: Working backward, 108 divided by 4 is 27.   This number fits the rules of Three and Nine, where the digits add up to a sum divisible by nine.   Answer is 27.
Answer: E
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?	Choose the correct choice from the following answers
A) 11
B) 18
C) 12
D) 99
E) 13

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/5 = 8 m/sec.   Relative speed = 12 + 8= 
12 + 8 = 20
20 m/sec.   Required time= (120 + 120)/20= 
(120 + 120)/20 = 12
12 sec.   Answer:12
Answer: C
How many different positive integers exist between 10^4 and 10^5, the sum of whose digits is equal to 2? Choose the correct answer:  A) 6  B) 7  C) 5  D) 8  E) 18

Solution: So, the numbers should be from 10,000 to 100,000   The following two cases are possible for the sum of the digits to be 2:   1. Two 1's and the rest are 0's:   10,001   10,010   10,100   11,000   4 numbers.   2. One 2 and the rest are 0's:   20,000   1 number.   Total = 5 numbers.   Answer: 5
Answer: C
A class of 60 students has an average height of 200 cm. Six students whose average height is 120 cm, left the class and six others whose average height is 134 cm, joined. Calculate the new average height of the students of the class (in cm) is?	Choose the correct choice from the following
A) 231.4 cm
B) 301.4 cm
C) 201.4 cm
D) 221.4 cm
E) 101.4 cm

Solution: Total height = 200 * 60= 
200 * 60 = 12_000
12000 cm.   Total height of those who left= 120 * 6= 
120 * 6 = 720
720   Total height of those who joined= 134 * 6= 
134 * 6 = 804
804   New average= [12000 - 720 + 804 ] / 60 = 12084/60 cm.   = 201.4   Answer:201.4 cm
Answer: C
A store owner estimates that the average price of type A products will increase by 35% next year and that the price of type B products will increase by 15% next year. This year, the total amount paid for type A products was $4000 and the total price paid for type B products was $5300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
Pick:
A) $14,755  B) $11,495  C) $16,000  D) $16,225  E) $17,155

Solution: cost of type A products next year = 1.35 * 4000= 
1.35 * 4000 = 5_400
5400   cost of type $11,495 products next year= 1.15* 5300= 
1.15* 5300 = 6_095
6095   total 5400 + 6095= 
5400 + 6095 = 11_495
11495   ANSWER:$11,495
Answer: B
If n = 3^6 – 2^8 which of the following is NOT a factor of n?  Choose the correct choice from the following options.
A) 11
B) 43
C) 1
D) 43
E) 5

Solution: 3^6 - 2^8   = (3^3)^2 - (2^4)^2   =(3^3 + 2^4)(3^3 - 2^4)   =(27+16)(27-16)   =43*11   Therefore, 5 is Not a factor of n.   5
Answer: E