MU-NLPC/Calc-aqua_rat huggingface dataset:
Henry got a weekly raise of $963. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.	Choose the correct choice from the following:
A) 693	B) 396	C) 963	D) 691	E) 961

Solution: Let the 1st paycheck be x (integer).   Henry got a weekly raise of $ 963.   So after completing the 1st week she will get $ (x+963).   Similarly after completing the 2nd week she will get $ (x + 963) + $ 963.   = $ (x + 963 + 963)   = $ (x + 1926)   So in this way end of every week her salary will increase by (963)$ 963.
Answer: C
Present ages of X and Y are in the ratio 2:3 respectively. Four years hence this ratio will become 3:4 respectively. What is X's present age in years? Choose the correct choice from the following choices
A) 8
B) 36
C) 37
D) 39
E) 40

Solution: Let the present ages of X and Y be 2x and 3x years respectively.   Then, (2x + 4)/(3x + 4) = 3/4   4(2x + 4) = 3(3x + 4) =>8x+16=9x+12 => x=4   X's present age = 2x = 2*4= 
2*4 = 8
8   8NSWER:8
Answer: A
A tree increases annually by 1/8th of its height. By how much will it increse after 2 years, if it stands today 64 cm high?	Choose the correct choice from the following answers:  A) 72 cm  B) 74 cm  C) 75 cm  D) 81 cm  E) 83 cm

Solution: Increase % = (1/8 x 100)%   = 12 1/2 % = 25/2 %   height after 2 years =(64 x(1+(25/2x100)power of 2)) cm   = (64 x 9/8 x 9/8 ) cm= 81 cm   Answer is 81 cm
Answer: D
If 32455 × 3145208 × m^100 is divisible by 5, which of the following could be the value of m?	Answers:
A) 6000209
B) 5644564
C) 2345678
D) 1000000
E) 2355232

Solution: The first two terms are not divisible by 5, so we need the third term to be divisible by %. The only way that (m^10) is going to be a multiple of 5 is if m is a multiple of 5. Therefore, we need the single answer that is a multiple of 5.   Answer =(1000000)
Answer: D
ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,45) and (-5,15). Which can be the coordinate of fourth vertex?
Options:
A) (-5,-5)  B) (5,45)  C) (-5,-25)  D) (-5,10)  E) (15,25)

Solution: A(-5, 15)   (5,45)(5, 15)   C(5, 45)   X(-5, 45): Parallelogram=Square=AXC(5,45), where AX||C(5,45), AX=C(5,45), XC||A(5,45), XC=A(5,45)   Y(-5, 5): Parallelogram=AY(5,45)C, where AY||(5,45)C, AY=(5,45)C, AC||Y(5,45), AC=Y(5,45)   Z(15, 45): Parallelogram=ACZ(5,45), where AC||Z(5,45), AC=Z(5,45), CZ||A(5,45), CZ=A(5,45)   Ans:(5,45)
Answer: B
{3, 5, 8, y}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y
Choose the correct answer.
A) 16/5, 28/3  B) 4, 16/5  C) 4, 16/5, 28/3  D) 4, 28/3  E) 3, 4, 5

Solution: The set can have the following forms:   1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3   2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4   3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4   4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case.   Thus the possible values are 4 and 28/3.   4, 28/3 is the correct answer.
Answer: D
A small college reduced its faculty by approximately 23 percent to 195 professors. What was the original number of faculty members?  Choose one.
A) 253  B) 208  C) 224  D) 254  E) 302

Solution: If x is the original number of faculty members, then after 23% reduction in faculty members number is .77x   but we are given .77x = 195   x = 253   So the original number of faculty members is 253   Correct 253nswer - 253
Answer: A
A book is bought for $32 and sold for $56. What is the profit in percentage?
Choose the correct answer
A) 15
B) 35
C) 75
D) 25
E) 85

Solution: 56/32= 
56/32 = 7/4 = around 1.75
1.75   The answer is 75.
Answer: C
There are many numbers that can be expressed as the sum of three squares in three different ways.
Can you find out the smallest of such number?
Choose the correct choice from the following options.
A) 87 B) 54 C) 29 D) 30 E) 70

