MU-NLPC/Calc-aqua_rat huggingface dataset:
Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 1.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn?	Options
A) 1/3
B) 1/18
C) 1/10
D) 2
E) 30

Solution: Pete covered 1.5*60= 
1.5*60 = 90
90 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/90=1/18.   Answer: 1/18.
Answer: B
Vijay invested Rs.50,000 partly at 10% and partly at 15%. His total income after a year was Rs.7000. How much did he invest at the rate of 10%? Select the correct option:
A) Rs.40,000
B) Rs.40,000
C) Rs.12,000
D) Rs.20,000
E) None

Solution: Solution:   The best way to solve this problem is by using the concept in Mixtures and Alligation.   Vijay earned a total income of Rs.7000 for his investment of 50,000.   Therefore, his average rate of return = 7000/50000 * 100   By rule of alligation, if the value of one of the products is 10 (cheaper) and the other is 15 (dearer) and if the two are mixed such that the average value of the mixture is 14 (mean price), then the two products have been mixed in the following ratio.   The ratio of   Cheaper product : Dearer product   (Dearer product price - mean price) : (Mean price - cheaper product price)   In our example, the cheaper product is the investment at 10%, the dearer product is the investment at 15% and the mean price is the average return of 14%.   Therefore, the amount invested @10% interest = 1/5 * 50,000 = 10,000.   Answer Rs.40,000
Answer: B
From a pack of 52 cards, 1 card is drawn at random. What is the probability that a red king is drawn?	Choose the correct choice from the following answers.
A) 1/2
B) 1/4
C) 1/13
D) 1/26
E) 1/52

Solution: The total number of cards is 52.   The number of red kings is 2.   P(red king) = 2/52 = 1/26   The answer is 1/26.
Answer: D
A person borrowed Rs.600 @ 3% per annum S.I and Rs.800 @ 4½ % per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.246. The number of years, after which the borrowed sum is to be returned, is	Choose one:
A) 2 years
B) 3years
C) 4 years
D) 5 years
E) 6 years

Solution: Let the time be x years. Then (600 *3* x)/100 + (800*9*x)/(2*100) = 24   18x+ 36x = 246 ; x = 246/54 = 4 years   Required time = 4 years   ANSWER:4 years
Answer: C
In a class exactly 10% students get 70 marks, exactly 25% get 80 marks, exactly 15% get 85 marks, exactly 25% get 90 marks and remaining get 95 marks.what is the minimum number of students in the class if the avg. of sum of marks is an even no.
Choose one
A) 20  B) 80  C) 100  D) 120  E) 200

Solution: Let total no. of students be x   (x(10*70 + 25*80 + 15*85 + 25* 90 + 25*90)/100)/ x = 86   Hence the avg is always 86 and does not depend upon the no. of students.   Hence the answer is the minimum value that is 20   20NSWER:20
Answer: A
What is the largest 4 digit number exactly divisible by 88
Choose the correct choice from the following options:
A) 9900
B) 9999
C) 9988
D) 9944
E) 9966

Solution: Explanation:   Largest 4 digit number is 9999   After doing 9999 ÷ 88 we get remainder 55   Hence largest 4 digit number exactly divisible by 88 = 9999 - 55= 
9999 - 55 = 9_944
9944   Answer: Option 9944
Answer: D
If m is a positive integer, and m/15 = 8.2, what is the remainder T when m is divided by 15? Choose the correct choice from the following.
A) A.1
B) B.2
C) C.3
D) D.4
E) E.8

Solution: If m were a multiple of 15, the quotient m/15 would be an integer. The fact that it's a decimal tells us that 15 goes into m eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let T be the remainder.   T/15 = 0.2 = 1/5   T = (15)*(1/5)= 
(15)*(1/5) = 3
3   Answer=(C.3)
Answer: C
The greatest common divisor of two positive integers is 25. If the sum of the integers is 350, then how many such pairs are possible?
Pick one
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 350 = 25 * 14   To have the GCD of two numbers to be 25, we need to split 14 into two co-prime numbers. Such pairs of numbers are: (1,13), (3,11), and (5,9).   Answer:3
Answer: C
If an amount of Rs 41,910 is distributed equally
amongst 22 persons, how much amount would each
person get?  Choose the correct choice from the following answers: A) Rs 1905 B) Rs 2000 C) Rs 745 D) Rs 765 E) None

