MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the least value of x. So that 23x57 is divisible by 3.	Choices.
A) 2	B) 0	C) 1	D) 3	E) 4

Solution: Explanation:   The sum of the digits of the number is divisible by 3, then the number is divisible by3.   2 + 3 + x + 5 + 7 = 17 + x   Least value of x may be 1   Therefore  17 + 1= 
 17 + 1 = 18
18 is divisible by 3.   Answer: Option 1
Answer: C
Ana climbs up stairs 20 floors building and back. She takes the exact same route both ways. On the trip up she climbs an average speed of 2 steps per second. On the trip back she climbs down at an average speed of 4 steps per second. What is her approximate average speed for the round trip in miles per hour? Choose the correct choice from the following answers: A) 1 B) 1.25 C) 1.33 D) 1.5 E) 1.75

Solution: Average speed = total distance/total time   Here number of steps to 20th floor and back is same as she takes the same route.   D = 2T1 and D=4T2   Therefore, T1 = D/2 and T2 = D/4   T1+T2 = 3D/4   Therefore, average speed  1+ 2= 
 1+ 2 = 3
3D/4   Therefore, average speed= 2d/3d/4 =2d * 4/3d   Answer is 1.3 Since, the options are far away we need not solve till the decimal points   So correct answer is option 1.33
Answer: C
A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 6 hats randomly out of the drawer and returning each hat before taking out the next one? Answers:
A) 3/8  B) 1/4  C) 5/8  D) 5/16  E) 7/16

Solution: Let's find the probability of getting exactly 3 red hats.   One possible case is red-red-red-blue-blue-blue.   The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64   There are 6C3 = 20 such cases so we need to multiply this by 20.   P(exactly 3 red hats) = 20*1/64 = 5/16   Note that when we get exactly 3 red hats, then we also get exactly 3 blue hats.   So we don't need to consider the case of exactly 3 blue hats separately.   The answer is 5/16.
Answer: D
The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 1 year ago?	Choose the correct choice from the following answers:  A) 152460  B) 214560  C) 168000  D) 210000  E) 200000

Solution: population 2 years ago = 176400/(1 + 5/100)   Answer is 168000
Answer: C
For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| =	Choose the correct answer:  A) ab-4  B) 2b-ab-4  C) ab+4  D) ab-2b+4  E) 4-ab

Solution: Given: |ab| = -ab and |a| = -a   Question: |b-4| + |ab-b| = ?   **** Looking at |ab| = -ab tells us that either one of a or b is negative.   **** Looking at |a| = -a tells us that a must be negative   **** Combine two observations: b is positive   Let a=-1 and b=1   |b-4| + |ab-b| = |1-4| + |-1-1| = 5   Test a) |ab-4| = |(1)(-1)-4| = |-5|=5   Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1   Test c) ab+4 = -1 + 4= 
-1 + 4 = 3
3   Test d) ab-2b+4= -1-2(1)+4=1   test e) 4-1=3   ab-4NSWER=ab-4
Answer: A
A train passes a 50 metres long platform in 14 seconds and a man standing on the platform in 10 seconds. The speed of the train is:  Choose the correct choice from the following answers:
A) 24 km/hr  B) 36 km/hr  C) 40 km/hr  D) 45 km/hr  E) None of these

Solution: Explanation:   Let the length of train be L m.   L/10 = (L+50)/14   14L= 10L+500   L= 125 m .   Speed = (25/2) m/s = (25/2) x 18/5= 45 Km/hr   Answer 45 km/hr
Answer: D
A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many F ways can the test be completed if every question is unanswered?	Choose the correct choice from the following
A) 24
B) 120
C) 625
D) 720
E) 1024

Solution: 5 choices for each of the 4 questions, thus total F of 5*5*5*5 = 5^4 = 625 ways to answer all of them.   Answer: 625.
Answer: C
A grocer has a sale of Rs. 6400, Rs. 7000, Rs. 6800, Rs. 7200 and Rs. 6500 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?  Options.
A) Rs. 4500
B) Rs. 4700
C) Rs. 4800
D) Rs. 5000
E) Rs. 5100