Solution: 54   54   7^2 + 2^2 + 1^1   6^2 + 3^2 + 3^2   2^2 + 5^2 + 5^2
Answer: B
In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 3/4 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have? Choose the correct choice from the following options:
A) 30	B) 45	C) 60	D) 120	E) 135

Solution: We can start with the known quantity and then go on to find the others.   Shiny igneous ricks are 30. These are (3/4) of total igneous rocks.   (2/3)*Total igneous rocks = 30   Total igneous rocks = 30 * (4/3)= 
30 * (4/3) = 40
40   Total sedimentary rocks= 2*Total igneous rocks = 2*40= 
2*40 = 80
80   Total number of rocks= 40 + 80= 
40 + 80 = 120
120   Answer (120)
Answer: D
Tough and Tricky questions: Probability.
Medical analysts predict that half of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days? Choose the correct choice from the following:
A) 16/81
B) 7/8
C) 2/3
D) 19/27
E) 65/81

Solution: At the end of each day we will have 1/2 alive. So after 3 days we will have (1/2)^3 people alive. Therefore, fraction of dead people will be 1-(1/2)^3=7/8.   The correct answer is 7/8.
Answer: B
10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day?  Options:
A) 4 days
B) 10 days
C) 20 days
D) 25 days
E) 26 days

Solution: Explanation:   10*12*15/20 = 24*20*x/32   X=4   4 daysnswer: Option 4 days
Answer: A
Five bells begin to toll together at 12:00 noon and toll respectively at intervals of 4, 5, 6, 8, and 9. seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 3:01 pm (i.e. three hours and one minute later)?	Select:  A) 25  B) 30  C) 35  D) 40  E) 45

Solution: The least common multiple is 2*2*2*3*3*5= 
2*2*2*3*3*5 = 360
360.   10860 seconds / 120= 30 + remainder.   The answer is 30.
Answer: B
The curved surface of a sphere is 64 pi cm2. Find its radius?  Select the correct option.
A) 1 cm
B) 4 cm
C) 2 cm
D) 3 cm
E) 5 cm

Solution: 4 Ï€r2 = 64 => r = 4   ANSWER 4 cm
Answer: B
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is :  Choose the correct choice from the following answers:
A) 15
B) 30
C) 45
D) 60
E) 65

Solution: Sol.   Let the three integers be x, x + 2 and x + 4. Then, 3x = 2(x + 4) + 3 = ⇔ x = 11.   ∴ Third integer = x + 4 =15.   15nswer 15
Answer: A
In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr? Choose the correct option: A) 2.5 sec B) 3 sec C) 8.9 sec D) 6.9 sec E) 2.9 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 120/40= 
120/40 = 3
3 sec.   Answer: 3 sec
Answer: B
The average score of a cricketer in 2 matches is 27 and in other 3 matches is 32. Then find the average score in all the 5 matches? Choose the correct option:
A) 25  B) 27  C) 30  D) 35  E) 42

Solution: Average in 5 matches = (2*27 + 3*32)/2+3 = 54+96 / 5 = 30   Answer is 30
Answer: C
The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?  Options:
A) 84% B) 94% C) 65% D) 64% E) 34%

Solution: r = 3 πr2 = 9   r = 5 πr2 = 25   25 π – 16 π   100 ---- ? => 64%   Answer:64%
Answer: D
A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.07. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the fifth day it is overdue?
Choose one:	A) $0.60	B) $0.70	C) $0.86	D) $0.90	E) $1.00

Solution: 1st day fine - 0.07   2nd day fine - 0.07*2 = 0.14 (as doubling gives lower value)   3rd day fine - 0.14*2 = 0.28 (as doubling gives lower value)   4rd day fine - 0.28*2 = 0.56 (as doubling gives lower value)   5th day fine - 0.56 + 0.3 = 0.86 (as doubling gives higher value we add 0.3 this time)   Answer: $0.86.
Answer: C
(2^2+4^2+6^2+.....+20^2)=?	Options:
A) 770
B) 1155
C) 1540
D) 385x385
E) None of them

