MU-NLPC/Calc-aqua_rat huggingface dataset:
The product of 4 consecutive even numbers is always divisible by:	Choose the correct choice from the following.
A) 384
B) 350
C) 400
D) 200
E) 250

Solution: The product of 4 consecutive numbers is always divisible by 4!.   Since, we have 4 even numbers, we have an additional 2 available with each number.   Now, using both the facts, we can say that the product of 4 consecutive even numbers is always divisible by,   2^4 * 4!    16 * 24= 
 16 * 24 = 384
384   384NSWER 384
Answer: A
Walking across campus, a student interviewed a group of students. 20% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?	Choose the correct choice from the following answers: A) 60% B) 50% C) 25% D) 15% E) 10%

Solution: {Total} = {finance} + {marketing} - {both} + {neither}   100 = 20 + 50 - {both} + 40   {both} = 10%.   The answer is 10%.
Answer: E
In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number R of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85? Pick one.
A) 144 B) 189 C) 234 D) 279 E) 309

Solution: Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2.   Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant.   If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279.   (10x+18x) < 85.   28x < 85, i.e. 28x <= 84 (Since number of balls cannot be in fraction). Thus, x<=3.   (45x+48x) = 93x.   Max (93x) R(45 +48 )= 
(45 +48 ) = 93
93x.   Max (93x) R= 279.   Answer is 279.
Answer: D
How many diagonals does a polygon with 23 sides have, if one of its vertices does not connect to any diagonal? Answers:
A) 201	B) 159	C) 179	D) 189	E) 209

Solution: If I calculate it using the formulae, #diagonals = n (n-3)/2209ach vertex sends of n-3 diagonals   n= 23-1 then 22*(22-3)/2= 
22*(22-3)/2 = 209
209   Correct Option:209
Answer: E
The difference between a five digit number and the number formed by reversing its digit is not a multiple of  Choose the correct choice from the following options:
A) 2
B) 4
C) 3
D) 1749
E) 5

Solution: Another approach is to TEST a number.   Let's say the original number is 12345   So, the R5V5RS5D number is 54321   The DIFF5R5NC5 = 54321-12345= 
54321-12345 = 41_976
41976   No check the answer choices   41976 is a multiple of2,3,4,1749   5 is NOT a multiple of 41976   Answer:5
Answer: E
Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/14 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? Choose the correct option: A) 21 B) 35 C) 39 D) 42 E) 65

Solution: The total number of the people in the room must be a multiple of both 7 and 14 (in order 3/7 and 5/14 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 14, which is 98.   Since, the total number of the people in the room is greater than 50 and less than 100, then there are 98 people in the room.   Therefore there are   3/7*98= 
  3/7*98 = 42
42 people in the room under the age of 21.   Answer: 42.
Answer: D
A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?	Choose the correct choice from the following answers:  A) 11  B) 88  C) 15  D) 27  E) 20

Solution: P(1 + R/100)5 = 2P => (1 + R/100)5 = 2   Let P(1 + R/100)n = 8P   => (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3   => (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.   Answer: 15
Answer: C
Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 1/2 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?	Choose the correct choice from the following choices.
A) 1/15 B) 1/5 C) 9/20 D) 1/3 E) 2/5

Solution: tot students=x   1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)   2nd year student=x/2---->maj=1/2(1/5(x/2))=1/20(x)--->non major=x/2-1/20(x)=9/20(x)   hence 9/20   9/20
Answer: C
A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of £90 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £42,000? Choose the most appropriate option:
A) £110  B) £120  C) £140  D) £160  E) £180

Solution: Explanation:   Let's say x is the amount that the manufacturer sells each unit for, then the profit per unit can be expressed as x-90. We also know that 600 units have been produced and that the total profit has to be at least £42,000.   600(x-90)≥42,000   x-90≥70   x≥160   Answer: Option £160
Answer: D
Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 55	Choose the correct choice:
A) 55
B) 6
C) 15
D) 31
E) 91

Solution: 1(result) + (1*1) = 2.   2(result) + (2*2) = 6.   6(result) + (3*3) = 15.   15(result) + (4*4) = 31.   31(result) + (5*5) = 56.   Now we are getting 56 not 55.. So 55 is the wrong number of the given.   answer : 55
Answer: A
The distance between A&B is 1540km. A person is traveling from A to B at 100km/hr started at 6AM and another person is traveling from B to A at 120km/hr and started at same time. Then at what time they meet together. Choose the correct choice:
A) 11AM
B) 1PM
C) 3PM
D) 10AM
E) 9AM