Solution: Required amount =41910/22= 
41910/22 = 1_905
Rs 1905   Rs 1905nswer Rs 1905
Answer: A
Rajan buys an old scooter for Rs. 7400 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 8800, his gain percent is :  Choose the correct choice from the following answers:
A) 20% B) 12% C) 10% D) 5% E) None of these

Solution: Explanation :   Solution: C.P. =Rs. (7400+600) =Rs. 8000; S.P. = Rs. 9600.   Gain% = (1600*100/8000)= 
(1600*100/8000) = 20
20%.   20%nswer : 20%
Answer: A
Find the slope of the line perpendicular to the line y = (1/6)x - 7	Pick one:	A) 1	B) 2	C) -6	D) 4	E) 5

Solution: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 6. If m is the slope of the line perpendicular to the given line, then   m × (1/6) = -1   Solve for m   m = - 6   correct answer -6) -6
Answer: C
If two dies are thrown simultaneously what is the prob. of one of the dice getting face 6 ?	Choose the correct choice from the following choices.
A) 11/36 B) 1/3 C) 12/35 D) 1/36 E) 5/36

Solution: Sample space for two dice = 36   Probability of getting one of the dice 6 is,   n={(1,6)(2,6)(3,6)(4,6)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}=11   n=11   Probability = Total possibilities(n)/Sample space   P = 11/36   11/36NSWER:11/36
Answer: A
The sector of a circle has radius of 21 cm and central angle 225o. Find its perimeter?	Choose the correct option:
A) 91.5
B) 92
C) 93
D) 94
E) 124.5

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (225/360 * 2 * 22/7 * 21) + 2(21)   = 124.5 cm   Answer: Option 124.5
Answer: E
If the productivity of a brigade grows by 5% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?  Choices.
A) 0.21
B) 0.82
C) 1.155
D) 1.21
E) 1.44

Solution: B = 10-men brigade   p = increase in the productivity = 5%   Solution: B x p = B x 1.05 = 1.05B -------> the productivity of 11 men brigade   1.05B x p = 1.05B x 1.1 = 1.155B -----> the productivity of 12 men brigade   The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.155B/B = 1.155   1.155
Answer: C
Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 4, while all other numbers remain the same, what is the new average of Set S?  Pick one:  A) 6.6  B) 6.7  C) 6.8  D) 6.85  E) 6.9

Solution: Old set S - Total is avg * no of elements = 6.2*10= 
6.2*10 = 62
62   If one number is increased by 4 then total increased to  62+4= 
 62+4 = 66
66   New avg - 66/10= 6.6.   Hence answer is 6.6.
Answer: A
There are 12 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?	Choose the correct choice.
A) 12	B) 18	C) 24	D) 36	E) 48

Solution: Note that each handshake includes two people.   The total number of handshakes is  12*3/2= 
 12*3/2 = 18
18   The answer is 18.
Answer: B
A number whose fifth part increased by 4 is equal to its fourth part diminished by 10, is :
Choose the correct choice from the following options:
A) 240
B) 260
C) 270
D) 280
E) 290

Solution: Let the number be x. Then,   ((1/5)x+4)=((1/4)x−10)   <=>   x/20   <=> x = 14 * 20= 
14 * 20 = 280
280.   ANSWER :280
Answer: D
If the compound interest on a certain sum for 2 years at 12% p.a. is Rs.1590, What would be the simple interest for same rate and same period? Options:	A) Rs.1500	B) Rs.1450	C) Rs.1550	D) Rs.1650	E) Rs.1750