Solution: Total sale for 5 months = Rs. (6400+ 7000 + 6800 + 7200 + 6500) = Rs. 33900   Required sale = Rs. [ (6500 x 6) - 34009 ]   = Rs. (39000 - 33900)   = Rs. 5100   ANSWRs. 5100R :Rs. 5100
Answer: E
In a room there are 11 people. Each person shook hands with every other person. How many hand shakes were there? Choose one: A) 52 B) 53 C) 54 D) 55 E) 56

Solution: 11C2 = 55   The answer is 55.
Answer: D
What is the dividend. divisor 16, the quotient is 8 and the remainder is 4	Options
A) 127	B) 128	C) 130	D) 131	E) 132

Solution: 132 = d * Q + R   132 = 16 * 8 + 4   132 = 128 + 4   132 = 132
Answer: E
How many total number of ways in which y distinct objects can be put into two different boxes is Select the correct option.
A) n2 B) 2y C) 2n D) 3n E) None of these

Solution: Let the two boxes be B1 and B2. There are two choices for each of the y objects. So, the total number of ways is   2 × 2 ×.....× 2 (y times ) = 2y   Answer 2y
Answer: B
Find the number of ways in which 7 different beads can be arranged to form a necklace.  Choose the correct choice from the following answers:	A) 30	B) 20	C) 420	D) 60	E) 80

Solution: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,7 beads can be arranged to form a necklace in(7-1)! /2ways   = 6*5*4*3*2/2 = 420 ways   Answer is 420
Answer: C
Five pieces of wood have an average length of 126cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?  Select:
A) a) 90  B) b) 105  C) c) 110  D) d) 130  E) e) 140

Solution: B. 105   sum of all lengths of all 5 pieces of wood = 126 * 5= 
126 * 5 = 630
630   3rd piece (sorted in increasing length) length= 140 (median)   for sum of first 2 wood length to become max, last two should be least.   let 4th, 5th wood also have length 140 each.   total of last 3 = 140 * 3= 
140 * 3 = 420
420   sum of first 2= 630 - 420= 
630 - 420 = 210
210   each of these 2 will have length 210/2= 
210/2 = 105
105   Aswer b) 105
Answer: B
A Vendor sells 10 clips for a rupee gaining thereby 40%. How many clips did he buy for a rupee?  Options.
A) 10
B) 12
C) 14
D) 15
E) None

Solution: S.P of 10 Clips=Re 1   Gain= 40%.   C.P of 10 Clips=Rs(100/140)*1=Re 5/7   For Rs 5/7, Clips bought=10.   For Re 1,14lips bought=10*(7/5)= 
10*(7/5) = 14
14
Answer: C
If c is an even integer and c/18 is an odd integer, which of the following is NOT an even integer?  Choose one:
A) (c^2)/54	B) (c^2)/16	C) (c^2)/9	D) (c^2)/6	E) (c^2)/2

Solution: since c is an even integer and c/18 is an odd integer. thus maximum power of 2 in a is one. why ?? because if the power of 2 in the expression has been 2 or greater, then the c/18 must have been an even integer. (18=2*3^2. as 18 contain only one 2 in the expression)   now, any expression in which we have 4 at the denominator will be odd. out of the given options only 16 is a multiple of 4. hence answer should be (c^2)/16
Answer: B
Out of nine consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels? Choose the most appropriate option:	A) 3180	B) 3510	C) 3920	D) 4320	E) 4750

Solution: 9C2 x 3C3 x 5! = 4320   The answer is 4320.
Answer: D
7 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
Choose the correct answer:	A) 445	B) 632	C) 720	D) 240	E) 256

Solution: it is like a circular arrangement.   total ways for n people to arrange in a circle is = factorial (n-1)   in this case n= 7   hence ans = 7 factorial = 720   hence 720
Answer: C
Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is?
Choose the correct choice:	A) 176 years	B) 168 years	C) 186 years	D) 108 years	E) 178 years

Solution: Let the present ages of the father and son be 2x and x years respectively.   Then, (2x - 18) = 3(x - 18) => x = 36   Required sum = (2x + x)   = 108 years.   Answer:108 years
Answer: D
If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
Choose the correct choice from the following choices:
A) 20% B) 35% C) 95% D) 15% E) 25%