Solution: Let x hours be they will meet together   distance covered by 1st person+distance covered by 2nd person = 1540km   100x+120x = 1540   x= 7 hr   They will meet = 6AM +7hr = 1PM   Answer is 1PM
Answer: B
Favid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
Choose one.
A) 5/6*d
B) 7/3*d
C) 10/3*d
D) 7/2*d
E) 9/2*d

Solution: Favid has d books;   Jeff has d/3 books;   Paula has 2d books;   Total = d+d/3+2d=10d/3.   Answer: 10/3*d.
Answer: C
find the next term 2,5,26...	Choices
A) 27
B) 45
C) 455
D) 555
E) 677

Solution: 2   2*2+1= 
2*2+1 = 5
5   5*5+1= 
5*5+1 = 26
26   26*26+1= 
26*26+1 = 677
677   ans=677   ANSW677R:677
Answer: E
A man walking at a rate of 10km/hr crosses a bridge in 12 minutes. The length of the bridge is?	Choose the correct choice from the following answers:
A) 2000  B) 1492  C) 1667  D) 1254  E) 1112

Solution: Speed = 10*5/18 = 50/18 m/sec   Distance covered in 10minutes = 50/18 *12 *60= 
50/18 *12 *60 = 2_000
2000 m   2000nswer is 2000
Answer: A
Which of the following CANNOT be the least common multiple of two positive integers x and y	Options
A) xy	B) x	C) y	D) x + y	E) x - y^2

Solution: The least common multiple of two positive integers cannot be less than either of them. Therefore, since x - y^2 is less than x, it cannot be the LCM of a x and y.   Answer: x - y^2
Answer: E
Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?	Answers:
A) 15  B) 14  C) 17  D) 12  E) 19

Solution: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on.   15NSWER 15
Answer: A
Which of the following numbers is not prime?
Choose the correct choice from the following options.
A) 50+70
B) 150 -23
C) 100+67
D) 156-7
E) 103+36

Solution: 10 can be factored out of both 50 and 70. -->50+70= 10*(5+7). The correct answer is 50+70.
Answer: A
Ram can finish a puzzle in 3 hours and Shyam can do the same in 2 hours. Both of them finish the puzzle and get 15 candies. What is Ram’s share?
Choose the correct choice from the following choices:
A) 6	B) 7	C) 5	D) 8	E) 9

Solution: Explanation:   The question is based on efficiency to do work.   Ram can finish a puzzle in 3 hours. Shyam can finish the puzzle in 2 hours.   =>In one hour Ram can finish 1/3rd of a puzzle   =>In one hour Shyam can finish half the puzzle   6 total of 15 candies are to be shared amongst both of them   Hence Ram’s share must be = ((Work done by Ram in 1 hour)/(Work done by Shyam in one hour)+(Work done by Ram in hour))*15   => 1/3/((1/2)+(1/3))*15   => (1/3/(5/6))*15= 
(1/3/(5/6))*15 = 6
> 6/15*(15)= 
6/15*(15) = 6
>6 candies   6NSWER: 6
Answer: A
The cost of 10 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg? Choose one:
A) Rs 52.50 B) Rs 56 C) Rs 58.50 D) Rs 84 E) None of these

Solution: Explanation :   Let the required cost be Rs. x. Then,   More packets, More cost (Rs 84irect Proportion)   More weight, More cost (Rs 84irect Proportion)   Packets 10 : 27   Weight 900 : 1000 :: 28 : x   (10 x 900 x x) = (27 x 1000 x 28)   x = (27 x 1000 x 28) /10 x 900   = 84   Answer Rs 84
Answer: D
Rs.3080 were divided among Jonathan, Kevin & Dawson in such a way that John had Rs.160 more than Kevin and Dawson had Rs 120 more than John . How much was Kevinâ€™s share?  Choose one:
A) Rs.1120
B) Rs.1130
C) Rs.1140
D) Rs.1150
E) Rs.1160

Solution: Let Kevin gets Rs x. Then We can say Jonathan gets Rs (x + 160 ) and Dawson gets Rs ( x + 280) .   x + 160 + x + x + 280 = 3080   3x = 2640   x = 880 .   Kevinâ€™s share = Rs ( 880+280 ) = Rs.1160   Rs.1160
Answer: E
A furniture store bought chairs for 60% of their list price and sold them for 10% off the list price. What is their percent gain?
Choose the correct choice from the following choices:
A) 25
B) 50
C) 60
D) 75
E) 110