Solution: Let principal be P.   Then Rs.1500mount = P + 1590   Rs.1500ccording to formula, Rs.1500mount = P*[1 + 0.12]^2   Hence, we get, P+ 1590 = P*[1.12]^2   So, P + 1590 = 1.2544P   So, 0.2544P = 1590   So, P = 6250   Hence, simple interest on â�¹6250 @ 12% for 2 years = 6250*12/100*2= 
6250*12/100*2 = 1_500
1500   Rs.1500NSWER :Rs.1500
Answer: A
If in a certain sequence of consecutive multiples of 50, the median is 825, and the greatest term is 1050, how many terms that are smaller than 825 are there in the sequence?  Pick.
A) 6	B) 5	C) 8	D) 12	E) 13

Solution: Since the median is 825 we know there must be a even number of integers because 50 is not a multiple of 825.   So the list around 625 must go. 750 800 (825) 850 900 950 1000 1050   Since we know there are 5 numbers greater than 825 then there must be 5 numbers less then 825.   answer:5
Answer: B
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
Choose the correct choice from the following options:
A) 21/46
B) 25/117
C) 1/50
D) 3/25
E) 4/25

Solution: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.   Then, n(S)= Number ways of selecting 3 students out of 25   = 25C3 `   =(25 x 24 x 23)/(3 x 2 x 1)   = 2300.   n(E)= (10C1 x 15C2)   =10 x((15 x 14)/(2 x 1))   = 1050.   P(4/25) =	n(4/25)/n(S)=(1050/2300)=21/46.
Answer: E
The current of a stream runs at the rate of 5 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?	Choose the most appropriate option.
A) A)7.63 B) B)2.6 C) C)8.83 D) D)6.69 E) E)3

Solution: S = 5   M = x   DS = x + 5   US = x - 5   6/(x + 5) + 6/(x - 5) = 2   x = 8.83   Answer:8.83
Answer: C
Which of the following numbers should not be included in the set?
331, 482, 551, 263, 384, 242, 111  Select
A) 263 B) 384 C) 242 D) 111 E) None of these

Solution: Solution   In each number except 384,the product of first and third digits is the middle one. Answer 384
Answer: B
The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter Choose one
A) 16500
B) 16538
C) 27778
D) 27788
E) 27781

Solution: Explanation:   l=5.5m w=3.75m   area of the floor = 5.5 x 3.75 = 20.625 sq m   cost of paving = 800 x 20.625 = Rs. 16500   16500nswer: 16500) Rs.16500
Answer: A
In a class composed of x girls and y boys what part of the class is composed of girls
Choose the correct choice:
A) y/(x + y)
B) x/xy
C) x/(x + y)
D) y/xy
E) 1/xy

Solution: total no. of boys and girls=x+y   no. of girls=x   therefore,, x/(x+y)   ANSWER:x/(x + y)
Answer: C
If 4 persons can do 4 times of a particular work in 4 days, then, 7 persons can do 7 times of that work in? Choose the correct choice
A) 2 days
B) 3 days
C) 5 days
D) 4 days
E) 9 days

Solution: That is, 1 person can do one time of the work in 4 days.   Therefore, 7 persons can do 7 times work in the same 4 days itself.   4 days)
Answer: D
A man walking at a rate of 10km/hr crosses a bridge in 10 minutes. The length of the bridge is? Choose the correct choice from the following choices: A) 1521 B) 1492 C) 1667 D) 1254 E) 1112

Solution: Speed = 10*5/18 = 50/18 m/sec   Distance covered in 10minutes = 50/18 *10 *60 = 1667m   Answer is 1667
Answer: C
3^13 is equal to which of the following?
Choose the correct choice from the following options:
A) 1,595,423  B) 1,595,401  C) 1,595,477  D) 1,595,432  E) 1,595,409

Solution: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 3^n has a cycle of 4.   3^1 = 3   3^2 = 9   3^3 = 27   3^4 = 81   3^5 = 243   Observe that the last digit of the resultant of 3^1 and 3^5 is 3. If we continue 3^n, the last digit follows the pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, .... So, all we need look for is the last digit in the pattern.   Cycle of 4, power of 13, last digit is 3.   1,595,423nswer: 1,595,423
Answer: A
In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 33, find the number?	Choose the correct choice from the following answers
A) 12119 B) 13919 C) 13119 D) 13016 E) 12015

