MU-NLPC/Calc-aqua_rat huggingface dataset:
A man borrowed Rs 24000 from two money lenders. For one loan, he paid 15% per annum and for the other 18% per annum. At the end of one year, he paid Rs 4050. How much did he borrow at each rate ? Choose the correct option:
A) Rs.16000 B) Rs.12000 C) Rs.15000 D) Rs.13000 E) Rs.18000

Solution: Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x).   {(x * 15 * 1)/100 } + { [(24000 – x) * 18 * 1]/100 } = 4050   or 15 x + 432000 - 18x = 405000 or x = 9000.   Money borrowed at 15% = Rs 9000 .   Money borrowed at 18% = Rs 15000.   answer :Rs.15000
Answer: C
How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane? Choose the correct choice from the following.
A) 03  B) 4  C) 5  D) 1  E) 7

Solution: You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines.   AB , AC   BA , BC   CA , CB   There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB.   The lines are: AB, BC and AC ; 3 lines only.   So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important.   03nswer:03
Answer: A
a locker opened by combination of 4 keys.a man have four key and he know that 3rd no. key will be placed at first key hole but don't know about rest.so tell me maximum no. of attempt he will make to open locker.  Pick:
A) 6 B) 8 C) 10 D) 5 E) 4

Solution: as no. 3rd key position get fixed.so we have to calculate total no. of configuration of rest three key.   which is permutation of three item,3P3=3!=6   answer 6
Answer: A
A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 5 characters in length. This year, it added the option of creating passwords having 6 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 72 unique alphanumeric case sensitive characters.	Choose the correct option.
A) 63^4 B) 62^5 C) 72^4 * 73 D) 73(62^4) E) 73(62^6)

Solution: Total number of passwords = number of 5 character password +number of 6 character password   = 72^4 + 72^5 (Since there is no limitation on repetition , each character can be chosen in 72 ways )   =72^4(1+ 72)   =72^4 * 73   Answer 72^4 * 73
Answer: C
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Select:
A) 228
B) 2197
C) 666
D) 100
E) 281

Solution: A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.Answer: 100
Answer: D
A man is 25 years older than his daughter. In two years, his age will be twice the age of his daughter. The present age of his daughter is:	Pick:  A) 20  B) 21  C) 22  D) 23  E) 24

Solution: Let the daughter's present age be x years. Then, man's present age = (x + 25) years.   (x + 25) + 2 = 2(x + 2)   x + 27 = 2x + 4   x = 23.   Answer:23
Answer: D
In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters?
Choose the correct choice from the following:
A) 125.5 meters
B) 126.5 meters
C) 127.5 meters
D) 128.5 meters
E) None of these

Solution: Explanation:   When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters.   Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8= 
6300/8 = 1_575/2 = around 787.5
787.5 meters.   So, in a race of 1000 meters, A beats C by   (1000 - 787.5)= 
  (1000 - 787.5) = 212.5
212.5 meters to C.   So, in a race of 600 meters, the number of meters by Which A beats C= (600 x 212.5)/1000 = 127.5 meters.   Answer: 127.5 meters
Answer: C
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?	Choose the correct choice from the following answers:
A) 724 m
B) 704 m
C) 287 m
D) 278 m
E) 927 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 500 * 2 * 22/7 * 22.4= 
500 * 2 * 22/7 * 22.4 = 70_400
70400 cm= 704 m   Answer:704 m
Answer: B
P is three times as old as Q. In 11 years, P will be twice as old as Q. How old was P three years ago?
Options:
A) 21  B) 24  C) 27  D) 30  E) 33

Solution: P = 3Q so Q = P/3   P+11 = 2(Q+11) = 2(P/3+11)   P/3 = 11   P = 33   Three years ago, P was 30.   The answer is 30.
Answer: D
A can do a piece of work in 12 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Choices:
A) 11 2/5 B) 10 2/0 C) 10 2/3 D) 10 2/1 E) 11 1/3

Solution: 2/12 + 4/15 + x/20 = 1   x = 34/3 = 11 1/3 Answer: 11 1/3
Answer: E
Two pipes A and B can fill a tank in 10hour and 15 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?  Choose the correct choice.
A) 2hrs B) 6hrs C) 5hrs D) 4hrs E) 1hr