Solution: Cost = 60% of List Price = .6*LSale = (100-10)% of List Price = .9*LGain Ratio = (Sale - Cost) / Cost = (.9*L - .6*L) / .6*L = .3*L / .6*L = 0.50Gain Percent = 100 * Gain Ratio = 100 * 0.5= 
100 * 0.5 = 50
50%= Answer 50
Answer: B
The area of a square garden is A square feet and the perimeter is p feet. If a=2p+26.25, what is the perimeter of the garden, in feet?  Options.
A) 28
B) 36
C) 40
D) 42
E) 64

Solution: Perimeter of square = P   Side of square = P/4   Area of Square = (P^2)/16 =A   Given that A = 2P + 26.25   (P^2)/16 = 2P + 26.25   P^2 = 32P + 420   P^2 -32P -420 = 0   P^2 -42P +10 P -420 = 0   P(P-42)+10(P+42) = 0   (P-42)(P+10) = 0   P = 42 or- 10   42iscarding negative value , P = 42   Answer is 42
Answer: D
What is the greatest integer m for which the number 20!/10^m is an integer?  Choose the correct choice from the following answers
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: 10^m = 2^m*5^m.   Let's figure out how many 5's are in the prime factorization of 20!   The multiples of 5 are: 5, 10, 15, 20.   Thus 5^4 will divide 20! but 5^5 will not.   Clearly 2^4 will divide 20!   So m=4 is the largest possible integer.   The answer is 4.
Answer: B
Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next five weeks be to decrease his average weekly income to $400 over the 10-week period? Choose the correct choice from the following options.
A) $385
B) $356
C) $367
D) $376
E) $386

Solution: OFFICIAL SOLUTION:   (E) First, we need to add up the wages over the past 5 weeks: $406 + $413 + $420 + $436 + $395 = $2070.   To average $400 over 10 weeks, the salesman would need to earn: $400 × 10 406 +  413 +  420 +  436 +  395= 
406 +  413 +  420 +  436 +  395 = 2_070
$2070.   To average $400 over 10 weeks, the salesman would need to earn: $400 × 10= $4000.   Subtract $2070 from $4000 to determine how much he would need to earn, in total, over the next 5 weeks to average $400 for the 10 weeks: $4000 – $2070 = $1930.   Dividing $1930 by 5 will give us the amount he needs to earn on average over the next 5 weeks: $1930/5= 
1930/5 = 386
$386.   The correct answer is choice ($386).
Answer: E
One-sixth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/15 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?	Choose the correct choice
A) 1.8% B) 2.9% C) 4.1% D) 5.6% E) 6.4%

Solution: 1/6 of the switches are defective.   The defective switches that are not rejected are 1/5*1/6 = 1/30 = 3/90 of all switches.   The non defective switches that are sold are 5/6*14/15 = 70/90 of all switches.   The percent of switches sold that are defective is 3/73 which is about 4.1%.   The answer is 4.1%.
Answer: C
If 5 spiders make 5 webs in 5 days, then 1 spider will make 1 web in how many days?  Select 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 1:5   Webs 5:1   1 x 5 x x = 5 x 1 x 5   => x= 5   Answer is 5
Answer: C
P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 6 days. How many days more will P take to finish the work? Pick.
A) 30
B) 15
C) 18
D) 20
E) 22

Solution: Let work done by P in 1 day = p,   Work done by Q in 1 day = q,   Work done by R in 1 day = r   p + q = 1/30   q + r = 1/24   r + p = 1/20   30dding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8   => p + q + r = 1/16   => Work done by P,Q and R in 1 day = 1/16   Work done by P, Q and R in 6 days = 6 × (1/16) = 6/16 = 3/8   Remaining work = 1 = 3/8 = 5/8   Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day   = 1/16 – 1/24 = 1/48   Number of days P needs to work to complete the remaining work = (5/8) / (1/48)= 
(5/8) / (1/48) = 30
30   Option 30
Answer: A
If p and q are positive integers each greater than 1, and 17(p+1)=28(q+1), what is the least possible value of p+q?
Pick one:  A) 36  B) 42  C) 44  D) 43  E) none

Solution: 17(p+1)=29(q+1) --> (p+1)/(q+1) = 28/17 --> the least positive value of p+1 is 28, so the least value of p is 27 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is   27+16= 
  27+16 = 43
43.   Answer: 43
Answer: D
An article is bought for Rs.1000 and sold for Rs.1100, find the gain percent?  Choose the correct choice
A) 33 1/7%	B) 10%	C) 33 1/3%	D) 38 1/3%	E) 33 2/3%

Solution: 1000 ---- 100   100 ---- ? => 10%   Answer:10%
Answer: B
By selling a watch for Rs.800/-, a man loses 20% what is that watch cost price?  Pick
A) s. 600/-  B) s. 700/-  C) s. 800/-  D) s. 850/-  E) s. 1000/-