Solution: 13119   13119   Let the three digit numbers be 100a + 10b + c   a = b + 2   c = b - 2   a + b + c = 3b = 33 => b = 11   So a = 13 and b = 9   Hence the three digit number is: 13119
Answer: C
In the xy-plane, the point (-2, 1) is the center of a circle. The point (-2, -3) lies inside the circle and the point (4, 1) lies outside the circle. If the radius r of the circle is an integer, then r =	Choose the correct choice from the following answers:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: An easy way to solve this question will be just to mark the points on the coordinate plane.   You'll see that the distance between the center (-2, 1) and the point inside the circle (-2, -3) is 4 units   (both points are on x=-2 line so the distance will simply be  1-(-3)= 
 1-(-3) = 4
4)   So the radius must be more than 4 units.   The distance between the center (-2,1) and the point outside the circle (4,1) is 6 units   (both points are on y=1 line so the distance will simply be  4-(-2)= 
 4-(-2) = 6
6)   So the radius must be less than 6 units, which implies 4 < r < 6, thus as r is an integer then r=5.   Answer: 5.
Answer: D
If the simple interest on a sum of a money for 2 years at 5% per annum is $50 what is the compound interest on the sum of the same rate and same time  Select
A) $57.96
B) $78.89
C) $88.45
D) $51.25
E) $78.24

Solution: sum= 50*100/10= 
50*100/10 = 500
500   amount=$(500(1+10/100)^2)   =500*21/20*21/20= 
500*21/20*21/20 = 2_205/4 = around 551.25
$551.25   C.I=$(551.25-50)=$51.25   Answer ($51.25)
Answer: D
Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 3 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked? Choose the correct option
A) 1/3  B) 2/5  C) 3/7  D) 1/2  E) 4/7

Solution: The time from beginning of March to the end of September is 7 months.   If x is the average monthly tip for all months other than August then his August month tip will be 3*x   His total tip for the 7 months = 6*(average tip for the months other than August) + 3x   =9x   August tips as a fraction of total tips = 3x/9x =1/3. So 1/3nswer is 1/3
Answer: A
A man buys an article for 15% less than its value and sells it for 15% more than its value. His gain or loss percent is:  Choose the correct choice
A) no profit, no loss  B) 20% profit  C) less than 35% profit  D) more than 35% profit  E) None

Solution: Let the article be worth Rs. x.   C.P. 85% of Rs. x = Rs. 85x/100   S.P. = 115% of Rs. x = Rs. 115x/100   Gain = (115x/100 - 85x/100) = Rs. 3x/10   Gain % = 3x/10 * 100/85x * 100 = 35 5/17 % > 35%   ANSWER:more than 35% profit
Answer: D
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
Choose the correct choice from the following options:
A) Rs.3630
B) Rs.2840
C) Rs.3200
D) Rs.5600
E) Rs.5700

Solution: 6300:4200:10500   3:2:5   3/10 * 12100= 
3/10 * 12100 = 3_630
3630   Rs.3630NSWER:Rs.3630
Answer: A
60% of a number is added to 120, the result is the same number. Find the number?	Options:  A) 300  B) 277  C) 266  D) 99  E) 121

Solution: :   (60/100) * X + 120 = X   2X = 600   X = 300   300nswer: 300
Answer: A
A batch of widgets costs p + 1 dollars for a company to produce and each batch sells for p(5 – p) dollars. For which of the following values of p does the company make a profit? Choose the correct choice from the following choices:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: to make profit, selling price should be greater than cost price   p(5-p) - p-1 >0   => p^2-4*p+1<0   hence p=3   3
Answer: A
If 40% of a certain number is 160, then what is 20% of that number?	Choose the correct option.
A) 75 B) 100 C) 120 D) 30 E) 80

Solution: 80xplanation:   40% = 40*4= 
40*4 = 160
160   20%= 20*4= 
20*4 = 80
80   Answer: Option 80
Answer: E
The value of “A” varies in inverse proportion as the square of “B”. If the value of “A” is equal to 40 when “B” is equal to 12. What would be the value of “A” when “B” is equal to 24 ?  Choose the correct choice:
A) 10  B) 15  C) 20  D) 22  E) None of these