Solution: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x10)^2   =2^2 x (1^2+2^2+3^2+.......+10^2)   formula is =1/6 n(n+1)(2n+1)   =(4x1/6x10x11x21)   =(4x5x77)=1540   Answer is 1540
Answer: C
If 3 spiders make 3 webs in 3 days, then 1 spider will make 1 web in how many days?
Choose the correct option.
A) 7  B) 6  C) 5  D) 4  E) 3

Solution: Let the required number days be x.   Less spiders, More days (Indirect Proportion)   Less webs, Less days (Direct Proportion)   spiders 1:3   Webs 3:1   1 x 3 x x = 3 x 1 x 3   => x= 3   Answer is 3
Answer: E
How many three digits numbers can be formed by using the digits 1,2,3,4,5.
Choose the correct choice from the following answers:
A) 255
B) 135
C) 225
D) 125
E) 175

Solution: We have to determine the total number of three digits numbers formed by using the digits 1,2,3,4,5. Clearly the repetition of digits allowed.Units place can be filled by any of the digits in 5 ways. Simillarly each one of the tens and hundreds place can be filled in 5 ways. Total number of required number =5x5x5 =125 Answer : 125
Answer: D
If 4 people are selected from a group of 5 married couples, what is the probability that none of them would be married to each other?  Choose the correct choice:
A) 1/33
B) 2/33
C) 1/3
D) 16/33
E) 8/21

Solution: If we are to select 4 people from 5 couples WITHOUT any restriction, how many ways can we make the selection? 10!/4!6! = 210   If we are to select 4 people from 5 couples WITH restriction that no married couple can both make it to the group, only a representative?   5!/4!1! = 5   But we know that to select a person from each couple, take 2 possibilities     5*2*2*2*2= 
  5*2*2*2*2 = 80
80   Probability= Desired/All Possibilities = 80/210 = 8/21   Answer: 8/21
Answer: E
What is the probability that a leap year has 53 Sundays and 52 Mondays?  Choose the correct choice from the following options:
A) 1/8
B) 1/7
C) 1/3
D) 1/5
E) 1/2

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability = 1/7   Answer: 1/7
Answer: B
If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 3.	Choose the correct choice from the following options:
A) 8 B) 5 C) 11 D) 3 E) 4

Solution: 6 * 15 * 3 = (√(6 + 2)(15 + 3) )/ (3 + 1)   = (√8 * 18) / 4   = (√144) / 4   = 12 / 4= 
12 / 4 = 3
3.   Answer is 3.
Answer: D
If 2^2n + 2^2n + 2^2n + 2^2n = 4^26, then n =	Answers
A) 3 B) 6 C) 12 D) 23 E) 25

Solution: 2^2n + 2^2n + 2^2n + 2^2n = 4^26   => 4 x 2^2n = 4^26 = 2^52   => 2^2 x 2^2n = 2^52   => 2^(2n+2) = 2^52   => 2n+2 = 52=> n =25   So. Answer will be 25
Answer: E
A train 125 m long passes a man, running at 7 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: Pick
A) 35 km/hr B) 50 km/hr C) 45 km/hr D) 52 km/hr E) 87 km/hr

Solution: Speed of the train relative to man   = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed   = (x - 7) km/hr. x - 7 = 45 ==> x = 52 km/hr.   Answer: 52 km/hr
Answer: D
A man's speed with the current is 20 kmph and speed of the current is 2 kmph. The Man's speed
against the current will be  Choose the correct choice from the following: A) 16 kmph B) 12 kmph C) 14 kmph D) 17 kmph E) None of these

Solution: Explanation:   Speed with current is 20,   speed of the man + It is speed of the current   Speed in sƟll water = 20 - 2= 
20 - 2 = 18
18   Now speed against the current will be   speed of the man - speed of the current= 18 - 2= 
18 - 2 = 16
16 kmph   16 kmphnswer: 16 kmph
Answer: A
A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
Choose one:
A) 33.8
B) 33.5
C) 33.3
D) 33.9
E) 33.1