Solution: Part filled by A in 1 hour = 1/10   part filled by B in 1 hour = 1/15   Part filled by A+B in 1 hour = 1/10 + 1/15 = 1/6   Both the pipes will together will fill the tank in 6 hours.   Answer is 6hrs
Answer: B
How many seconds will a 800 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?  Choose the correct option
A) 26 sec
B) 32 sec
C) 13 sec
D) 48 sec
E) 56 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 800 * 3/50= 
800 * 3/50 = 48
48 sec.   Answer:48 sec
Answer: D
At a certain health club, 30 percent of the members use both the pool and sauna, but 25 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?  Choose the correct choice from the following choices.
A) 33 1/3%	B) 40%	C) 50%	D) 62 1/2%	E) 56%

Solution: P = pool S = sauna   given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x   25% of (70-x) = x => 17.5 - 0.25x = x => x = 14% so only P = 70 -x = 56%   Answer 56%
Answer: E
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:	Choose the correct choice from the following choices:
A) 18  B) 24  C) 42  D) 81  E) 83

Solution: Let the two digit number is 10x+y   Product of the digits x*y=8   10x+y+18=10y+x   on solving this we get X-y=-2   x+y=6   by solving the above two equations we get x=2 and y=4   therefore the digit is   10*2+4= 
  10*2+4 = 24
24   ANSWER:24
Answer: B
Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article? Choose the correct choice from the following.
A) 15000  B) 15029  C) 26882  D) 82976  E) 26717

Solution: Let the CP be Rs. x.   Had he offered 10% discount, profit = 8%   Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x   = 18000 - 10/100(18000)   = 18000 - 1800   = Rs. 16200   => 1.08x = 16200   => x = 15000   15000nswer:15000
Answer: A
The average weight of 16 children in a class is 50.25 kg and that of the remaining 8 children is 45.15 kg. Find the average weights of all the children in the class.	Choose the correct choice
A) A)48.55
B) B)49
C) C)51
D) D)61
E) E)62

Solution: Required average   = (50.25 x 16 + 45.15 x 8)/(16 + 8)   = (804 + 361.20)/24   = 1165.20/24= 
1165.20/24 = 48.55
48.55kg   48.55nswer is 48.55
Answer: A
The price of a microchip declines by 67 percent every 6 months. At this rate, approximately how many years will it take for the price of an $81 microchip to reach $1?
81- 67% * 81 = 27 approx
27 - 0.67*27 = 9 approx
9- 0.67*9 = 3 approx
3-0.67*3= $1 approx	Select:
A) 1.5 years
B) 2 years
C) 3 years
D) 13 years
E) 13.5 years

Solution: not sure whether you like this:   81 - (81 x 67%)/3 = 81 - (81 x 2) / 3 = 27 = 81 / 31 = 81 / (3x3x3x3) = 81 / 3^4   so the time = 4 x 6 months = 24 months or 2 years. answer is 2 years
Answer: B
Set A consists of the integers from 4 to 17, inclusive, while set B consists of the integers from 6 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?
Choose the correct choice:
A) 5  B) 7  C) 8  D) 9  E) 12

Solution: A={4,5,6,7,8,9,10,11,12,...17}   B={6,7,8,9,10,11,12...,20}   Thus we see that there are 12 distinct integers that are common to both. 12 is the correct answer.
Answer: E
Convert 0.32 in to a vulgar fraction ?	Options:
A) 8/25
B) 16/50
C) 17/50
D) 19/50
E) None

Solution: 8/25nswer   0.32 = 32/100 = 8/25   Correct Option: 8/25
Answer: A
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
Choices:
A) 240 B) 99 C) 278 D) 277 E) 128

Solution: (3*8 + 2*4):(4*8 + 5*4)   8:13   8/21 * 630= 
8/21 * 630 = 240
240   240nswer: 240
Answer: A
The ratio of the radius of two circles is 2: 5, and then the ratio of their areas is?
Pick
A) 4:25
B) 2:9
C) 1:9
D) 3:7
E) 3:4

Solution: r1: r2 = 2: 5   Î r1^2: Î r2^2   r1^2: r2^2 = 4:25   4:25nswer: 4:25
Answer: A
For any number y, y* is defined as the greatest positive even integer less than or equal to y. What is the value of 7.2 – 7.2*? Choose the correct choice from the following answers:	A) 1.2	B) 0.2	C) 1.8	D) 2.2	E) 4.0