Solution: Given that, cost price of 50 article is equal to selling price of 40 articles.   Let cost price of one article = Rs. 1   Selling price of 40 articles = Rs. 50   But Cost price of 40 articles = Rs. 40   Therefore, the trader made profit.\Percentage of profit = 10/40 * 100= 
10/40 * 100 = 25
25%   Answer: 25%
Answer: E
The length of a rectangle is halved, while its breadth is tripled. What is the % change in area?	Pick:	A) 30%	B) 40%	C) 50%	D) 60%	E) 65%

Solution: Let original length = x and original breadth = y.   Original area = xy.   New length =	x	.   2   New breadth = 3y.   New area = x	x 3y =	3	xy.   2	2   Increase % = 1	xy x	1	x 100	%	= 50%.   2	xy   50%
Answer: C
The largest 5 digit number exactly divisible by 91 is?
Choose the correct choice from the following options
A) 99918 B) 99919 C) 99921 D) 99923 E) 99929

Solution: Largest 5-digit number = 99999   91) 99999 (1098   91   ---   899   819   ----   809   728   ---   81   ---   Required number = (99999 - 81)= 
(99999 - 81) = 99_918
99918.   Option 99918
Answer: A
5^100 is divided by 18 then what is the remainder?
Select
A) 10
B) 11
C) 13
D) 15
E) 16

Solution: Here N = 18=2×32   ϕ(18)=18(1−12)(1−13) = 6   So 56 when divided by 18, remainder is 1.   So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49   Now 49 when divided by 18, remainder is 13.   13
Answer: C
In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what S percent of all the people in Smithtown are left-handed women? Choices.
A) 50% B) 40% C) 25% D) 20% E) 10%

Solution: looking at the ratio we can take total number of people=20..   ans 5/20 or 25% 25%
Answer: C
60kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3:2 and alloy B has tin and copper in the ratio 1:4, then the amount of tin in the new alloy is?  Choose the most appropriate option: A) 24kg B) 44kg C) 20kg D) 30kg E) 52kg

Solution: Quantity of tin in 60kg of A = 60*2/5= 
60*2/5 = 24
24kg   Quantity of tin in 100kg of 44kg= 100*1/5= 
100*1/5 = 20
20kg   Quantity of tin in the new alloy= 24+20= 
24+20 = 44
44kg   Answer is 44kg
Answer: B
Find the highest common factor of 36 and 84. Select the correct option:
A) 4
B) 6
C) 12
D) 18
E) 20

Solution: 36 = 22 x 32   84 = 22 x 3 x 7   H.C.F. = 22 x 3 = 12.   Answer: Option 12
Answer: C
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 5720 votes were polled, then how many valid votes did B get?	Answers:
A) 1859
B) 2999
C) 2834
D) 2777
E) 2991

Solution: Let the total number of votes polled in the election be 100k.   Number of valid votes = 100k - 20% (100k) = 80k   Let the number of votes polled in favour of A and B be a and b respectively.   a - b = 15% (100k) => a = b + 15k   => a + b = b + 15k + b   Now, 2b + 15k = 80k and hence b = 32.5k   It is given that 100k = 5720   32.5k = 32.5k/100k * 85720 = 1859   The number of valid votes polled in favour of B is 1859.   1859nswer: 1859
Answer: A
People are allowed to add an apple or take an apple from a large barrel. If people are only adding apples, the barrel can be filled in 5 hours. If people only take apples, the barrel can be emptied in 15 hours. If it is desired that the barrel should be filled, from empty, exactly 6 hours after people begin adding apples at 9:30am, then at what time should people begin taking apples?  Choose the most appropriate option:
A) 10:00am  B) 10:45am  C) 12:00pm  D) 12:30pm  E) 1:30pm

Solution: In 6 hours the amount of apples added equals to 6*1/5 = 6/5 of the barrel. So, 1/5 more than necessary, which should be compensated by people taking apples. To rid 1/5 of the apples people take, it will require   15/5= 
  15/5 = 3
3 hours.   Therefore, people should begin taking apples at 9:30am + 6 hours - 3 hours= 12:30pm.   Answer: 12:30pm.
Answer: D
A women walking at 4 Kmph reaches her office 8 minutes late. If she walks at 6 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
Choose the correct choice from the following:	A) 2 1/5 Km	B) 3 1/5 Km	C) 4 1/3 Km	D) 5 Km	E) 5 1/3 Km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Km)
Answer: B
A began business with 12500 and is joined afterwards by B with 25000. When did B join, if the profits at the end of the year are divided equally?
Choose the correct choice from the following options:  A) 8 months  B) 9 months  C) 10 months  D) 6 months  E) None of these