Solution: 80 % ------> 800 (80 * 10 = 640)   100 % ------>1000 (100 * 10 = 1000)   Cost price = Rs. 1000/-   s. 1000/-)
Answer: E
85% of a number is added to 24, the result is the same number. Find the number?
Choose the correct choice:
A) 257	B) 267	C) 187	D) 160	E) 122

Solution: (85/100) * X + 24 = X   3X = 480   X = 160   Answer:160
Answer: D
A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?  Select
A) 100% B) 80% C) 75% D) 66(2/3)% E) NOne

Solution: Solution: Let the CP of the article be Rs. x, since he earns a profit of 20%, hence SP= X + 20% of X = 1.2x.   It is given that he incurs loss by selling 16 articles at the cost of 12 articles [loss = (16-12)/16 = 25%]   His selling price = SP - 25% of SP = SP*0.75;   Hence, SP*0.75 = 1.2X.   Or, SP = (1.2*x/0.75) = 1.6X.   This SP is arrived after giving a discount of 20% on MP.   Let MP = Y.   Y - 20% of Y = SP   0.80Y = 1.6X.   Y = 2X.   It means that the article has been marked 100% above the cost price. Or Marked Price was twice of cost price.   100%nswer: Option 100%
Answer: A
At present, the ratio between the ages of Shekhar and Shobha is 4:3. After 6 years, Shekhar's age will be 26 years. Find out the age of Shobha at present?
Answers
A) 10 B) 12 C) 14 D) 15 E) 20

Solution: After 6 years, Shekhar's age will be 26 years   Therefore, Present age of Shekhar =26−6=20   Let present age of Shobha =x   Then,   20x=43x=20×34=15   Answer is 15.
Answer: D
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?  Choose the correct choice.
A) 177	B) 156	C) 199	D) 750	E) 155

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 25 è x = 25 * 60 / 2= 
25 * 60 / 2 = 750
750   Answer:750
Answer: D
P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
Choose the correct answer.
A) 5  B) 5 3/5  C) 5 5/7  D) 6  E) None

Solution: P can complete the work in (12 x 8) hrs. = 96 hrs.   Q can complete the work in (8 x 10) hrs. = 80 hrs.   P's1 hour's work =	1	and Q's 1 hour's work =	1	.   96	80   (P + Q)'s 1 hour's work = 1	+	1 =	11	.   96	80	480   So, both P and Q will finish the work in 480 hrs.   11   Number of days of 8 hours each = 480	x	1 =	60	days = 5	5	days.   11	8	11	11   Option 5 5/7
Answer: C
A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Choose the correct option:	A) 21	B) 16	C) 18	D) 12	E) 112

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 280 * 2/35= 
280 * 2/35 = 16
16 sec.Answer: 16
Answer: B
Let a be a positive integer. If e is divisible by 2^a and e is also divisible by 3^(2a), then it is possible that e is NOT divisible by
Choose the correct choice from the following choices
A) 6 B) 3 × 2^a C) 2 × 3^(2a) D) 6^a E) 6^(2a)

Solution: Since, e is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1   Only for 6^(2a), 6^(2a) doesn't satisfy, if a = 1 and e=18, it is not divisible by 6^2 (i.e 36)   Hence answer is 6^(2a)
Answer: E
If 0.20: x : : 4 : 2, then x is equal to	Choose the most appropriate option
A) 0.2
B) 0.3
C) 0.1
D) 0.5
E) None

Solution: Sol.   (x×4) = (0.20×2) ⇒ x = 0.4/4 = 0.1.   Answer 0.1
Answer: C
Today Mary’s father is four times as old as Mary. Ten years ago, he was 14 times as old. How old is Mary today?	Pick one.
A) 7
B) 9
C) 11
D) 13
E) 15

Solution: 13ad's age = 4M   14*(M-10) = 4M-10   10M = 130   M = 13   The answer is 13.
Answer: D
A father is two times as old as his daughter. 2 decades ago, the age of the father was 12 times the age of the daughter. The current age of the father is Choose one
A) 44 years B) 43 years C) 42 years D) 48 years E) 49 years

Solution: A   44 years   Let daughter’s age = A.   Then father’s age = 244 years   12 (44 years – 20) = (244 years – 20)   1044 years = 220   44 years = 22   Father’s current age = 44 years.
Answer: A
John,Anny, Markov, David and Philip line up at a theatre ticket window. In how many ways can they arrange themselves so that philip is second in line from the window?  Choose the correct answer:
A) a 24  B) b 12  C) c 9  D) d 6  E) e 3

