MU-NLPC/Calc-aqua_rat huggingface dataset:
Anil invested a sum of money at a certain rate of simple interest for a period of five years. Had he invested the sum for a period of eight years for the same rate, the total intrest earned by him would have been sixty percent more than the earlier interest amount. Find the rate of interest p.a.  Choose the correct choice from the following answers:	A) 5352	B) 5355	C) 2789	D) 2689	E) 2688

Solution: Let the sum lent by Manoj to Ramu be Rs.P.   Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100   = Rs.824.85   27P = 62100   = 82485   P = (82485 + 62100)/27 = 3055 + 2300   = Rs.5355   Answer: 5355
Answer: B
From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer?  Choices:
A) a) 1/21
B) b) 35/2
C) c) 4/21
D) d) 2/7
E) e) 3/7

Solution: Total number of ways to choose 5 out of 9 = 9C5 = 144.   Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520.   P = favorable/total = 2520/144 = 35/2.   Answer: b) 35/2.
Answer: B
A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Pick one:
A) 6	B) 9	C) 7	D) 5	E) 1

Solution: 45*12 : 54*x = 2: 1   x = 5   12 -5= 
12 -5 = 7
7   Answer: 7
Answer: C
W is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can W be?  Choose the correct option.
A) 300,000  B) 349,999  C) 350,000  D) 399,999  E) 400,000

Solution: W 1,000,000-300,000=700,000 integers   700,000/2= 350,000 even integers.   350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.   350,001-2=349,999   349,999
Answer: B
A rainstorm increased the amount of water stored in State J reservoirs from 125 billion gallons to 150 billion gallons. If the storm increased the amount of water in the reservoirs to 80 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
Choose the correct choice from the following answers:	A) 9	B) 14	C) 25	D) 30	E) 44

Solution: After the reservoir is filled to 150 gallons the amount of water is at 80% - which means that 20% of the reservoir is empty. To figure out what that 20% is approximate: 150 gallons /80 percent = x gallons /20 percent , therefore, x = 37.5 gallons , answer choices A,B,C,D are below 37.5 . We know that the reservoir must be short more than 37.5 gallons, therefore, the only possible choice is 44.
Answer: E
If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE	Pick one.
A) 110 B) 114 C) 118 D) 120 E) 122

Solution: Total no'of arrangements 5P5 = 5! = 120   no'of arrangements start with AE = 1 × 6 = 6   no'of arrangements which do not start with AE = 120 - 6= 
120 - 6 = 114
114.   114)
Answer: B
At a recent small town election for mayor a total of 967 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place?  Choose the correct answer:
A) 134 B) 178 C) 196 D) 166 E) 194

Solution: The number of votes the winning candidate received was   967 + 53 + 79 + 105	/4= 301.   The fourth place received 301 – 105 = 196.   196
Answer: C
Find the value of x from the below equation? : x^2+5x+4 = 0 Choose the correct choice from the following options:  A) 1  B) -3  C) 3  D) 2  E) 0

Solution: a = 1, b = 5, c = 4   x1,2 = (-5 Â± âˆš(5^2 - 4Ã—1Ã—4)) / (2Ã—1) = (-5 Â± âˆš(25-16)) / 2 = (-5 Â± 3) / 2   x1 = (-5 + 3)/2 = -2/2 = -1   x2 = (-5 - 1)/2 = -6/2 = -3   -3
Answer: B
In a sequence of 39 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 281, what is the smallest term in the sequence?  Choose the correct answer:
A) 2  B) -2  C) 0  D) 18  E) 6

Solution: Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term.   An = 281 + (39- 1)*(-7)   An = 281 - 266= 
281 - 266 = 15
15   18
Answer: D
Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.
Choose the correct choice from the following choices:
A) 20%	B) 10%	C) 40%	D) 50%	E) 60%

Solution: Explanation:   Let the sum be x   Simple interest on x for 2 years = Rs.2000   Simple interest = PRT/100   2000 = x × R × 2100   ⇒ xR = 100000 --- (1)   40%ompound Interest on x for 2 years = 2400   P(1+R/100)T−P=2400   x(1+R/100)2 − x = 2400   x(1+2R/100 + R2/10000) − x = 2400   x(2R/100 + R2/10000) = 2400   2xR/100 + xR2/10000 = 2400 --- (2)   Substituting the value of xR from (1) in (2) ,we get   (2 × 100000)/100 + (100000×R)/10000 = 2400   2000 + 10R = 2400   10R = 400R = 40%   Answer: Option 40%
Answer: C
A man sells a horse for Rs.600 and loses something, if he had sold it for Rs.720 , his gain would have been double the former loss. Find the cost price of the horse?
Options:
A) 27
B) 98
C) 27
D) 40
E) 71