Solution: Explanation:   We have, A α 1/B2   A * B2 = K (constant)   When B = 12, A = 40 …..Given   K = 40 * (12)2 = 5760   Now, B = 24. Hence, 10 = 5760 / 576= 
5760 / 576 = 10
10   10NSWER: 10
Answer: A
A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on Conveyance. If he has $1400 left with him,find his expenditure on food and Conveyance.	Choose the correct choice:
A) $8600	B) $2400	C) $1000	D) $3000	E) $3400

Solution: Remaining Part of salary left=1-(2/5+3/10+1/8) =1 - (33/40) = 7/40   Let the monthly salary be $X   Then, 7/40 of X=$1400   X=(1400*40/7)   =$8600   $3400xpenditure on food=$(3/10*800)=$2400   $3400xpenditure on Conveyance=$(1/8*8000)= 
(1/8*8000) = 1_000
$1000   $2400 + $1000 = $3400   so the answer is option $3400) $3400 2400 +  1000= 
 2400 +  1000 = 3_400
$3400   so the answer is option $3400) $3400
Answer: E
Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months.	Choose the correct answer
A) Rs. 9009 B) Rs. 9008 C) Rs. 9002 D) Rs. 9202 E) Rs. 9001

Solution: Explanation:   P = Rs. 78000, R = 77/5 % p.a and T = 9/12 years = ¾ years   Therefore,   S.I = (P*R*T)/100   = (78000* 77/5 * ¾ * 1/100)   = Rs. 9009   Rs. 9009NSWER: Rs. 9009
Answer: A
The y intercept of a line L is 2. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6  Pick one:
A) I only
B) II only
C) III only
D) I and II
E) I and III

Solution: C) III only   The y-intercept is 2. Therefore we have y=mx+2   It is given that the slope is negative. Therefore the line must go from top left to bottom right.   i.e: the x-intercept has to be positive. That itself rules out III.   If you choose to go with the options directly, here's an approach.   y=mx+2. For the x-intercept, y=0.   i.e. mx+2=0.   We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+2 =0 would never be satisfied.   If x=6, we have 6m+2=0. A value of m=-1/3 would satisfy this equation. (ANSWER III only)
Answer: C
Find the next term in series - 25, 37, 49, 61, ?	Choose the correct choice from the following.
A) 71	B) 72	C) 73	D) 74	E) 75

Solution: Series is Increased by 12.   25 +12= 
25 +12 = 37
37   37 +12= 
37 +12 = 49
49   49 +12= 
49 +12 = 61
61   61 +12= 
61 +12 = 73
73   ANSWER:73
Answer: C
If 1st October is Sunday, then 1st November will be	Answers.
A) sunday	B) monday	C) thursday	D) friday	E) Wednesday

Solution: Given that 1st October is Sunday   Number of days in October = 31   31 days = 3 odd days   (As we can reduce multiples of 7 from odd days which will not change anything)   Hence 1st November = (Sunday + 3 odd days) = Wednesday   Answer:Wednesday) Wednesday
Answer: E
In what time a sum of money double itself at 3% per annum simple interest?	Choose the most appropriate option:
A) 33 1/9%	B) 33 1/3%	C) 332 1/3%	D) 33 9/3%	E) 13 1/3%

Solution: P = (P*3*R)/100   R = 33 1/3%   Answer:33 1/3%
Answer: B
In honor of the year 2015, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
Choose the correct choice from the following answers.
A) 18	B) 36	C) 42	D) 56	E) 58

Solution: All options other than 'E' are factors of 2015. Hence, '58' is the answer
Answer: E
Dravid has x dollars more than Gayle has, and together they have a total of y dollars. Which of the following represents the number of dollars that Gayle has?
Select the correct option:
A) (y – x)/2x	B) (y – x)/2y	C) (y – x)/2	D) 3(y – x)/2	E) 5(y – x)/2