Solution: Since y* is defined as the greatest positive even integer less than or equal to y, then 7.2* = 6 (the greatest positive even integer less than or equal to 7.2 is 6).   Hence, 7.2 –7.2* = 7.2 - 6= 
7.2 - 6 = 1.2
1.2   1.2nswer: 1.2.
Answer: A
B @ K I 9 D Â© 5 2 T $ M 4 E J # U R 1 A Î´ K 5 W 6 % F Q 7 H P 8 Z
Which of the following is the ninth to the right of the twentieth element from the right end of the above arrangement? Select the correct option: A) 9 B) 7 C) $ D) 5 E) None of these

Solution: Explanation:   5 is the ninth to the right of the twentieth element from the right end of the above arrangement   ANSWER IS 5
Answer: D
10^222 ÷ 10^220 = ?  Answers
A) 10  B) 1000  C) 100  D) 10000  E) 100000

Solution: 10^222 ÷ 10^220 = 10^(222 - 220) = 10^2 = 100   Answer is 100
Answer: C
Statements: Government has spoiled many top ranking financial institutions by appointing bureaucrats as Directors of these institutions.
Assumptions:
1) Government should appoint Directors of the financial institutes taking into consideration the expertise of the person in the area of finance.
2) The Director of the financial institute should have expertise commensurate with the financial work carried out by the institute.  Options
A) Only conclusion I follows  B) Only conclusion II follows  C) Either I or II follows  D) Neither I nor II follows  E) Both I and II follow

Solution: According to the statement, Government has spoiled financial institutions by appointing bureaucrats as Directors. This means that only those persons should be appointed as Directors who are experts in finance and are acquainted with the financial work of the institute. So, both I and II follow.   Both I and II follow
Answer: E
A train passes a man standing on the platform. If the train is 180 meters long and its speed is 36 kmph, how much time it took in doing so?
Choices: A) 15 sec B) 18 sec C) 19 sec D) 28 sec E) 16 sec

Solution: D = 180   S = 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 180/10= 
180/10 = 18
18 sec   Answer:18 sec
Answer: B
A startup company which received a government loan is expected to make a monthly payment till it repays a total of $1093500. Every month it is expected to triple the amount it paid the previous month. The payment for the first month is $500.	Choose the correct choice from the following options:
A) 6 B) 7 C) 9 D) 10 E) 5

Solution: First payment--$500   Total amount to be repaid--$1093500   First month payment--$500   Second month payment--$500*3=$4500   Third month payment--$4500*3=$13500   Fourth month payment--$13500*3 -- 4500*3= 
 -- 4500*3 = 13_500
$13500   Fourth month payment--$13500*3=$40500   Fifth month payment--$40500*3  -- 13500*3= 
  -- 13500*3 = 40_500
$40500   Fifth month payment--$40500*3=$121500   Sixth month payment--$121500*3 -- 40500*3= 
 -- 40500*3 = 121_500
$121500   Sixth month payment--$121500*3=$364500   Seventh month payment--$364500*3 -- 121500*3= 
 -- 121500*3 = 364_500
$364500   Seventh month payment--$364500*3=$1093500   Answer is 7-- 364500*3= 
-- 364500*3 = 1_093_500
$1093500   Answer is 7
Answer: B
Dave can answer each problem on a certain test in 6 minutes. Michael
can answer each problem in 1 minute. Suppose Michael rests for two
hours in the middle of answering the problems but Dave works straight
through the test without stopping. Suppose further that they nish
the test at the same time. How long did it take Dave to answer all the
problems?  Choose one:
A) 2 hours and 10 minutes
B) 2 hours and 12 minutes
C) 2 hours and 15 minutes
D) 2 hours and 18 minutes
E) 2 hours and 24 minutes

Solution: Let n be the number of problems on the test. Then Dave took 6n minutes   to complete the test and Michael took 2 hours and n minutes (i.e., 120 + n minutes) to   complete the test. Therefore, 6n = 120 + n which implies that n = 24. Since the amount   of time to complete the test was the same for Dave and Michael, it took Dave 2 hours and   24 minutes to answer all the problems   correct answer 2 hours and 24 minutes
Answer: E
Frances can complete a job in 12 hours, and Joan can complete the same job in 9 hours. Frances starts the job at 9 a.m., and stops working at 5 p.m. If Joan starts working at 5 p.m. to complete the job, at what time is the job finished?	Select
A) 6 p.m. B) 7 p.m. C) 8 p.m. D) 10 p.m. E) 12 p.m.