Solution: CP = SP + 1CP = SP - g   600 + x = 720 - 2x   3x = 120 => x = 40   Answer:40
Answer: D
In what ratio must a grocer mix rice worth Rs.60 a kg and Rs.65 a kg.So that by selling the mixture at Rs. 68.20 a kg, He may gain 10%?
Answers:
A) 1:2
B) 3:2
C) 4:5
D) 1:3
E) 1:5

Solution: S.P of 1kg mix = RS.68.20,   Gain = 10% C.P of 1kg mix =Rs.(100/110 x 68.20) =Rs.62 = 3 : 2   ANSWER 3:2
Answer: B
A and B enter into partnership with capitals in the ratio 3 : 4. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 4. Find how long B remained in the business?
Choose the correct choice from the following.
A) 9 months	B) 8 months	C) 7 months	D) 6 months	E) None of these

Solution: Initially A’s investment = 3x and B’s investment = 4x   Let B remain in the business for ‘n’ months.   ⇒ 3x × 10 : 4x × n = 5 : 4   ∴ 3x × 10 × 4 = 4x × n × 5   ⇒ n = 6   Answer 6 months
Answer: D
A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 6 miles per day and it will take them two days, how many miles long is the route down the mountain?  Choose the correct choice from the following answers:	A) 16	B) 17	C) 18	D) 19	E) 20

Solution: On the way down, the rate is  1.5*6= 
 1.5*6 = 9
9 miles per day.   The distance of the route down the mountain is   2*9= 
  2*9 = 18
18 miles.   The answer is 18.
Answer: C
Peter is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 4 miles per hour and returns along the same route at an average speed of 6 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?	Choose the correct choice from the following:
A) 4.8
B) 5.8
C) 6.0
D) 6.3
E) 6.5

Solution: to calculate average of 2 speeds a and b when distance is constant   Formula - 2ab/(a+b)   Here Peter's uphill speed = 4 mph   Peter's downhill speed = 6 mph   2*4*6/(4+6) = 48/10= 
48/10 = 24/5 = around 4.8
4.8   Correct answer - 4.8
Answer: A
Calculate the different number of ways 7 boys and 2 girls can sit on a bench?	Choose the correct choice from the following answers: A) 362881 B) 362880 C) 311880 D) 362280 E) 362810

Solution: npn = n!   9p9 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362880   362880
Answer: B
The population of a town increased from 1,75,000 to 2,10,000 in a decade. The average percent increase of population per year is
Select.
A) 2%
B) 5%
C) 6%
D) 8.75%
E) None

Solution: Solution   Increase in 10 years	= (210000 - 175000)= 
(210000 - 175000) = 35_000
35000.   Increase%= (35000/175000Ã—100)%   = 20%.   Required average	= (20/10)= 
(20/10) = 2
2%.   2%nswer 2%
Answer: A
Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/6 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?	Select
A) 36
B) 60
C) 108
D) 60
E) 180

Solution: The number of ornaments = a   Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6   1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12   1/6 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/6   => 5 + a/12 = a/6 => a = 60   Ans: 60
Answer: D
The smallest 4 digit prime number is?  Options
A) A)101
B) B)1003
C) C)109
D) D)113
E) E)None

Solution: The smallest 3-digit number is 1000, which is divisible by 2.   1000 is not a prime number.   1003< 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.   1003 is a prime number.   Hence 1003 is the smallest 4-digit prime number.   1003)
Answer: B
The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? Pick one
A) 1994 B) 1494 C) 1349 D) 1496 E) 1596

Solution: L1349M = 1400   1400 - 6= 
1400 - 6 = 1_394
1394   ANSWER:1349
Answer: C
What is the unit digit in (4137)^754?  Choose the correct option
A) 1
B) 3
C) 7
D) 5
E) 9

Solution: Unit digit in (4137)^754 = Unit digit in {[(4137)^4]^188 x (4137)^2}   Unit digit of 7^4 is 1 and of 4137^2 is 9.   so the required unit digit = 1 x 9 = 9.   Answer 9) 9.
Answer: E
a bank was to give a loan out to a newly married couple for 800,000 with no interest for 2 years and raise the price to 900,000 after 2 years. what is the interest rate?
Choose the correct choice from the following
A) 17%  B) 13%  C) 12%  D) 7%  E) 6%