Solution: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.   ∴ Profit ratio is 12 × 12500 : (12 – x) × 25000   or 12 : 2(12 – x)   Since profit is equally divided so   12 = 2(12 – x) or x = 6. Thus B joined after 8 months.   Answer 6 months
Answer: D
At a circular table for ten will sit eight adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the ten people be arranged around the table.
Answers.
A) 1220	B) 1660	C) 2440	D) 2880	E) 3200

Solution: Consider the two parents and two children as one unit.   Then there are six adults and one family unit.   The number of ways 7 can form a line is 7!   Around a circular table, there would be 7 rotations so we divide this number by 7.   There are 6! ways for 7 to sit around the circular table.   Then the two children have two options and the two parents have two options.   Then the total number of ways is 6!*2*2= 2880   The answer is 2880.
Answer: D
The perimeters of two squares are 60 cm and 40 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?  Choose the most appropriate option
A) 76 cm B) 24 cm C) 88 cm D) 44.8 cm E) 34 cm

Solution: We know perimeter of square = 4(side)   So Side of first square = 60/4= 
60/4 = 15
15 cm   Side of second square= 40/4= 
40/4 = 10
10 cm   Area of third Square= 15*15 - 10*10= 
15*15 - 10*10 = 125
125 cm   So side of third square= 11.2 [because area of square = side*side]   Perimeter = 4*Side = 4*11.2= 
4*11.2 = 44.8
44.8 cm   Answer:44.8 cm
Answer: D
Of the diplomats who attended a summit conference: 20 spoke Latin, 32 did not speak Russian and 20% of the diplomats spoke neither Latin nor Russian. If 10% of the diplomats spoke both Latin and Russian, then how many diplomats attended the conference?	Pick one.
A) 70 B) 96 C) 108 D) 120 E) 150

Solution: 2X2 matrix will be the easiest way to calculate this.   Text in black: given statements   Text in red: calculated values   Thus 120=120 is the correct answer
Answer: D
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?  Choose the correct option:  A) 37  B) 25  C) 36  D) 08  E) 12

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer: 36
Answer: C
If 0.75: x :: 5:7, then x is equal to:
Choose one:
A) 1.05
B) 1.16
C) 1.2
D) 1.3
E) None of these

Solution: Explanation:   (x * 5) = (0.75 *7)= 
(0.75 *7) = 5.25
5.25/5= 
5.25/5 = 1.05
1.05   1.05nswer: 1.05
Answer: A
If a man crosses a 650 m long street in 5 minutes. What is his speed?  Pick:
A) 7 km/hr  B) 7.1 km/hr  C) 7.8 km/hr  D) 8 km/hr  E) 8.5 km/hr

Solution: distance = 650 meter   time = 5 minutes = 5 x 60 seconds = 300 seconds   Speed = distance/time=650/300=2.17m/s   =2.17×18/5=7.8 km/hr   7.8 km/hr
Answer: C
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?  Choose the correct option
A) 1000  B) 970  C) 765  D) 654  E) 780

Solution: X * (110/100) * (95/100) = 1045   X * (11/10) * (1/100) = 11   X = 1000   1000NSWER 1000
Answer: A
Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team E. If team A's average speed was 5 mph greater than team E's, what was team E's average mph? Choices:
A) 12	B) 15	C) 18	D) 20	E) 25

Solution: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.   Say Team E's speed was s. Then Team E's time is 300/s.   Team A's speed was then s+5, and Team A's time was then 300/(s+5).   We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team E. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer 20, you find the time for Team E is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, 20 is correct.
Answer: D
Find the largest 6 digit number which is exactly divisible by 88?
Choose the correct choice from the following answers.
A) 998765 B) 998907 C) 999944 D) 999954 E) 999990

Solution: Largest 6 digit number is 999999   After doing 999999 ÷ 88 we get remainder 55   Hence largest 6 digit number exactly divisible by 88 = 999999 - 55= 
999999 - 55 = 999_944
999944   999944
Answer: C
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?	Choose the correct answer.
A) 120 metres  B) 180 metres  C) 324 metres  D) 150 metres  E) 170 metres