Solution: To solve, we will set up two equations. Let's start by defining two variables.   A = number of dollars Gayle has   B= number of dollars Dravid has   We are given that Dravid has x dollars more than Gayle. We set up an equation:   B= x + A   We are next given that together they have a total of y dollars. We can set up our second equation:   A + B = y   Since we know that B = x + A, we can substitute x + A for B into the second equation A+ B = y.   Notice that, after the substitution, we will only have variables of A, x, and y. Thus, we have:   A + x + A = y   2A + x = y   2A = y – x   A = (y – x)/2   Answer : (y – x)/2
Answer: C
The y intercept of a line L is 1. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6	Select the correct option:	A) I only	B) II only	C) III only	D) I and II	E) I and III

Solution: C) III only   The y-intercept is 1. Therefore we have y=mx+1   It is given that the slope is negative. Therefore the line must go from top left to bottom right.   i.e: the x-intercept has to be positive. That itself rules out III.   If you choose to go with the options directly, here's an approach.   y=mx+1. For the x-intercept, y=0.   i.e. mx+1=0.   We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+1 =0 would never be satisfied.   If x=6, we have 6m+1=0. A value of m=-1/6 would satisfy this equation. (ANSWER III only)
Answer: C
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field? Select the correct option:
A) 54  B) 32  C) 75  D) 28  E) 11

Solution: A/8 = 8 * 8 => A = 8 * 8 * 8   x * 2x = 8 * 8 * 8   x = 16 => 2x = 32   Answer:32
Answer: B
If t is an odd integer, which of the following must also be odd?  Select the correct option:
A) 2t + 8 B) t + t C) 3t + 3 D) 2t + t E) t^2 + 1

Solution: Things to keep in mind:   Odd + odd = even   Odd + even = odd   Odd*odd = odd   Odd*even = even   On checking each option   A. 2t + 8   2t = even, 2t + 8 = even + even = even.   B. t + t   Odd + odd = even. This will be even   C. 3t + 3   3t = odd, 3t + 3 = odd + odd = even   D. 2t + t   2t = even, 2t + t = even + odd = odd   E. t^2 + 1   t^2 = odd, t^2 + 1 = odd + odd = even   Correct option: 2t + t
Answer: D
For a certain exam,a score of 42 was 5 standard deviations below mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam?
Choose the correct choice from the following options
A) 74
B) 76
C) 78
D) 58.67
E) 82.2

Solution: Mean-5SD=42   Mean+2.5SD=67   By solving above equations we get,   SD (absolute value)=3.33   Mean=58.67   ANS. 58.67
Answer: D
If M equals the sum of the odd integers from 1 to 111, inclusive, and T equals the sum of the even integers from 2 to 50, inclusive, what is the value of M + T?  Choose the correct choice from the following answers:
A) 400
B) 5550
C) 6922
D) 3786
E) 5553

Solution: Use following formulae for such problems:   Sum of evenly spaced integers = (# of integers)*(mean of integers)   # of integers = [(last - first)/2] + 1   Mean of integers = (last + first)/2   In above problem:   # of integers = [(111 - 1)/2] + 1= 56 and [(50-2)/2]+ 1 (111 - 1)/2  + 1= 
(111 - 1)/2  + 1 = 56
56 and [(50-2)/2]+ 1 = 25   Mean of integers (50-2)/2 + 1= 
(50-2)/2 + 1 = 25
25   Mean of integers= (111 + 1)/2= 
(111 + 1)/2 = 56
56 and   (50 + 2)/2= 
  (50 + 2)/2 = 26
26   Sum of integers= (56*56)= 
(56*56) = 3_136
3136 and   (25*26)= 
  (25*26) = 650
650   Thus their sum (M + T)= 3786   ANSWER:3786
Answer: D
The sum of three consecutive numbers is 87. The greatest among these three numbers is: Choose the correct choice from the following options.
A) 26 B) 28 C) 29 D) 30 E) 31

Solution: Let the numbers be x, x+1 and x+2   X+x+1+x+2=87   3x=84   X=28   Greatest number is =30   ANSWER 30 30
Answer: D