Solution: for 0 years = (900,000- 800,000) = 100,000.   for 2 years = (100,000 x 2)/2= 100,000   Principal = (800,000 - 100,000) = 700,000.   Hence, rate = (100 x 100,000)/(700,000x2) = 7% ANSWER: 7%
Answer: D
A horse chases a pony 8 hours after the pony runs. Horse takes 12 hours to reach the pony. If the average speed of the horse is 320 kmph, what s the average speed of the pony?
Choose one
A) 182kmph B) 192kmph C) 193kmph D) 196kmph E) 190kmph

Solution: pony take 20 hours and horse take 12 hours...then Distance chased by them is 320*12.so speed of pony is   (320*12)/20= 
  (320*12)/20 = 192
192kmph.   ANSWER IS 192kmph
Answer: B
The speed of a car is 100 km in the first hour and 80 km in the second hour. What is the average speed of the car?	Choose the correct choice from the following answers.
A) 12  B) 75  C) 88  D) 54  E) 90

Solution: S = (100 + 80)/2= 
(100 + 80)/2 = 90
90 kmph   Answer: 90
Answer: E
How much time will take for an amount of Rs. 480 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Choose the correct option
A) 8 years  B) 4 years  C) 3 years 9 months  D) 9 years  E) 5 years

Solution: Time = (100 * 81) / (480 * 4.5)   = 3 years 9 months   Answer: 3 years 9 months
Answer: C
In a kickball competition of 11 teams, how many possible matches can each team play with each other?
Choose the correct choice from the following options.
A) 9  B) 16  C) 24  D) 36  E) 55

Solution: 11C2 = 55   Option 55
Answer: E
A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? Choose the correct choice from the following answers:
A) 388
B) 299
C) 266
D) 400
E) 2871

Solution: 2*12 : 3*12 : 4*24   1: 3: 4   1/8 * 3200= 
1/8 * 3200 = 400
400.Answer: 400
Answer: D
195,383,575,763,955,___
Choose the most appropriate option
A) 1153	B) 1143	C) 1243	D) 1343	E) 1148

Solution: 19*1= 
19*1 = 19
19 5   19*2= 
19*2 = 38
38 3   19*3= 
19*3 = 57
57 5   19*4= 
19*4 = 76
76 3   19*5= 
19*5 = 95
95 5   19*6= 
19*6 = 114
114 3   so ans=1143   ANSWER:1143
Answer: B
Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
Choose the correct choice
A) 1446  B) 1440  C) 1444  D) 1441  E) 1421

Solution: In the word, "MATERIAL" there are three vowels A, I, E.   If all the vowels are together, the arrangement is MTRL'AAEI'.   Consider AAEI as one unit. The arrangement is as follows.   M T R L A A E I   The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.   Number of required ways of arranging the above letters = 5! * 4!/2!   = (120 * 24)/2= 
(120 * 24)/2 = 1_440
1440 ways.   Answer:1440
Answer: B
In a manufacturing plant, it takes 36 machines 8 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
Select.
A) 3 B) 6 C) 8 D) 9 E) 12

Solution: the choices give away the answer..   36 machines take 4 hours to fill 8 standard orders..   in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 8*36/72*12/8= 
8*36/72*12/8 = 6
6   Ans 6
Answer: B
A sum of money deposited at C.I. amounts to Rs.6000 in 6 years and to Rs.7500 in 7 years. Find the rate percent?  Pick one:
A) 25%
B) 20%
C) 15%
D) 10%
E) 5%

Solution: 6000 --- 1500   100 --- ? => 25%   25%nswer: 25%
Answer: A
Find the fourth proportion to 11,12,66
Choose the most appropriate option:
A) 80 B) 120 C) 90 D) 25 E) 72

Solution: 72xplanation:   11:12 :: 66:x   => 11/12 = 66/x   => x = 792/11   => x =72   Option 72
Answer: E
In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr?
Choose one:
A) 3 sec	B) 2.9 sec	C) 3.5 sec	D) 7.5 sec	E) 2.4 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 120/40= 
120/40 = 3
3 sec.   3 secnswer: 3 sec
Answer: A
The speeds of three motor bikes are in the ratio 6 : 5 : 4. The ratio between the time taken by them to
travel the same distance is :  Choose the correct choice from the following answers: A) 10 : 12 : 15 B) 12 : 10 : 8 C) 15 : 12: 10 D) 10 : 15 : 12 E) None of these

Solution: Expl : Ratio of time taken : 1/6 :1/5 : 1/4 = 10 : 12 : 15   10 : 12 : 15nswer: 10 : 12 : 15
Answer: A
A sum of money at simple interest amounts to $ 780 in 3 years and to $930 in 4 years. The sum is:  Select.
A) $153
B) $698
C) $330
D) $549
E) $675