Solution: Let the total work be 24 units.   Frances can complete 2 units/hr   Joan can complete 2.67 units/hr   Work done by Frances in 8 hours is 16 units ; work left for Joan is 8 units ( 24 - 16)   Time required by Jones to complete the remaining work will be 8/2.67 => 3 hours   Given Jones starts at 5PM , so she would complete the work at 8 PM   Answer will be (8 p.m.)
Answer: C
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?	Answers
A) 11	B) 88	C) 25	D) 88	E) 21

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (100 - 75)= 
(100 - 75) = 25
25 points to 25.Answer: 25
Answer: C
If P is a prime number greater than 100, what is the remainder when P^2 is divided by 4.
Choose the correct choice from the following choices.
A) 4
B) Cannot be determined
C) 2
D) 3
E) 1

Solution: take square of any prime number   remainder will be 1   Ans 1
Answer: E
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 the Deepak? Answers:  A) 15  B) 20  C) 18  D) 22  E) 35

Solution: Let the present age of 15run and Deepak be 4x and 3x   4x+6 = 26   4x = 20   x = 5   Deepak's age = 3x = 15 years   15nswer is 15
Answer: A
In what time will a train 180 meters long cross an electric pole, if its speed is 154 km/hr Choose the correct option.
A) 5 seconds
B) 4.3 seconds
C) 3 seconds
D) 2.5 seconds
E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 154*(5/18) = 42 m/sec   Time = Distance/speed   = 180/42 = 4.3 seconds   Option 4.3 seconds
Answer: B
If (A-B-C+D = 13) and (A+B-C-D = 9), what is the value of (B-D)^2? Choose the correct answer: A) 4. B) 8. C) 12. D) 16. E) 64.

Solution: EQ1: 4. - B - C + D = 13   EQ2: 4. + B - C - D = 9   (1) Subtract EQ1 from EQ2   4. - B - C + D = 13   - 4. +B - C - D = 9   ------------------------   -2B + 2D = 4   (2) Simplify   -B + D = 2   B - D = -2   (B-D)^2 = (-2)^2 = 4   My answer: 4.
Answer: A
The least number which when divided by 3, 4, 5 and 6 leaves a remainder 6, but when divided by 9 leaves no remainder, is Options: A) 117 B) 126 C) 252 D) 336 E) None of these

Solution: Explanation:   L.C.M of 3, 4, 5, 6 = 60   therefore Required Number is of the form 60k+6.   Least value of k for which (60k+6) is divisible by 9 is k = 2   therefore Required Number = (60 x 2+6)=126.   Answer: 126
Answer: B
In how many ways can the letters of the word EMULATION be arranged such that all the vowels always appear together? Pick
A) 9! B) 9!*4! C) 5!*4! D) 9!*5! E) 5!*5!

Solution: The 9 letters can be grouped into 4 consonants and one set of 5 vowels.   The number of ways to arrange 5 units is 5!   Then, for each arrangement, the 5 vowels can be arranged in 5! ways.   The total number of arrangements is 5!*5!   The answer is 5!*5!.
Answer: E
Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 12 phone numbers by using the readable digits followed by 12 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?	Choose one.
A) 1/9  B) 10/243  C) 2/45  D) 10/271  E) 1/1000000

Solution: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).   If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).   P = 12/(9*9*3+9*3) = 2/45.   Answer: 2/45.
Answer: C
If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 25 percent, how much would she earn per week?	Choose the correct answer:
A) $374	B) $382	C) $385	D) $392	E) $375

Solution: (348/116)125 =375   In this case long division does not take much time.   (348/116)= 
(348/116) = 3
3   3*125= 
3*125 = 375
375(300+75)   Answer $375
Answer: E
If the cost price of 10 articles is equal to the selling price of 20 articles, what is the % profit or loss made by the merchant?  Choose the correct choice from the following choices.
A) 25% loss
B) 25% profit
C) 20% loss
D) 20% profit
E) 50% loss

Solution: Let the cost price of 1 article be $1.   Therefore, cost price of 10 articles = 10 * 1= 
10 * 1 = 10
$10   The selling price of 20 articles= cost price of 10 articles = $10.   Now, we know the selling price of 20 articles. Let us find the cost price of 20 articles.   Cost price of 20 articles = 20 * 1= 
20 * 1 = 20
$20.   Therefore, profit made on sale of 20 articles= Selling price of 20 articles - cost price of 20 articles   = 10 - 20 = -$10.   As the profit is in the negative, the merchant has made a loss of $10.   Therefore, % loss = loss/cp * 100   % loss = -10/20 * 100 = 50% loss.   50% loss
Answer: E
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 56 years now, the son's age 4 years back was: Choose the correct choice from the following: A) 12 years. B) 24 years. C) 17 years. D) 16 years. E) 19 years.