Solution: A   Philip's position is fixed. Now we need to arrange all others around philip.   There are 4x3x2x1= 24 ways to arrange four people.
Answer: A
A bat is bought for Rs.430 and sold at a gain of 20% find its selling price
Choose the correct choice from the following answers:	A) s.430/-	B) s.480/-	C) s.400/-	D) s.516/-	E) s.616/-

Solution: 100 % ------> 430   120 % ------> 430*120/100   Selling price = Rs.516   s.516/-
Answer: D
Average of all prime numbers between 30 to 50  Choose the correct choice from the following answers:
A) 37 B) 37.8 C) 39 D) 39.8 E) None of these

Solution: Explanation:   Prime numbers between 30 and 50 are:   31, 37, 41, 43, 47   Average of prime numbers between 30 to 50 will be   (31+37+41+43+475)=1995=39.8   Answer: Option 39.8
Answer: D
Water tax is increased by 40% but its consumption is decreased by 40%. The increase or decrease in the expenditure is? Pick one:
A) 16% decrease
B) 16% increase
C) 8% decrease
D) 8% increase
E) None of these

Solution: Since Tax x Consumption = Expenditure .   Therefore, Net % change in expenditure   = ( x + y + xy/100) %   = [40 - 40 + (40 x - 40)/100]% or -16%.   Therefore, expenditure decreased by 16%.   16% decreaseNSWER:16% decrease
Answer: A
The speed of light is approximately 93 * 10^5 miles per second. This approximate speed is how many miles per hour?  Choose the correct choice from the following options:	A) 3,35 * 10^8	B) 70 * 10^7	C) 11 * 10^8	D) 16 * 10^8	E) 70 * 10^8

Solution: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.   (.93*10^5)*3600 = (.93*10^5)*(3.6*10^3) = some number*10^8...   The key is realizing that thesome numberhas to be bigger thatn .93(because .93*3.6), and the only answer that fits that is 3,35 * 10^8
Answer: A
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?	Choose the correct choice from the following answers
A) 30 kmph
B) 10 kmph
C) 5 kmph
D) 25 kmph
E) 30 kmph

Solution: Explanation:   US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30 kmph   30 kmphnswer: 30 kmph
Answer: A
Bernice's income is 70 percent more than Cathy's income, and Cathy's income is 65 percent less than Camilla's income. What percent of Camilla's income is Bernice's income?
Choose the correct choice from the following answers.
A) 54.5%
B) 52.5%
C) 59.5%
D) 51.5%
E) 55.5%

Solution: Camilla's income = 100 (assume);   Cathy's income = 35 (65 percent less than Camilla's income);   Bernice's income = 59.5 (70 percent more than Cathy's income).   Thus, Bernice's income (59.5) is 59.5% of Camilla's income (100).   Answer: 59.5%
Answer: C
A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7,8}. If no digit may be repeated and each password must be at least 7 digits long, how many passwords are possible?
Choices:
A) 7! + 8!  B) 2 x 8!  C) 7! x 8!  D) 15!  E) 16!

Solution: If we choose the 8 different digits then they can be arranged in 8! ways.   The number of possible 7-digit passwords is 8*...*2 = 8!   The total number of passwords is 8! + 8! = 2*8!   The answer is 2 x 8!.
Answer: B
In baseball, the batting average is defined as the ratio of a player’s hits to at bats. If a player had anywhere from 6 to 9 at bats in a recent game and had anywhere from 4 to 5hits in the same game, the player’s actual batting average for that game could fall anywhere between	Select: A) 0.25 and 1.50 B) 0.25 and 0.75 C) 0.30 and 1.00 D) 0.30 and 0.50 E) 0.56 and 0.66

Solution: Average Range = Hits to Bats i.e 4/9 to 5/6 = 0.44 to 0.83   Answer: 0.30 and 1.00
Answer: C
Q, B, C are three consecutive positive integers (Q>B>C). What is the value of the expression 2Q +B +3C? Options.
A) 6A+7. B) 5A+1. C) 5A-1. D) 6A-5. E) 6Q-7.

Solution: => Q+Q+(Q-1)+3(Q-2)   Ans E. 6Q-7.
Answer: E
At the end of a business conference the 18 people present all shake hands with each other once. How many handshakes will there be altogether ?
Choose the correct choice from the following options.
A) 20	B) 45	C) 153	D) 90	E) 95

Solution: number of handshakes = 181532= 18*17/2= 
18*17/2 = 153
153   ANSWER:153
Answer: C