Solution: Explanation:   Speed= 60 x	5/18	m/sec	= 50/3	m/sec.   Length of the train = (Speed x Time).   Length of the train = 50/3	x 9	m = 150 m   ANSWER IS 150 metres
Answer: D
How many of the positive divisors of 600 are also multiples of 4 not including 600? Choose the correct choice from the following answers: A) 6 B) 8 C) 9 D) 11 E) 12

Solution: 600 = 2^6 * 3 * 5 = (4) * 2 * 3 * 5^2   Besides (4), the exponents of 2, 3, and 5 are 1, 1, and 2.   There are (1+1)(1+1)(2+1) = 12 ways to make multiples of 4.   We must subtract 1 because one of these multiples is 600.   The answer is 11.
Answer: D
A bookseller has two display windows. She plans to display 4 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?	Choose the correct choice from the following answers:
A) 24
B) 72
C) 144
D) 336
E) 420

Solution: Explanations   1) The left window will have permutations of the 4 fiction books, so the number of possibilities for that window is   permutations = 4! = (4)(3)(2)(1) = 24   The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is   permutations = 3! = (3)(2)(1) = 6   Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 24*6= 
24*6 = 144
144   Answer: 144.
Answer: C
How many even 4-digit integers greater than 8000 are there such that all their digits are different?  Pick one:	A) 240	B) 369	C) 469	D) 520	E) 599

Solution: Case 1: Numbers starting with 8 followed by EVEN number   The hundreds digit can take 4 numbers (0,2,4,6) so 4 ways   The unit digit can take remaining 3 EVEN numbers left after using 2, to be EVEN so 3 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways   Total=4*3*7= 
4*3*7 = 84
84   Case 2: Numbers starting with 8 followed by ODD number   The hundreds digit can take 5 numbers (1,3,5,7,9) so 5 ways   The unit digit can take remaining 4 EVEN numbers (0,2,4,6) to be EVEN so 4 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways   Total=5*4*7= 
5*4*7 = 140
140   Case 3: Numbers starting with 9 followed by EVEN number   The hundreds digit can take 5 numbers (0,2,4,6,8) so 5 ways   The unit digit can take remaining 4 EVEN numbers left after using 1, to be EVEN so 3 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways   Total=5*3*7= 
5*3*7 = 105
105   Case 4: Numbers starting with 9 followed by ODD number   The hundreds digit can take 4 numbers (1,3,5,7) so 4 ways   The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways   Total=4*5*7= 
4*5*7 = 140
140   Hence 84+140+105+140= 
84+140+105+140 = 469
469, correct answer is 469
Answer: C
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand K nor Brand B soap, 60 used only Brand K soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? Pick one.
A) 15  B) 20  C) 30  D) 40  E) 45

Solution: SOLUTION FOR SOAP K AN40 SOAP B   (40) 40
Answer: D
John deposited $10,000 to open a new savings account that earned 2 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?	Choose the correct choice from the following options: A) $10,100.25 B) $10,101.50 C) $10,200.75 D) $10,201.00 E) $10,400.35

Solution: 2 percent annual interest compounded quarterly --> 0.5% in 3 moths.   For the first 3 moths interest was 0.5% of $10,000, so $50;   For the next 3 moths interest was 0.5% of $10,000,plus0.25 earned on previous interest of $100, so $50+$0.25=$50.25;   Total interest for 6 months was $50+$50.25  50+ 0.25= 
  50+ 0.25 = 50.25
$50.25;   Total interest for 6 months was $50+$50.25=$100.25, hence balance after 6 months was $10,000+ $100.25 50+ 50.25= 
 50+ 50.25 = 100.25
$100.25, hence balance after 6 months was $10,000+ $100.25=$10,100.25.   $10,100.25nswer: $10,100.25.
Answer: A
If 3<(7-x)/3, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive Choose the correct choice from the following.
A) II only B) III only C) I and II only D) II and III only E) I, II and III

Solution: 12<7-x   x<-5   x+5<0   1.5<x...not possible   2.True.....Check for values x=-6,-7,-8....... etc   3.True.. Since x+5<0 -(x+5) will always be positive   Hence, Ans is I and II only..
Answer: C