Solution: C   $330   S.I. for 1 year = $(930 - 780)= 
(930 - 780) = 150
$150.   S.I. for 3 years= $(150 x 3) = $450.   Principal = $(780 - 450)= 
(780 - 450) = 330
$330.
Answer: C
A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?	Select:	A) 240	B) 120	C) 150	D) 200	E) 100

Solution: Let x be the number he chose, then   2⋅x−138=102   2x=240   x=120   So answer is 120
Answer: B
In how many ways can the letters {U, R, R, R, R} be arranged?	Options.
A) 5  B) 20  C) 120  D) 720  E) 840

Solution: My answer : 5   There is 5! ways to arrange those letters in total, however letter U repeats 1! times and letter R repeats 4! times   => the way to arrange without repeating = 5!/ [1!x4!] = 5
Answer: A
In how many different ways can the letters of the word ‘JAMELS’ be arranged? Choose the correct choice from the following choices:	A) 120	B) 354	C) 626	D) 214	E) 720

Solution: E   720   The word SMART has 6 distinct letters.   Number of arrangements = 6!   = 6 x 5 × 4 × 3 × 2 × 1 = 720   Answer is 720
Answer: E
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 9 seconds. What is the length of the fast train? Options:
A) 23 m
B) 23 (2/9)m
C) 27 (7/9)m
D) 29 m
E) 50 m

Solution: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.   Therefore Length of faster train =	((50/9)	x 9) m =	(450/9)= 
(450/9) = 50
50	m.   50 m
Answer: E
A local elementary school has 1049 students and nine teachers, How many students would have to be added to the school to make sure each teacher has the same amount of students in their classroom?
Choose the correct option:
A) 4
B) 6
C) 5
D) 1
E) 2

Solution: Using the rule on the divisibility of nine, we add the digits of 1049 together to get 14. Since we are doing addition, the next number that is divisible by nine would be 18. Therefore, our answer 4(option 4)
Answer: A
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? Select:
A) 14028
B) 14038
C) 14079
D) 14000
E) 14023

Solution: 25*12: 30*12: 35*8   15:18:14   14/47 * 47000= 
14/47 * 47000 = 14_000
14000   Answer:14000
Answer: D
If the roots of a quadratic equation are 20 and -7, then find the equation?	Select the correct option:  A) x2 + 13x - 140 = 0  B) x2 - 13x + 140 = 0  C) x2 - 13x - 140 = 0  D) x2 + 13x + 140 = 0  E) None of these

Solution: Explanation:   Any quadratic equation is of the form   x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)   where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.   ANSWER IS x2 - 13x - 140 = 0
Answer: C
38, 87, 22,76, 31,47, 13, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above? Choose the correct option.
A) a- 55
B) b- 68
C) c- 79
D) d- 81
E) e- 85

Solution: Important:- Arrange the numbers in ascending order first.   13, 22, 31, 38, 47, 76, 82, 87   3/4th of the number list represents- 76 (6th number)   remaining 1/4th list represents 82 (7 th number)   79 fits in between above 2   Answer:- c- 79
Answer: C
Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder .	Pick one:
A) 1638 B) 1863 C) 1683 D) 1836 E) None of them

Solution: L.C.M. of 5,6,7,8 = 840.   Required number is of the form 840k + 3   Least value of k for which (840k + 3) is divisible by 9 is k = 2.   Required number = (840 X 2 + 3)=1683   Answer is 1683.
Answer: C
How many 9-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 123454321.  Choices
A) 100	B) 610	C) 729	D) 900	E) 90000

Solution: Take the task of building palindromes and break it intostages.   Stage 1: Select the 9th digit   We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 1 in9ways   Stage 2: Select the 8th, 7th, 6th, 5th digit   We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 2 in10ways   IMPORTANT: At this point, the remaining digits are alreadylocked in.   Stage 3: Select the 4th, 3rd, 2nd, 1st digit   So, we can complete this stage in1way.   By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 9-digit palindrome) in(9)(10)(10)(10)(10)(1)(1)(1)(1)ways (= 90000 ways)   Answer: 90000
Answer: E
Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many T minutes it takes John to reach the station?	Choose the most appropriate option.
A) 5 min
B) 6 min
C) 7 and 1/2 min
D) 8 min
E) 10 min