Solution: Let B = 100   A = 50   33.3 * (150/100) = 50   333.3 = 100   33.3 = 33.3 then '33.3' 33.3heapest   Answer:33.3
Answer: C
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	Choices:  A) 28 sec  B) 16 sec  C) 39 sec  D) 18 sec  E) 17 sec

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 150= 
240 + 150 = 390
390 m.   Time taken= 390/10= 
390/10 = 39
39 sec.   Answer:39 sec
Answer: C
Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 3 kg more than Peter. Together the three of them picked 27 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
Choose one
A) 6, 9 and 12 B) 12, 9 and 6 C) 9, 6 and 12 D) 12, 6 and 9 E) 6, 12 and 9

Solution: M = 2P   L = P+3   M + P + L = 27   2P + P + (P+3) = 27   P = 6, M = 12, L = 9   Therefore, Mary, Peter, and Lucy picked 12, 6, and 9 kg, respectively.   The answer is 12, 6 and 9.
Answer: D
Two members of a club are to be selected to represent the club at a national meeting. if there are 55 different possible selections of the 2 members, how many members does the club have?
Choose the correct choice from the following answers:
A) 11
B) 27
C) 40
D) 57
E) 95

Solution: I have done this problem by substituting numbers   We have n!/2!(n-2)! = 55   or n(n-1)/2 = 110 or n^2-n -110 =0 or n^2-11n+10n-110 =0 or n(n-11) +10(n-11) =0 or (n-11)(n+10)=0   n=11 satisfies the equation   11
Answer: A
If N = 3^0.15 and N^b = 9, b must equal  Pick one
A) 3/80	B) 3/5	C) 4	D) 5/3	E) 40/3

Solution: 15/100 = 3/20   N = 3 ^ 3/20   N^b = 3^2   (3^3/20)^b = 3^2   b = 40/3   Answer: 40/3
Answer: E
The ratio of 2 numbers is 5:2 and their H.C.F. is 20. Their L.C.M. is ?  Choose the correct answer:  A) 400  B) 300  C) 200  D) 100  E) 40

Solution: Let the numbers be 5x and 2x   Their H.C.F. = 20   so the numbers are 5*20 , 2*20 = 100, 40   L.C.M. = 200   Answer is 200
Answer: C
If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?  Choose the correct choice from the following choices.
A) 2:5	B) 2:4	C) 3:0	D) 2:1	E) 2:3

Solution: 5M + 2B = 4(1M + 1B)   5M + 2B = 4M + 4B   1M = 2B   The required ratio of work done by a man and a boy = 2:1 .Answer: 2:1
Answer: D
The effective annual rate of interest corresponding to a nominal rate of 8% per annum payable half-yearly is?	Choose the correct option:
A) 6.06% B) 8.16% C) 6.08% D) 6.09% E) 6.19%

Solution: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 4/100)2] = Rs. 108.16 Effective rate = (108.16 - 100)= 
(108.16 - 100) = 8.16
8.16%   ANSWER:8.16%
Answer: B
If x is real, find the maximum value of the expression -2x^2 + 5x + 7. Pick one
A) 6.125
B) 8.125
C) 10.125
D) 12.125
E) 14.125

Solution: This is an equation of a downward facing parabola.   The maximum value is the top point of the parabola.   -2x^2+5x+7 = (-2x+7)(x+1)   The roots are 7/2 and -1.   The maximum value must be when x is halfway between these two points.   x = 1.25   The maximum value is -2(1.25)^2+5(1.25)+7 = 10.125   The answer is 10.125.
Answer: C
Angelo and Isabella are both salespersons. In any given week, Angelo makes $540 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
Choose the most appropriate option:
A) 23,000 B) 24,500 C) 25,500 D) 26,500 E) 27,500