Solution: Let the son's present age be x years. Then, (56 - x) = x   2x = 56.   x = 28   Son's age 4 years back (28- 4)= 
(28- 4) = 24
24 years.   ANSWER :24 years.
Answer: B
A container holding 15 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution?  Options
A) 2:5  B) 3:7  C) 3: 5  D) 4:7  E) 7:16

Solution: Container 1 has 15 ounces in the ratio 1:2   or,   x+2x=15 gives x(alcohol)=5 and remaining water =10   container 2 has 8 ounces in the ratio 1:3   or,   x+3x=8 gives x(alcohol)=2 and remaining water =6   mixing both we have alcohol=5+2 and water =10+6   ratio thus alcohol/water =7/16   Answer 7:16
Answer: E
After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
Choose the most appropriate option: A) 1/2 B) 6/7 C) 0 D) 1/12 E) 1/55

Solution: Explanation :   Answer is Zero. Question is asking whether there is any chances of one letter getting inserted in an improper envelope, but there can-not be onr case as if one gets improper there is another letter who will be inserted in the improper envelope too...   Hence C is the answer.   Answer : 0
Answer: C
SID has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If SID needs to pay exactly $128, what is the least number of bills he will need to use?	Pick:
A) 16
B) 121
C) 45
D) 456
E) 57

Solution: 128 is the total sum of money.   as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils   128-120= 
128-120 = 8
8   so now we need to get 8 from either 5 dollar bills or 1 dollar bills   8 - 5 (use only 1 5 dollar bill)= 3   so we can get 3 from using 3 $1 bills.   Hence 16 ( 12+1+3 )   16NSWER IS 16
Answer: A
How many positive integers between 1 and 400 are there such that they are multiples of 25? Choose the correct answer.
A) 12
B) 13
C) 16
D) 15
E) 11

Solution: Multiples of 25 = 25,50,75,-----400   Number of multiples of 25 => 25*16= 
25*16 = 400
400   Answer is 16
Answer: C
If A:B is 7:5, B:C is 3:4 and C is 30 then what is the value of A?  Choose the correct choice from the following options.
A) 31.5  B) 25.5  C) 32.5  D) 33.8  E) 35.7

Solution: 31.5/B=7/5,   B/C=3/4,C=30   B=90/4   431.5/90=7/5   31.5=630/20   31.5=31.5   31.5NSWER:31.5
Answer: A
The sum of four consecutive even numbers is 140. What would be the largest number?  Select
A) 33	B) 38	C) 70	D) 123	E) 12

Solution: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)   Their sum = 8x - 4 = 140 => x = 18   Smallest number is: 2(x +1) = 38.   Answer: 38
Answer: B
Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L Choose the correct choice
A) 1/3.	B) 3.	C) 2.	D) 1/2.	E) 6.

Solution: Difference = Average   H - L = (H + L)/2,   Solving for H/L gives 3. A quick check, H be 18 and L be 6, 18 - 6 = (18 + 6)/2   3.
Answer: B
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?  Select
A) 1/26  B) 1/07  C) 1/22  D) 1/29  E) 1/21

Solution: Let E1 be the event of drawing a red card.   Let E2 be the event of drawing a king .   P(E1 ∩ E2) = P(E1) . P(E2)   (1/26s E1 and E2 are independent)   = 1/2 * 1/13 = 1/26   1/26nswer:1/26
Answer: A
The purchase price of an article is $48. In order to include 25% of cost for overhead and to provide $12 of net profit, the markup should be	Choices:	A) 50%	B) 25%	C) 35%	D) 40%	E) 45%

Solution: Cost price of article = 48$   % of overhead cost = 25   Net profit = 12 $   We need to calculate % markup   Net profit as % of cost price = (12/48)*100= 
(12/48)*100 = 25
25%   Total markup should be= 25 + 25= 
25 + 25 = 50
50%   50%nswer 50%
Answer: A