Solution: Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minutes. As he has to travel 5/4km more, it is going to take him 6(5/4) minutes. Hence, T=6(5/4)=15/2 minutes. The correct answer is 7 and 1/2 min.
Answer: C
How many 1/4s are there in 37 1/2?	Choose the correct choice from the following choices:
A) 150 B) 450 C) 500 D) 650 E) 700

Solution: Required number = (75/2)/(1/4)   = (75/2 x 4/1)   = 150.   150NSWER:150
Answer: A
When a certain number X is divided by 52, the remainder is 19. What is the remainder when X is divided by 7?  Select:
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: When a certain number X is divided by 52, the remainder is 19. What is the remainder when X is divided by 7?   Putting a value say x = 19 we get remainder as 19 when divided by 52.   When 19 divided by 7 we get 5 as remainder.   5 is the answer.
Answer: D
A cycle is bought for Rs.800 and sold for Rs.1080, find the gain percent?	Options:	A) 22	B) 20	C) 35	D) 88	E) 11

Solution: 800 ---- 180   100 ---- ? => 35%   Answer:35
Answer: C
The cost of producing x tools by a company is given by
C(x) = 2500 x + 5500 (in $)
a) What is the cost of 100 tools?
Choose the correct choice from the following
A) 222500 $  B) 125800 $  C) 225900 $  D) 255500 $  E) 122500 $

Solution: Solution   C(100) = 2500*100 + 5500= 
2500*100 + 5500 = 255_500
255500 $   Answer 255500 $
Answer: D
A can do a job in 10days and B in 20days. If they work on it together for 4 days, then the fraction of the work that is left is?  Choices.
A) 2/5 B) 8/15 C) 3/11 D) 1/12 E) 6/13

Solution: 2/5's 1 day work = 1/10   B's 1day work = 1/20   2/5+B 1day work = 1/10 + 1/20 = 3/20   2/5+B 4days work = 3/20*4 = 3/5   Remaining work = 1 - 3/5 = 2/5   2/5nswer is 2/5
Answer: A
Which of the following inequalities is equivalent to −4 < x < 8?
Choose one.
A) |x - 1| < 7 B) |x + 2| < 6 C) |x + 3| < 5 D) |x - 2| < 6 E) None of the above

Solution: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0   Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format   -4+y < x+y < 8+y   Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2   Thus, -6< x-2 < 6 => |x-2| < 6.   Hence, answer is |x - 2| < 6
Answer: D
If (x - 1)^2 = 324, which of the following could be the value of x - 3?
Choose the correct choice from the following answers.
A) 17	B) 15	C) 13	D) -20	E) -22

Solution: (x - 1)^2 = 324   (x - 1) = 18 or -18   x = 19 or -17   x - 3 = 16 or -20   The answer is -20.
Answer: D
The average of five numbers is 27. If one number is excluded, the average becomes 20. The excluded number is?  Choose the correct choice from the following options.
A) 52 B) 53 C) 54 D) 55 E) 56

Solution: Excluded number = (27 * 5) - (20 * 4)   = 135 - 80= 
135 - 80 = 55
55.   Answer: 55
Answer: D
If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 118, what is the value of K? Choose the correct choice from the following answers
A) 11	B) 15 3/4	C) 22	D) 118	E) 25 3/10

Solution: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1   (11K -1)/4 = 118   11K = 118 * 4 +1 = 472 +1= 
472 +1 = 473
473   K= 473 / 11= 
473 / 11 = 43
43.   Answer 118.
Answer: D
A boy was asked to multiply a number by 22. He instead multiplied the number by 44 and got the answer 308 more than the correct answer. What was the number to be multiplied?  Choose the correct answer.
A) 10  B) 12  C) 08  D) 14  E) 16

Solution: Let the number be x   22x + 308 = 44x   => 44x - 22x = 308   => 22x = 308   => x = 308/22 = 154/11= 
154/11 = 14
14   Answer is 14.
Answer: D
The average weight of 2 person's increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?  Choose the correct choice from the following answers:
A) 74 kg
B) 76.5 kg
C) 85 kg
D) 78
E) None of these

Solution: Explanation:   Total weight increased = (2 x 4.5) kg = 9 kg.   Weight of new person = (65 + 9)= 
(65 + 9) = 74
74 kg.   74 kgnswer: 74 kg
Answer: A
A pair of articles was bought for $720 at a discount of 10%. What must be the marked price of each of the article?
Select: A) $300 B) $500 C) $350 D) $400 E) $600

Solution: S.P. of each of the article = 720/2= 
720/2 = 360
$360   Let M.P= $x   90% of x = 360   x = 360*100/90= 
360*100/90 = 400
$400   Answer is $400
Answer: D