Solution: Let the weekly sales of both = x   540+(x−1000)8/100=10/100x   x = 23000   23,000NSWER:23,000
Answer: A
A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 90 km/hr. When will he overtake the thief?	Choose the correct answer:
A) 6 p.m	B) 9 p.m	C) 4 p.m	D) 2 p.m	E) 1 p.m

Solution: :   Suppose the thief is overtaken x hrs after 2.30 p.m.   Then, distance covered by the owner in (x - 1/2) hrs.   60x = 90(x - 1/2) => x = 3/2 hrs.   So, the thief is overtaken at 4 p.m.'   Answer: 4 p.m
Answer: C
REDO’s manufacturing costs for sets of horseshoes include a $10,500 initial outlay, and $30per set. They can sell the sets $60. If profit is revenue from sales minus manufacturing costs, and the company producessells 1000 sets of horseshoes, what was their profit?	Choose one:
A) $19500	B) $15500	C) $29500	D) $39500	E) $1500

Solution: Total Manufacturing cost = 10500+1000*30= 
10500+1000*30 = 40_500
40500   Total Selling cost= 1000*60= 
1000*60 = 60_000
60000   Profit= 60000-40500= 
60000-40500 = 19_500
19500   $19500nswer : $19500
Answer: A
The sum of ages of 5 children born at the intervals of 3 years each is 65 years. What is the age of the youngest child?	Choose one.
A) 3 years	B) 4 years	C) 6 years	D) 7 years	E) 8 years

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 65   5x = 35   x = 7.   Age of the youngest child = x = 7 years.   7 years)
Answer: D
If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of EVEN integers from 30 to 50, inclusive, what is the value of x+y ?
Choose the most appropriate option
A) 810	B) 811	C) 830	D) 850	E) 851

Solution: Since the integers from 30-50 are consecutive we can use the "median x # of terms formula" to determine x. There are 21 terms and the median is 40. This gives a total of 21x40 = 840. There are 11 even integers from 30-50 = y. Therefore, x+y = 851. Answer: 851
Answer: E
A farmer has a rose garden. Every day he either plucks 7 or 6 or 24 or 23 roses. The rose plants are intelligent and when the farmer plucks these numbers of roses, the next day 37 or 36 or 9 or 18 new roses bloom in the garden respectively. On Monday, he counts 189 roses in the garden. He plucks the roses as per his plan on consecutive days and the new roses bloom as per intelligence of the plants mentioned above. After some days which of the following can be the number of roses in the garden?	Choose the correct option:
A) 6  B) 7  C) 6  D) 4  E) 1

Solution: If he plucks 23, then only 18 grows the next day. This means total roses get decreases by 5. So after n days assume the number of roses got decreased 185 where n = 37, then 4 roses left.   Answer:4
Answer: D
Find the cost of fencing around a circular field of diameter 30 m at the rate of Rs.5 a meter?	Choose the correct choice:
A) 288
B) 132
C) 772
D) 592
E) 471.25

Solution: 2 * 22/7 * 15 = 94.25   94.25 * 5 = Rs.471.25   Answer: 471.25
Answer: E
If y > 0, (9y)/20 + (3y)/10 is what percent of y?	Choose one:
A) 40%
B) 50%
C) 60%
D) 70%
E) 75%

Solution: can be reduced to 9y/20+6y/20 =15y/20=75%   Answer 75%
Answer: E
A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible?	Select.
A) 230 B) 360 C) 420 D) 840 E) 5,040

Solution: we have 6 letters out of which 3 are of one kind, 2 are of another kind..   so total ways = 6!/2!1!=360   ans 360
Answer: B
In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards W will he need to gain this Sunday if he wants to keep his season average above 100 yards? Choose the correct choice from the following options.
A) 101
B) 116
C) 130
D) W=131
E) W=141

Solution: Sorry the answer W=141 is W=131.
Answer: D
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. 4200. What was Simran share in the profit? Choose the correct choice:
A) s 9500	B) s 1080	C) s 1008	D) s 1820	E) s 1800

Solution: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.   Simran's share = Rs.4200x 3/7	= Rs. 1,800.   ANSWs 1800R :s 1800
Answer: E
Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.  Select: A) 2:3 B) 1:1 C) 3:4 D) 4:3 E) 5:5

Solution: 5/100A+4/100B = 2/3(6/100A+8/100B)   =>1/20A+1/25B= 1/25A+4/75B   => (1/20-1/25)B= 1/25A+4/75B   (1/20-1/25)A = (4/75-1/25)B   1/100A=1/75B   A/B=100/75=4/3   REQ RATIO = 4:3   ANSWER 4:3
Answer: D
A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number, its digits are interchanged. Find the number.
Choose the correct choice from the following answers.
A) 81	B) 90	C) 100	D) 61	E) 73

Solution: Let the ten's digit be x. Then, unit's digit = (9 - x).   Number = l0x + (9 - x) = 9x + 9.   Number obtained by reversing the digits = 10 (9 - x) + x = 90 - 9x.   therefore, (9x + 9) - 63 = 90 - 9x => 18x = 144 => x = 8.   So, ten's digit = 8 and unit's digit = 1.   Hence, the required number is 81.   81nswer 81)81.
Answer: A
The number 219 can be written as sum of the squares of 3 different positive integers. What is the difference of these 2 different larger integers?
Choose the correct choice from the following choices
A) 6  B) 2  C) 3  D) 5  E) 4

Solution: sum of the squares of 3 different positive integers = 219   13^2 + 7^2 + 1^2 = 219   now,   difference of these 2 different larger integers = 13 - 7= 
13 - 7 = 6
6   6ns - 6
Answer: A
Brand A coffee costs twice as much as brand B coffee. If a certain blend is 3/4 brand A and 1/4 brand B. what fraction of the cost of the blend is Brand A?	Choose the correct choice from the following choices.
A) a. 1/3	B) b. 2/5	C) 3. 1/2	D) 4. 2/3	E) 5. 6/7

Solution: Assume Cost of A= Ca = 200 , Cost of B = Cb=100   The blend contains 0.75 A and 0.25 B ---> Cost of the blend = Cbl = 0.75*200+0.25*100= 
0.75*200+0.25*100 = 175
175   Thus fraction of A in the blend= 0.75*200/175 = 6/7.   Answer : 5. 6/7
Answer: E
A car manufacturer produces only red and blue TCS Models which come out of the final testing area at random. What are the odds that five consecutive cars of same color will come through the test area at any one time?  Choose the correct answer.
A) 1 in 16  B) 1 in 125  C) 1 in 32  D) 1 in 25  E) 1 in 15

Solution: p(5 consecutive cars of same color)=p(5 red)+p(5 blue)   =1/2^5+1/2^5   =1/16   1 in 16NSWER:1 in 16
Answer: A
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (14, 2), (14,-5)? Choose the correct choice from the following options
A) 90	B) 95	C) 104	D) 117	E) 182

Solution: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:   Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.   We can now determine the area of the quadrilateral:   Area = 1/2 × (8 + 7) × 12 = 90.   The answer is 90.
Answer: A
Find the income derived from 88 shares of $ 25 each at 5 premium,
brokerage being (1/4) per share and the rate of dividend being 7(1/2)% per annum. Also, find the rate of interest on the investment.  Options: A) 6.2% B) 7.5% C) 6.5% D) 8.2% E) 4.6%

Solution: Cost of 1 share = $ [25+5+1/4)] = $ (121/4).   Cost of 88 shares = $[(121/4)*88= 
(121/4)*88 = 2_662
$ 2662.   Therefore Investment made= $ 2662.   Face value of 88 shares = $ (88*25)= 
(88*25) = 2_200
$ 2200.   Dividend on $ 100= (15/2).   Dividend on $ 2200 = $ [(15/20*(1/100)*2200] = $ 165.    Income derived = $ 165.   Rate of interest on investment = [(165/2662)*100] = 6.2 %.   6.2%nswer 6.2%.
Answer: A